JP3855005B2 - Material analysis system and material test system - Google Patents

Description

【数２】

【数３】

【００３０】
この各々の式において、各大括弧のなかの第１項（中括弧の項）は変位の周期性を示すフーリエ級数であり、第２項はべき乗的な変位の量を示しており、第３項は上記定数である。
上述した各係数及び定数の仮の値とは、実験的に求められた値や、以前に同様な材料の解析によって求められた値などの、ある程度実際に近いと考えられる値が用いられる。
【００３１】
次に、ステップＳ３において、変位量演算部４は、（１），（２），（３）式から求められた変位量ｕ（ｘ，ｙ，ｚ），ｖ（ｘ，ｙ，ｚ），ｗ（ｘ，ｙ，ｚ）に基づき、各々のピクセルを移動させる。
すなわち、上記変位量ｕ，ｖ，ｗに基づき、ｐ（ｘ，ｙ，ｚ）を移動させることにより、（ｘ，ｙ，ｚ）の位置にあったピクセルは、（ｘ＋ｕ，ｙ＋ｖ，ｚ＋ｗ）の位置に移動し、すなわち、ｐ（ｘ，ｙ，ｚ）がｐ（ｘ＋ｕ，ｙ＋ｖ，ｚ＋ｗ）となる。
【００３２】
このピクセル値ｐ（ｘ＋ｕ，ｙ＋ｖ，ｚ＋ｗ）を、ピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）とする。ここで、Ｘ＝ｘ＋ｕ，Ｙ＝ｙ＋ｖ，Ｚ＝ｚ＋ｗである。
そして、変位量演算部４は、上述したピクセルの３次元座標における移動の処理を、非荷重ボクセルモデルを構成する各ピクセルに対して行う。
ここで、ピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）は、変位量演算部４により求められた仮想の荷重状態にある試料の荷重ボクセルモデル、すなわち、シミュレーション結果としての荷重ボクセルモデル（シミュレーションボクセルモデル）である。
【００３３】
次に、ステップＳ４において、変位量演算部４は、荷重ボクセルモデルにおける座標値（Ｘ，Ｙ，Ｚ）におけるピクセル値Ｐ（Ｘ，Ｙ，Ｚ）と、上記ピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）との数値の比較を、荷重ボクセルモデルにおける各座標値において行う。
すなわち、変位量演算部４は、荷重ボクセルモデルの各座標値におけるピクセル値Ｐ（Ｘ，Ｙ，Ｚ）の数値と、移動後の非荷重ボクセルモデルの各座標値におけるピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）の数値とが一致（または所定の範囲を有していて、略一致する場合も含む）するか否かの判定を行う。
【００３４】
ここで、変位量演算部４は、荷重ボクセルモデルの各座標値におけるピクセル値Ｐ（Ｘ，Ｙ，Ｚ）の数値と、移動後の非荷重ボクセルモデルの各座標値におけるピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）の数値とが一致した場合、各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗを出力して処理を終了するが、一致しない場合、処理をステップＳ５へ進める。
このとき、変位量演算部４は、下記に示す（４）式により、ボクセルモデル全体のピクセル値に対して、ピクセル値Ｐ（ｘ，ｙ，ｚ）が移動されたピクセル値Ｐ（Ｘ，Ｙ，Ｚ）と、ｐ^＊（Ｘ，Ｙ，Ｚ）との差分を合計して、２５５（階調度）×Ｍにより正規化して、ｆとして出力する。
【数４】

ここで、Ｍは総ボクセル数であり、Σは画像内の全ボクセルに対して総和を取ることを表している。
そして、変位量演算部４は、誤差関数ｆの誤差関数値が求められる毎に、順次前回のｆの数値と比較して、上記誤差関数値の谷（最も誤差関数値の小さい点、すなわち極小値）を検出し、この点をボクセルモデル全体の各ピクセル値の階調度の一致した点とする。
【００３５】
次に、ステップＳ５において、変位量演算部４は、各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗの変更量を、非線形計画法などの最適化手法によって、このアルゴリズに従った演算により、上記係数及び定数の数値を逐次変更する。
そして、変位量演算部４は、変更された各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗにより、新たな変位量ｕ（ｘ，ｙ，ｚ），ｖ（ｘ，ｙ，ｚ），ｗ（ｘ，ｙ，ｚ）を求めるため、処理をステップＳ２へ戻す。
【００３６】
上述したように、変位量演算部４は、荷重ボクセルモデルの各座標値におけるピクセル値Ｐ（Ｘ，Ｙ，Ｚ）の数値と、移動後の非荷重ボクセルモデルの各座標値におけるピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）の数値とが一致するまで、ステップＳ２からステップＳ５の処理を繰り返して行う。
そして、変位量演算部４は、最終的に、荷重ボクセルモデルの各座標値におけるピクセル値Ｐ（Ｘ，Ｙ，Ｚ）の数値と、移動後の非荷重ボクセルモデルの各座標値におけるピクセル値ｐ^＊（Ｘ，Ｙ，Ｚ）の数値とが一致（階調度が一致）すると、このときの各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗを出力する。
【００３７】
次に、力学演算部５は、上記各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗを入力し、これらに基づき、（１），（２），（３）式により、変位量ｕ（ｘ，ｙ，ｚ），ｖ（ｘ，ｙ，ｚ），ｗ（ｘ，ｙ，ｚ）を求める。
そして力学演算部５は、上記変位量ｕ，ｖ，ｗに基づき、変位ひずみの式から、ひずみε_ｉｊを求める演算を行う。
【００３８】
このとき、力学演算部５は、幾何学的非線形を伴う大変形理論で対応しなければならない材料であると、以下に示す変位−ひずみの関係式である（５）式を用いてひずみε_ｉｊを求める。
【数５】

そして、力学演算部５は、以下に示す応力−ひずみ関係を示す演算式である（６）式において、ひずみと応力との間の構成則（構成マトリクス）を与えて、単位面積当たりの力である応力σ_ｉｊを求める演算を、荷重増分解析により行う。
【００３９】
すなわち、材料に非線形性がある場合には、応力状態に依存して変化する行列、すなわち、構成マトリクス[Ｄ^ｐ]を用いて増分形により（６）式で与えられ、応力「０」の状態から計算を開始して、順次、応力の変化量を算出し、得られた応力を加算することにより全体の応力を求める。
【数６】

ここで、（５）式は大変形理論に対応した変位−ひずみ関係式として用い、また、（６）式は非線形・増分形の演算式であり、非線形材料の応力を求めるときに用いる。
【００４０】
一方、力学演算部５は、幾何学的に線形な微小変形理論で対応する材料であると、以下に示す変位−ひずみの演算式である（７）式を用いてひずみε_ｉｊを求める。
【数７】

そして、力学演算部５は、以下に示す応力−ひずみ関係式である（８）式において、ひずみと応力との間の構成則を与え、単位面積当たりの力である応力σ_ｉｊを求める演算を行う。
例えば、線形材料の場合には、応力状態によらず、一定の行列、すなわち構成マトリクス[Ｄ^ｅ]を用いた（８）式により求めることができる。
【数８】

ここで（７）式は微小変形理論に対応した変位−ひずみ関係式として用い、また、（８）式は線形材料の応力を求めるときに用いる。
【００４１】
すなわち、力学演算部５は、材料（被試験体１４）の変形が微小な場合、微小変形理論に基づく、変位−ひずみ関係式に対応した（７）式を用い、材料の変形が大きい場合、大変形理論に基づく変位−ひずみ関係式に対応した（５）式を用いて、ひずみを演算する。
そして、力学演算部５は、材料（被試験体１４）が線形材料の場合、線形構成則による（８）式を用い、印加した荷重に基づく被試験体１４各部の応力を演算し、また、材料が非線形材料の場合、非線形・増分形の構成則の（６）式を用いて、印加した荷重に基づく被試験体１４各部の応力を演算する。
【００４２】
ここで、通常の材料試験では、応力あるいはひずみを簡単に算出できる単純な形状の試験片を用い、単純負荷により、荷重と変位との関係を計測し、その後に荷重から応力を換算し、変位からひずみを換算して、構成マトリクス［Ｄ^ｐ］や［Ｄ^ｅ］を求めている。
上述の説明では、構成マトリクスを求める流れにおいて、微小変形理論と線形材料の線形構成則とを対応させ、また大変形理論と非線形材料とを対応させて説明したが、当然、荷重の状態及び材料の材質により、微小変形理論と非線形材料との組み合わせ、または大変形理論と線形材料との組み合わせで演算する場合もある。
【００４３】
しかしながら、（６）式及び（８）式における構成マトリクス［Ｄ^ｐ］および［Ｄ^ｅ］は、内部が不均一な材料に対応した関係であるため、上述したように、荷重と変位とから単純に、応力−ひずみの関係を算出することはできない。
このため、以下に、材質が不均一でかつ形状が単純でない被試験体に対応する応力−ひずみ関係を求める方法の説明を、図１及び図４を用いて行う。
図４は、力学演算部５の応力−ひずみの関係を算出する動作例を説明するフローチャートである。
ステップＳ１１において、力学演算部５は、変位量演算部４から、所定の荷重に対応した被試験体１４各部の変位量ｕ（ｘ，ｙ，ｚ），ｖ（ｘ，ｙ，ｚ），ｗ（ｘ，ｙ，ｚ）を入力する。
【００４４】
次に、ステップＳ１２において、力学演算部５に対して、過去の実験例から近いと思われる材料を例として、この材料のモデルを仮に設定する。
被試験体１４が微小変形理論で扱い得る線形材料であれば、演算に用いるモデルとして、応力−ひずみ関係式を（８）式と仮定する。
一方、被試験体１４が非線形材料であれば、演算に用いるモデルとして、応力−ひずみ関係式を増分形の（６）式と仮定する。
この設定は、図示しない入力装置から、被試験体１４が線形材料または非線形材料のいずれかであるかのデータの入力を行うことにより設定する。
【００４５】
また、被試験体１４が非線形材料のとき、応力状態等による構成マトリクス［Ｄ^ｐ］の変化を適時モデル化して、算出方法を設定する。例えば、弾塑性材料の場合には、結合流れ則に基づき設定する。
次に、ステップＳ１３において、解析対象の被試験体１４に対応する構成マトリクス［Ｄ^ｅ］または［Ｄ^ｐ］に含まれる各材料パラメータ（各材料のヤング率、ポアソン比等）を、未知の変数として仮に設定する。
【００４６】
次に、ステップＳ１４において、力学演算部５は、仮のパラメータが設定された構成マトリクス［Ｄ^ｅ］または［Ｄ^ｐ］に基づき、有限要素解析を行う。
このとき、試験対象の被試験体１４が線形材料であれば、以下に示す（９）式による演算から要素剛性マトリクス［Ｋ_ｅ］を算出する。
そして、力学演算部５は、仮に設定された構成マトリクス［Ｄ^ｅ］により求めた上記要素剛性マトリクス［Ｋ_ｅ］に基づき、印加された荷重と被試験体１４の各部の変位量（以下、演算変位量）との関係を求める。
【００４７】
この印加される荷重は、ステップＳ１１において入力された所定の荷重と同等の数値が用いられる。
【数９】

この（９）式において、マトリクス［Ｂ］は、変位−ひずみマトリクスであり、∫_ｖｅdvは有限要素法における解析の１要素に関する体積分を表している。
次に、力学演算部５は、試験対象の被試験体１４に対して、以下に示す（１０）式による演算から、応力状態等に依存する要素剛性マトリクス［Ｋ_ｐ］を算出する。
【００４８】
すなわち、力学演算部５は、仮に設定された構成マトリクス［Ｄ^ｐ］により求めた上記要素剛性マトリクス［Ｋ_ｐ］に基づき、印加された荷重と被試験体１４の各部の変位量（以下、演算変位量）との関係を、増分解析により求める。
【数１０】

さらに、大変形（幾何学的非線形性）に対する考慮が必要な場合には、ひずみの定義を、以下に示す式（１１）として、接線剛性マトリクスを算出して、増分解析を行う。
【数１１】

【００４９】
次に、ステップＳ１５において、力学演算部５は、有限要素法により求められた被試験体１４各部の演算変位量と、ステップＳ１１で入力された被試験体１４各部の変位量とが一致するか否かの判定を行う。
このとき、力学演算部５は、有限要素法から求めた演算変位量と、入力された変位量とが一致しない場合、処理をステップＳ１６へ進める。
【００５０】
次に、ステップＳ１６において、力学演算部５は、所定の最適化法により材料に対する構成マトリクス［Ｄ^ｅ］または［Ｄ^ｐ］の各パラメータの変更量を求め、新たな各パラメータを設定し、処理をステップＳ１４へ進め、再度、有限要素法により演算変位量を求める。
また、ステップＳ１５において、力学演算部５は、有限要素法から求めた演算変位量と、入力された変位量とが一致した場合、このときの構成マトリクス［Ｄ^ｅ］または［Ｄ^ｐ］を求める構成関係として、図示しない出力装置へ出力し、構成関係を求める処理を終了する。
【００５１】
そして、力学演算部５は、得られた構成マトリクス［Ｄ^ｅ］または［Ｄ^ｐ］を用いて（８）式または（６）式により、被試験体１４の各部にかかる応力の計算を行う。
すなわち、力学演算部５は、変位量演算部４の求めた変位量から、材料（被試験体１４）が線形材料の場合、線形構成則による（８）式を用い、構成関係を求め、この線形材料の構成関係に基づき、上記（８）式により被試験体１４各部の応力を演算し、材料が非線形材料の場合、非線形・増分形の構成則の（６）式を用いて、非線形材料の構成関係を求め、この非線形材料の構成関係に基づき（６）式により、被試験体１４各部の応力を演算する。
【００５２】
上記ステップＳ３において、変位量演算部４の行う各ピクセル値Ｐ^＊（Ｘ，Ｙ，Ｚ）の値の求め方について、以下に説明する。
まず、変位量演算部４は、図７（ａ）に示すボクセルモデルにおいて、各画素に対応して空間格子を作成し、図７（ｂ）に示すように、各ピクセル値を対応する格子の重心に各々割り付ける。
そして、変位量演算部４は、演算した「ｕ，ｖ，ｗ」により上記重心を、図７（c）に移動させる（重心を変形写像により移動させる、（Mapping，x=D(X)））。
移動後の重心（以下、移動点（Mapped Points）：黒丸）と、変形画像を構成する空間固定格子の重心（以下、対応点（Fixed Points）：白丸）とは、図７（ｃ）で分かるように一般的には一致しない。
次に、変位量演算部４は、最終的に、各空間固定格子毎に、移動点（：変形写像）のピクセル値を、対応点に割り付けることにより、図７（ｄ）に示すように、シミュレーションボクセルモデルを生成する。
【００５３】
このため、以下の条件により、各移動点のピクセル値から、各空間固定格子の対応点のピクセル値を決定する。
基本的に、本実施形態においては、各対応点に対して最も近傍に存在する移動点のピクセル値を、この対応点のピクセル値とする、最近隣内挿法を基礎とした８近傍最近隣近似法を用いている。
すなわち、変位量演算部４は、移動点が、対応点を含む空間固定格子内へ移動したとき、移動点がこの空間固定格子内に１つの場合、移動点のピクセル値を対応点のピクセル値とし、移動点が空間固定格子内に複数ある場合、これら移動点のピクセル値の平均値を演算し、この平均値を対応点のピクセル値とする。
【００５４】
また、対応点の空間固定格子内に移動点が存在しない場合、その周囲３×３格子内の８近傍格子内の探索を行う。
このとき、周囲３×３格子内に移動点が存在しない場合、ピクセル値を「０」とし、移動点が存在する場合、その移動点のなかから対応点の位置に最も近傍にある移動点のピクセル値を、この対応点のピクセル値とする。
上述の説明は説明を簡略化するために２次元で行ったが、三次元の場合には、その空間固定格子内に移動点が無い場合、近接格子周囲３×３×３格子内の２６格子として移動点の探索を行い、８近傍格子の場合と同様の手法により対応点の格子点を決定する。
【００５５】
次に、ステップＳ５における各係数及び定数各々の数値の求め方について説明する。
すでに述べたように、ステップＳ５において、変位量演算部４は、上述したように、各係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗの変更量を、非線形計画法などの最適化手法によって、このアルゴリズに従った演算により、上記係数及び定数の数値を逐次変更する。
ここで、ボクセル値は離散値であるため、また最近隣近似に基づいて離散的な画像処理を行うため、目的関数の感度情報（各係数及び定数の変化量に対応する数値ｆの変化の度合い）を得ることができない。
【００５６】
このため、本実施形態において、変位量演算部４は、遺伝的アルゴリズム（Genetic Algorithm）等（以下説明するa)及びb)のアルゴリズム）の離散的最適化方法により誤差最小化処理を行う。
a)遺伝的アルゴリズムを用いる場合
変位量演算部４は、例えば、変数及び定数のデータ容量として、各々８ビットバイナリを割り当て、各変数及び定数毎に２５６段階の数値を有しているとする。
この２５６段階の数値は、予め変形の範囲（探索範囲として）として想定される所定の範囲（ボクセルモデルのピクセル数や寸法など）を、２５５分割したものである。
そして、遺伝的アルゴリズムのシミュレーションの条件として、各個体は、変位量演算部４において、上記各変数及び定数の数値から選択されて、１０００個の組み合わせとして構成される。
各個体の組み合わせを変更する遺伝子操作としては、一様交叉（交叉率７５％），線形ランキング選択，エリート戦略及び突然変異（突然変異率１.０％）などを用いた。
【００５７】
b)SCE-UA(Shuffled Complex Evolution Method developed at the University Arizona)法
このSCE-UA方法は、遺伝的アルゴリズム類似の進化手法を取り入れ、物理的な意味を持つ解の探索領域を設定できることと、計算の途中で、複数の個体群で独立に進化させるため、最終的に解を得る場合、計算不能や発散などが発生せず、必ず解が求まることを特徴としている。
【００５８】
すなわち、SCE-UA法は、競争進化及び集団混合の概念を組み合わせた帯域探索による最適化手法である。以下に計算手順を簡単に示す。
▲１▼ 決定変数（（１）〜（３）式における係数ａ_ｕｎ〜ｊ_ｗｍ及び定数ｐ_ｕ〜ｒ_ｗ、または（１'）〜（３'）式における変数ａ_ｕ１３（k_１,k_２,k_３）等）の個数ｎ，集団数ｐ，各集団内の個体数ｍ(＝２ｎ＋１)を設定し、各個体を決定変数を座標値とするｎ次元空間上の点とみなす。
例えば、係数および定数の数が合計ｎ個ある場合、ｐ個の集団に、各々「２ｎ＋１」個の個体群を振り分ける。
▲２▼ 初期世代として、各決定変数値をランダムに与え、例えば、（４）式の誤差関数の誤差関数値が低い順に個体を並べる。
【００５９】
▲３▼ ▲２▼において並べた順に、先頭の個体から、１番目の個体を第１集団に含め、２番目の個体を第２集団へ、…、ｐ番目の個体を第ｐ集団へ、ｐ＋１番目の個体を第１番目の集団へ、２ｐ(すなわち、ｐ＋ｐ)番目の個体を第ｐ集団へ、…と、全ての集団へ順次個体を振り分ける。
すなわち、この振り分け方法は、ｐ（Ｘ，Ｙ，Ｚ）と、このピクセル値に対応する各係数および定数を選択して組み合わせて演算されたｐ^＊（Ｘ，Ｙ，Ｚ）とにより、誤差関数ｆを求めて、誤差関数値が小さい順にｐ個の各集団に順次振り分けていく。
例えば、係数および定数の数が合計ｎ個ある場合、ｐ個の集団に、各々「２ｎ＋１」個の個体群を振り分ける。
【００６０】
▲４▼ 各集団毎に独立させて、CCE（Conditional Class Entropy）アルゴリズムにより、個体群の進化を行わせる。
上記CCEアルゴリズムにおいては、誤差関数ｆの誤差関数値が高い個体を、より誤差関数値の低い個体とするよう、係数および定数を変化させて、各個体を進化させてゆく。
▲５▼ 最終的に、ｐ個の集団を、すなわち全集団を１つにまとめて、全集団に含まれていた全個体を、再度、誤差関数値の低い順番に並べ替えて、この全個体の内の最も優れた個体の誤差関数値が、予め設定された収束判定値の範囲内になるか、または、係数および定数の最適化処理の繰り返し回数が予め設定された繰り返し設定値となるか、のいずれかに対応するまで、▲３▼〜▲５▼を繰り返して、係数および定数の最適化処理を行う。
【００６１】
上述してきたように、本発明の材料解析システムは、３次元透視画像を取ることが可能であり、ピクセルのピクセル値が異なった値で分布している材料（構造が不均一）であれば、非荷重透視画像と荷重透視画像とを得ることにより、各不均一なひずみ及び応力を３次元的に解析することが可能である。
【００６２】
次に、図５及び図６を用いて、実際の非荷重透視画像と荷重透視画像との応力及びひずみの評価の例として、被試験体にテキスタイル材料である八つ打ちロープ（材料の形状が複雑であり、かつ材質が均一でない材料）を例にとり、３次元透視画像を用いた、荷重印加状態における被試験体内の応力及びひずみに対する評価の流れを以下に説明する。
例えば、ロープの直径は１０mmものを使用し、Ｘ線の照射条件は電圧８５ｋＶ，電流５０μＡとし、ロープ自重分の１Ｎ（ニュートン）を印加した状態（以下、非荷重状態とする）と、５０Ｎを印加した状態（以下、荷重状態）とで、Ｘ線ＣＴ装置による撮像を評価を行った。
【００６３】
図５（ｂ）は荷重を印加しない状態（上記非荷重状態）の断層像であり、図５（ａ）は非荷重状態の３次元ボクセルモデル、すなわち非荷重透視画像である。図６（ｂ）は荷重を印加した状態（上記荷重状態）の断層像であり、図６（ａ）は荷重状態の３次元ボクセルモデル、すなわち荷重透視画像である。
図５，６の双方ともに、Ｘ線の透過量が少ないほど白く表示されており、これらの図からのみでも、八つ打ちロープが荷重を上下方向に印加したことにより、対軸方向に引っ張られることで伸びてロープの繊維が詰まっていることが確認できる。
【００６４】
この例においては、図５（ｂ），図６（ｂ）の断層像を１０２４×１０２４ピクセル（ピクセルの階調度を２５６としている）とし、この断層像を０.２mm間隔（体軸方向に対して）で上下の評点間隔約１７mmの範囲で撮像を行っている。図５（ａ），図６（ａ）は、上述した評点間隔の範囲で撮像した、図５（ｂ），図６（ｂ）の複数の断層像を、上記軸方向の解像度（軸方向の撮像枚数）に対応させるため、複数のピクセルの階調度のデータの平均化処理を行い、１０２４×１０２４ピクセルから１００×１００ピクセルに、画像の解像度を低下させて変換した３次元ボクセルモデルである。
ここで、図５（ａ）が非荷重ボクセルモデルであり、図６（ａ）が荷重ボクセルモデルである。
すなわち、画像処理部２は、画像記憶部３から上記非荷重透視画像及び上記荷重透視画像を読み出し、各３次元透視画像を所定の画像サイズの１００×１００ピクセルの解像度に変更し、各ピクセルの階調度を抽出し、この各ピクセルの階調度を示すピクセル値の分布で構成される、各々の３次元ボクセルモデルを生成する。
【００６５】
そして、変位量演算部４は、図５（ａ）の非荷重ボクセルモデルにおける各ピクセルにおいて、すでにのべた（１）〜（３）式を用いたシミュレーション（図３のフローチャートの各ステップに基づいて行われる）から、変位量ｕ，ｖ，ｗを求める。
次に、力学演算部５は、八つ打ちロープが大きく変形するため、大変形理論のに基づく（５）式により、上記変位量ｕ，ｖ，ｗから、非荷重ボクセルモデルに対応した荷重ボクセルモデルにおけるひずみを求める。
そして、力学演算部５は、八つ打ちロープが非線形材料のため、（６）式により、変位量ｕ，ｖ，ｗに基づき、非荷重ボクセルモデルに対応した荷重ボクセルモデルにおける構成関係（応力とひずみとの関係を、すでに説明した図４のフローチャートの各ステップに従い求める。
【００６６】
次に、変位量演算部４が変位量u,v,wの算出に用いている（１），（２）及び（３）式を、下記に示す各々（１'），（２'）及び（３'）に換えて、変位量u,v,wを算出する場合について説明する。
【数１２】

【数１３】

【数１４】

【００６７】
これら（１'），（２'）及び（３'）式は、（１），（２）,（３）式各々に対して、フーリエ級数の項に、複数の座標軸における変位の影響を含ませたものである。
（１'），（２'）及び（３'）式各々において、Ｍu，Ｍv，Ｍw及びＮu，Ｎv，Ｎwは各々整数値で問題により適宜設定する定数であり、ωは基本周波数であり、同様に問題により適宜設定する定数である。
また、α_ｉｊｋ，β_ｉｊｋ，γ_ｉｊｋは、i,j,kが異なれば、異なる変数として定義され、ＧＡ等の最適化アルゴリズムにより、誤差関数から求められる誤差関数値が最小となるように決定される変数である。
そして、ａ_ｕ１３(ｋ1,ｋ2,ｋ3)，ａ_ｖ１３(ｋ1,ｋ2,ｋ3)，ａ_ｗ１３(ｋ1,ｋ2,ｋ3)等も、ｋ1,ｋ2,ｋ3が異なれば、異なる変数として定義され、ＧＡ等の最適化アルゴリズムにより、誤差関数から求められる誤差関数値が最小となるように決定される変数である。
【００６８】
このため、（１'），（２'）及び（３'）式を用いることにより、各々の座標軸方向の変位に対して、他座標軸方向からの影響、すなわち補正量を含ませることとなり、（１），（２）,（３）式を用いた場合に比較して、変位量u,v,wを算出する際に、より精度の高いシミュレーションが行える。
例えば、材料解析の試料をプチトマトとし、荷重をかけない非荷重状態において、Ｘ線ＣＴ装置１により、１ボクセルの１辺の長さを０.４ｍｍとして、透視画像を撮像することで、非荷重透視画像が得られる。
そして、画像処理部２は、非荷重状態の試料（プチトマト）に対して、Ｘ線ＣＴ装置１により得られた非荷重透視画像から、図８（図８(a)：全体の1/2の部分、図８(b)：全体の1/8の部分）に示す初期画像の３次元ボクセルモデル（非荷重ボクセルモデル：１ボクセルの１辺の長さを０.４ｍｍ）を生成する。
【００６９】
次に、試料のプチトマトの上下を平行な板で挟み、この板に対して垂直に４００ｍＮの荷重を印加して圧縮し、Ｘ線ＣＴ装置１により、１ボクセルの１辺の長さを０.４ｍｍとして、透視画像を撮像することで、荷重透視画像が得られる。
そして、画像処理部２は、荷重状態の試料に対して、Ｘ線ＣＴ装置１により得られた荷重透視画像から、図９（図９(a)：全体の1/2の部分、図９(b)：全体の1/8の部分）に示す３次元ボクセルモデル（荷重ボクセルモデル，ボクセルサイズ：１ボクセルの１辺の長さを０.４ｍｍ）を生成する。
そして、変位量演算部４は、図３のフローチャートに従い、非荷重ボクセルモデルのピクセルを変位させて求めたｐ^＊（Ｘ，Ｙ，Ｚ）と、荷重ボクセルモデル（図９）から得られるｐ（Ｘ，Ｙ，Ｚ）との比較を行い、（４）式の誤差関数が極小となる点を探索し、探索された極小点における各係数及び定数を最適値として出力する。
【００７０】
このとき得られるシミュレーション結果のシミュレーションボクセルモデル（ボクセルサイズ：１ボクセルの１辺の長さを０.４ｍｍ）を図１０（図１０(a)：全体の1/2の部分、図１０(b)：全体の1/8の部分）に示す。
また、図９の荷重ボクセルモデルと、図１０のシミュレーションボクセルモデルとにおける、各位置におけるピクセル値の差分を示す差分ボクセルモデルを図１１（全体の1/2の部分）に示す。
図１１において、差分の多い部分の階調度を高くしてあり、結果として階調度の高い部分がほぼないことから、図１１の差分値のグラフから（１'），（２'）及び（３'）式及び図３のフローチャートに基づいて、各演算により求められたシミュレーションボクセルモデルが、実際の荷重ボクセルモデルに良く一致していることが分かる。
特に、図９及び図１０とにおいて、楕円で囲んで示しているプチトマトの「へた」と「芯」の部分が非常に一致したボクセルモデルとなっていることが確認できる。
【００７１】
次に、力学演算部５は、最適値として得られたα_ｉｊｋ，β_ｉｊｋ，γ_ｉｊｋと、ａ_ｕ１３(ｋ1,ｋ2,ｋ3)，ａ_ｖ１３(ｋ1,ｋ2,ｋ3)，ａ_ｗ１３(ｋ1,ｋ2,ｋ3)等を入力して、変位量ｕ，ｖ，ｗを各々求める。
そして、力学演算部５は、求めた変位量ｕ，ｖ，ｗにより、（５）あるいは（７）式を用いて、ひずみε_ｉｊを算出する。
以降は、すでに述べた（１）〜（３）式を用いて行った、変位−ひずみマトリクス，要素剛性マトリクス［Ｋ_ｐ］，構成マトリクス［Ｄ^ｐ］，接線剛性マトリクス算出の演算と同様であるため、説明を省略する。
【００７２】
上述したように、本発明の材料解析システムを用いることにより、従来、材質が均質でなく、形状が複雑であり、材料試験において全体としての挙動が判るのみで、局所的な状態が不明である被試験体に対して、荷重を印加することにより被試験体内部の各部位に発生する応力及びひずみの分布を定量的に求めることができるため、被試験体を構造部材とする構造体の構造設計を、使用する用途に応じて精度良く行うことが可能となる。
【００７３】
また、被試験体に荷重をかける装置を具備する構成のＸ線ＣＴ装置１を用いて、本発明の構成を説明してきたが、本発明によれば、例えば、人体に埋め込む人工臓器（人工骨など）により、周囲の人体組織（構造部材と考えられる）にかかる荷重の評価を行うことが可能である。
この場合、まず、画像処理部２は、通常の医療用等に用いられるＸ線ＣＴ装置の撮像する断層像から、変形させない状態において、人工臓器を埋め込む部位の筋肉組織等の非荷重ボクセルモデル、すなわち非荷重透視画像をすでに説明した方法により作成し、画像記憶部３に格納する。
【００７４】
次に、画像処理部２は、医療用のＸ線ＣＴ装置の撮像する断層像から、所定の荷重を印加して変形させた状態において、人工臓器を埋め込む部位の筋肉組織等の荷重ボクセルモデル、すなわち荷重透視画像を、すでに説明した方法により作成し、画像記憶部３へ格納する。
このとき、被試験体である筋肉組織等の上記非荷重ボクセルモデルと上記荷重ボクセルモデルとは、同様な解像度で撮像した断層像を用い、同一の縮尺であり、かつ、ピクセル構成が同一の数、例えば双方とも１００×１００ピクセルとする。
【００７５】
そして、荷重透視画像については、所定の荷重を印加される筋肉組織等の部位を、体形を変化させながら異なった荷重がこの筋肉組織等にかかる各々の状態毎に荷重透視画像を作成する。
そして、画像処理部２は、非荷重ボクセルモデルと上記複数の荷重ボクセルモデルとの画像データを画像記憶部３へ記憶させる。
次に、変位量演算部４は、すでに述べた（１），（２），（３）式、あるいは（１'），（２'），（３'）式により、変位量ｕ，ｖ，ｗを、各々の体形の荷重ボクセルモデル毎に求める。
【００７６】
次に、力学演算部５は、荷重を印加された筋肉組織等を被試験体とする場合、変形としては大変形であるため、（５）式により変位量ｕ，ｖ，ｗに基づき、非荷重ボクセルモデルに対応した荷重ボクセルモデルにおけるひずみを、図３のフローチャートの各ステップに従い求める。
そして、力学演算部５は、筋肉組織等が非線形材料のため、（６）式により、変位量ｕ，ｖ，ｗに基づき、非荷重ボクセルモデルに対応した荷重ボクセルモデルにおける構成関係を、すでに説明した図４のフローチャートの各ステップに従い求める。
【００７７】
ここで、力学演算部５は、有限要素法により、被試験者の体形毎に筋肉組織等にかかるひずみ及び応力を求める。
すなわち、力学演算部５は、被試験者の複数の体形各々において、人体に埋め込まれる人工臓器により、周囲の筋肉組織等にかかる荷重を想定し、この筋肉組織等（血管や神経等も含め）に発生する応力及びひずみを演算する。
上述した演算により、各患者毎における生体組織の力学的な構造の特性、すなわち応力及びひずみの関係を得て、埋め込む人工臓器と、被試験体（上述の場合には筋肉組織等）とを構造部材とする構造体（ここでは人体）の構造設計を精度良く行うことができる。
【００７８】
そして、埋め込み周囲の筋肉組織等の応力及びひずみの関係に基づき、埋め込む人工臓器の構造設計を行い、この筋肉組織に対応する大きさや応力及びひずみ関係を有する人工臓器を作成する。
そして、この作成された人工臓器を人体に埋め込む場合に、筋肉組織にした上述の試験と同様な試験をこの人工臓器に対して行う。
【００７９】
すなわち、画像処理部２は、通常の医療用等に用いられるＸ線ＣＴ装置の撮像する断層像から、埋め込む前の人工骨の非荷重ボクセルモデル、すなわち非荷重透視画像をすでに説明した方法により作成し、画像記憶部３に格納する。
次に、画像処理部２は、医療用のＸ線ＣＴ装置の撮像する断層像から、人体に埋め込んだ後の人工骨の荷重ボクセルモデル、すなわち荷重透視画像を、すでに説明した方法により作成し、画像記憶部３へ格納する。
【００８０】
このとき、被試験体である人工骨の上記非荷重ボクセルモデルと上記荷重ボクセルモデルとは、同様な解像度で撮像した断層像を用い、同一の縮尺であり、かつ、ピクセル構成が同一の数、例えば双方とも１００×１００ピクセルとする。
そして、荷重透視画像については、人工骨を埋め込んだ人体の部位を、体形を変化させながら異なった荷重がこの人工骨にかかる各々の状態毎に荷重透視画像を作成する。
【００８１】
そして、画像処理部２は、非荷重ボクセルモデルと上記複数の荷重ボクセルモデルとの画像データを画像記憶部３へ記憶させる。
次に、変位量演算部４は、すでに述べた（１），（２），（３）式により、変位量ｕ，ｖ，ｗを、各々の体形の荷重ボクセルモデル毎に求める。
次に、力学演算部５は、人体に埋め込まれた人工骨を被試験体とする場合、変形としては微小な変形であるため、（６）式により変位量ｕ，ｖ，ｗに基づき、非荷重ボクセルモデルに対応した荷重ボクセルモデルにおけるひずみを、図３のフローチャートの各ステップに従い求める。
そして、力学演算部５は、人工骨が線形材料のため、（７）式により、変位量ｕ，ｖ，ｗに基づき、非荷重ボクセルモデルに対応した荷重ボクセルモデルにおける応力を、すでに説明した図４のフローチャートの各ステップに従い求める。
【００８２】
ここで、力学演算部５は、非荷重ボクセルモデルの各ピクセルに対する、荷重ボクセルモデル毎の各ピクセルの変位量に基づき、被試験者の体形毎に人工骨にかかるひずみ及び応力を求める。
すなわち、力学演算部５は、被試験者の複数の体形各々において、人体の他の生体組織から人工骨にかかる荷重により、この人工骨各部（内部も含め）に発生する応力及びひずみを演算する。
そして、すでに演算されている筋肉組織等の応力及びひずみの関係に対応しているか否かの判定、すなわち、この筋肉組織等に不都合な荷重がかかっているか否かの判定を行い、人工臓器の構造設計の妥当性を検討する。
これにより、発明の材料解析システムを用いることにより、各患者の人体の個体差に合わせた人工臓器の構造設計を、他の構造部材（例えば、筋肉組織等）に対する適合性を向上させ、高い精度で設計することが可能となる。
【００８３】
上述した本発明の材料解析システムを用いることにより、従来評価できなかった人体に埋め込んだ人工臓器の評価において、人工臓器を埋め込む前に、人工臓器を埋め込むことにより周囲の生体組織にかかる応力およびひずみと、周囲の生体組織から印加される荷重によりこの人工臓器の各部にかかる応力およびひずみとを、３次元において定量的に求めることにより、構造部材としての生体組織や人工臓器の強度などに対する構造設計及び材料設計を、人体の個体差及び使用環境に対応して行うことができ、埋め込む人体の各個体差に対して適合性の高い人工臓器の製造を可能とすることができる。
【００８４】
また本発明の材料解析システムを用いることにより、健常人の臓器、例えば骨などに、外部から荷重を印加したり、体型を変えて荷重のかかり具合を調整して、３次元ボクセルモデルで、各状態の荷重に基づいてこの骨の各部に発生する応力及びひずみを、３次元において定量的に求め、この評価結果を人工骨の構造設計及び材料設計にフィードバックすることにより、より実際の骨に近い人工骨の開発・製造を行うことが可能である。
【００８５】
＜第２の実施形態：材料試験システム＞
本発明の第２の実施形態の材料試験システムは、第１の実施形態の材料解析システムの構成が用いられており、異なる部分は固定装置２０が第１の実施形態に含まれていない点である。
本発明は、荷重が印加されていない状態での被試験体の３次元透視画像（以下、被荷重透視画像）と、所定の荷重が印加された状態での被試験体の３次元透視画像（以下、荷重透視画像）とを、Ｘ線ＣＴ装置からのＸ線の透過強度に基づくＸ線データから生成する。
しかしながら、本発明はＸ線ＣＴ装置に限らず、ＭＲＩ（磁気共鳴画像）や超音波装置による３次元透視画像を用いることも可能である。
そして、後に述べる変位量演算部４が所定の演算式を用いて非荷重透視画像の各ピクセルを３次元的（空間的）に移動させる。
【００８６】
このとき、第２の実施形態の材料試験システムは、第１の実施形態の材料解析システムと同様に、上記移動後の非荷重透視画像と上記荷重透視画像との形状が一致するまで、演算式の係数及び定数を逐次変化させながらシミュレーションを行い、他の材料に埋め込まれた被試験体（内部の構造が力学的に不均質な構造体）の各部にかかる応力及びひずみの定量的な解析を行うことが可能となる。
【００８７】
以下、図面を参照して、第２の実施形態について説明する。図１２は本発明の第２の実施形態による材料試験システムの構成例を示すブロック図である。この図において、本発明の材料試験システムは、少なくとも、Ｘ線ＣＴ装置１，画像処理部２，画像記憶部３，変位量演算部４，力学演算部５及び固定装置２０を有している。
上記Ｘ線ＣＴ装置１，画像処理部２，画像記憶部３，変位量演算部４，力学演算部５各々は、第１の実施形態の図１における各構成と同様のため（同様の処理を行うため）、同一符号を付して説明を省略する。
【００８８】
次に、図２を参照して、上記Ｘ線ＣＴ装置１の構成を簡単に説明する。図２はＸ線ＣＴ装置の構成例を示す概念図である。
Ｘ線ＣＴ装置１は、Ｘ線を放射するＸ線管１１と、このＸ線の強度を検出するＸ線検出器１３とを対向する位置に有し、被試験体１４がＸ線管１１とＸ線検出器１３との間に、図示しない固定装置２０により固定されている。
上記固定装置２０は、つかみ具などにより、図における被試験体１４の上部及び下部を固定して、引張／圧縮／ねじり等の荷重を被試験体１４に印加する。
【００８９】
この固定装置２０は、上記荷重を印加した状態で、被試験体１４の体軸に沿って、この被試験体をＲ方向に、３６０°の角度範囲において回転させることができる。
ここで、Ｘ線管１１が扇状に広がるＸ線１２を放射するため、固定装置２０は、この扇状に広がったＸ線１２が被試験体１４の横幅となるように、Ｘ線管１１及びＸ線検出器１３の位置を調整する。
そして、Ｘ線検出器１３は、例えば、被試験体１４の断面１４ｎの部分において、被試験体１４を透過した後のＸ線１２のＸ線強度を測定する。
【００９０】
また、上記固定装置２０は、上記体軸に沿って、同期してＺ1方向またはＺ2方向に移動可能となっている。
そして、Ｘ線ＣＴ装置１は、この固定装置２０を、回転及び移動させつつ、被試験体１４を透過するＸ線１２のＸ線強度の測定を行 う。
このとき、Ｘ線ＣＴ装置１は、被試験体１４に対して、上記荷重を印加した状態，及び印加しない状態の双方の状態において、被試験体１４を透過するＸ線１２のＸ線強度の測定を行う。
【００９１】
上述した固定装置２０を図１３を用いて説明する。図１３は固定装置２０の構成例を示す概念図である。
被試験体１４は、掴み具２１により上部が把持され、掴み具２２により下部が把持されている。
アーム２３は掴み具２１を有し、またアーム２４は掴み具２２を有しており、固定装置２０は、掴み具２１及び掴み具２２を、これら掴み具の対向方向に沿う荷重軸に対して平行に、上下に駆動させる負荷機構を内部に有している。
また、掴み具２１及び２２は、固定装置２０内の駆動部により、同期して駆動され、掴んでいる試料を図２のＲ方向へ、被試験体１４の上記荷重軸に平行な中心軸を中心として回転させられる。
【００９２】
また、固定装置２０には、上記他の駆動部により回転が与えられるスプライン軸２５が設けられている。
そして、アーム２３及びアーム２４の掴み具２１，掴み具２２には、上記スプライン軸２５の回転を伝達される回転伝達機構が設けられている。
これにより、掴み具２１，掴み具２２は、試料を掴んだ状態において、同期してＲ方向への回転を行うこととなる。
ここで、上部にある掴み具２１の回転伝達機構の駆動側要素がスプライン軸２５に対してスプライン結合されている。
こうすることで、掴み具２１及び２２は、固定装置２０内に設けられた負荷機構により試料に荷重をかけつつ、同期した状態において、Ｒ方向へ回転させることができる。
【００９３】
したがって、掴み具２１が上記負荷機構により上部方向に所定の力で引っ張られるとき、掴み具２２が同様に負荷機構により下部方向に同一の力で引っ張られ、被試験体１４に対して引張荷重が印加されることとなる。
また、掴み具２１が負荷機構により下部方向に所定の力で押し出されるとき、掴み具２２が同様に負荷機構により上部方向に押し出され、被試験体１４に対して圧縮荷重が印加されることとなる。
【００９４】
この被試験体１４に印加される荷重は、掴み具２１に埋め込まれたロードセルにより測定される。
固定装置２０の駆動制御部は、この上記ロードセルにより測定された荷重検出結果を用いて、被試験体１４に印加される荷重が予め設定された数値となるように、上記負荷機能を制御する。
【００９５】
加えて、掴み具２１及び２２は、被試験体１４に荷重をかけた状態で、固定装置２０内の駆動部が同期させつつ、微小角度毎に角度を変化させ、この被試験体１４を３６０°回転することができる。
これにより、Ｘ線管１１から放射されるＸ線１２が、荷重をかけられた状態の被試験体１４を透過して、Ｘ線検出装置１３で検出され、Ｘ線検出装置１３から、図１２の画像処理部２において層画像を生成するために用いられるＸ線データとして出力される。
【００９６】
図１２に戻り、上述した構成により、Ｘ線ＣＴ装置１は、被試験体（図２における被試験体１４）の断面のＸ線データを出力する。
そして、画像処理部２は、Ｘ線ＣＴ装置１から出力される、被試験体が３６０°回転する間のＸ線データ（Ｘ線透視画像）を集積し、この集積されたＸ線データを再構成演算を行うことにより、被試験体の断面、すなわち体軸に垂直な被試験体の断層像を生成する。
【００９７】
また、画像処理部２は、体軸に沿って、同期してＺ1方向またはＺ2方向に、微小間隔に移動させて得られた上記断層像を、体軸方向に重ねて、被試験体の３次元透視画像（３次元ボクセルモデル）を生成する。
このとき、Ｘ線ＣＴ装置において、上述の処理により、荷重を印加していない非荷重透視画像の非荷重ボクセルモデルと、所定の荷重を印加した状態における荷重透視画像の荷重ボクセルモデルとを、画像処理部２に生成させる。
【００９８】
さらに、画像記憶部２は、得られたこれらの非荷重ボクセルモデル，荷重ボクセルモデルを画像記憶部３に記憶させるとともに、これら非荷重ボクセルモデル，荷重ボクセルモデルを、図示しない画像表示装置の表示画面に表示する。
以下、変位量演算部４と力学演算部５とで行われる変位量，応力及びひずみの算出を行う演算の演算式及びアルゴリズム（図３及び図４のフローチャートの処理）については、第１の実施形態と同様のため（同一符号の構成が同様の処理を行うため）省略する。
【００９９】
上述したように、本発明の材料試験システムを用いることにより、従来、評価が行えなかった、荷重をかけた状態における被試験体に対して、荷重をかけた状態で被試験体１４を３６０°回転させることが可能な固定装置２０により、荷重をかけた状態での被試験体１４の３次元ボクセルモデル、すなわち荷重透視画像を生成することが可能となるため、内部の構造が力学的に不均質であり、複雑な形状の被試験体１４の、荷重による３次元変形の形状を検出することが可能である。
【０１００】
また、本発明の材料試験システムを用いることにより、材質が均一でなく、形状が複雑であり、従来、破壊試験を用いることでしか強度／延性／靱性の評価が行えない被試験体の試験を行う場合にも、被試験体の破壊を行うことなく、荷重を印加することにより被試験体内部の各部位に発生する応力及びひずみの分布を定量的に、３次元において求めることができるため、被試験体の構造設計及び材料設計を使用する用途に応じて精度良く行うことが可能となる。
【０１０１】
このように、本発明の材料試験システムを用いることにより、従来、材質が均質でなく、形状が複雑であり、材料試験において全体としての挙動が判るのみで、局所的な状態が不明である被試験体に対して、荷重を印加することにより被試験体内部の各部位に発生する応力及びひずみの分布を定量的に求めることができるため、被試験体を構造部材とする構造体の構造設計を、使用する用途に応じて精度良く行うことが可能となる。
【０１０２】
なお、上記した本発明の実施形態においては、材料解析システム及び材料試験システムにおいて実行される手順をコンピュータ読取り可能な記録媒体に記録し、この記録媒体に記録されたプログラムをコンピュータシステムに読み込ませ、実行することにより本発明の材料解析システムが実現されるものとする。ここでいうコンピュータシステムとは、ＯＳや周辺機器等のハードウアを含むものである。
【０１０３】
更に、「コンピュータシステム」は、ＷＷＷシステムを利用している場合であれば、ホームページ提供環境（あるいは表示環境）も含むものとする。
また、「コンピュータ読取り可能な記録媒体」とは、フレキシブルディスク、光磁気ディスク、ＲＯＭ、ＣＤ−ＲＯＭ等の可搬媒体、コンピュータシステムに内蔵されるハードディスク等の記憶装置のことをいう。さらに「コンピュータ読取り可能な記録媒体」とは、インターネット等のネットワークや電話回線等の通信回線を介してプログラムが送信された場合のシステムやクライアントとなるコンピュータシステム内部の揮発性メモリ（ＲＡＭ）のように、一定時間プログラムを保持しているものも含むものとする。
【０１０４】
また、上記プログラムは、このプログラムを記憶装置等に格納したコンピュータシステムから、伝送媒体を介して、あるいは、伝送媒体中の伝送波により他のコンピュータシステムに伝送されてもよい。ここで、プログラムを伝送する「伝送媒体」は、インターネット等のネットワーク（通信網）や電話回線等の通信回線（通信線）のように情報を伝送する機能を有する媒体のことをいう。
また、上記プログラムは、前述した機能の一部を実現するためのものであっても良い。さらに、前述した機能をコンピュータシステムにすでに記録されているプログラムとの組み合わせで実現できるもの、いわゆる差分ファイル（差分プログラム）であっても良い。
【０１０５】
以上、本発明の第１及び第２の実施形態を図面を参照して詳述してきたが、具体的な構成はこの実施形態に限られるものではなく、本発明の要旨を逸脱しない範囲の設計変更等があっても本発明に含まれる。
【０１０６】
【発明の効果】
本発明の材料解析システムによれば、他の材料に埋め込まれた（例えば、人体に埋め込まれた人工臓器）のように、材質が不均一であり、形状が複雑な被試験体の各部（内部を含めた）の変形を３次元ボクセルモデルによりで評価することができ、各部における応力及びひずみを定量的に測定することが可能となり、使用する環境、すなわち荷重のかかり具合に対応した構造設計及び材料設計を行うことができる。
【０１０７】
本発明の材料試験システムによれば、材質が不均一であり、形状が複雑な被試験体の各部（内部を含めた）の変形を３次元ボクセルモデルによりで評価することができ、各部における応力及びひずみを定量的に測定することが可能となり、使用する環境、すなわち荷重のかかり具合に対応した構造設計及び材料設計を行うことができる。
【図面の簡単な説明】
【図１】 本発明の第１の実施形態による材料解析システムの構成例を示すブロック図である。
【図２】 図１のＸ線ＣＴ装置１の構成を示す概念図である。
【図３】 図１における変位量演算部４の変位量算出の動作例を示すフローチャートである。
【図４】 図１における力学演算部５の応力算出の動作例を示すフローチャートである。
【図５】 本発明におけるＸ線ＣＴ装置１により撮像された層画像から生成された非荷重状態の八つ打ちロープの透視画像である。
【図６】 本発明におけるＸ線ＣＴ装置１により撮像された層画像から生成された荷重状態の八つ打ちロープの透視画像である。
【図７】 変位量演算部４における各ピクセル値Ｐ^＊（Ｘ，Ｙ，Ｚ）の値の算出方法の説明を行う概念図である。
【図８】 Ｘ線ＣＴ装置１により撮像された断層画像から生成された試料（プチトマト）の非荷重状態での３次元ボクセルモデル（非荷重ボクセルモデル）の図である。
【図９】 Ｘ線ＣＴ装置１により撮像された断層画像から生成された試料（プチトマト）の荷重状態での３次元ボクセルモデル（荷重ボクセルモデル）の図である。
【図１０】 非荷重ボクセルモデルから、シミュレーションによって得られた荷重ボクセルモデル（１ボクセルの１辺の長さ０.４ｍｍ）の図である。
【図１１】 図９の荷重ボクセルモデルと、図１０のシミュレーションボクセルモデルとにおける、各位置におけるピクセル値の差分を示す差分ボクセルモデルの図である。
【図１２】 本発明の第２の実施形態による材料試験システムの構成例を示すブロック図である。
【図１３】 図１２における被試験試料１４を固定する固定装置２０の構成例を示す概念図である。
【符号の説明】
１ Ｘ線ＣＴ装置
２ 画像処理装置
３ 画像記憶部
４ 変位量演算部
５ 力学演算部
１１ Ｘ線管
１２ Ｘ線
１３ Ｘ線検出装置
１４ 被試験体
２０ 固定装置
２１，２２ 掴み具
２３，２４ アーム
２５ スプライン軸[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a material analysis system and a material test system for analyzing stress and strain applied to each part of a material based on a three-dimensional image of the material before and after a load is applied.
[0002]
[Prior art]
There are several types of material testing machines depending on the purpose. Generally, a compression test is performed by applying a load such as tension / compression / bending to a test piece of material (test object). Test machines that can perform tensile tests, bending tests, etc. are widely used.
That is, the material testing machine evaluates mechanical properties such as strength / ductility / toughness based on the results of a compression test, a tensile test, a bending test, and the like on the test piece.
[0003]
In addition, the material testing machine supports various environments by changing the environment around the device under test by changing the temperature of the device under test or performing repeated tests when applying a load. Compressed test, tensile test, bending test, etc.
As mentioned above, various materials such as artificial organs (artificial bones, artificial joints, artificial ligaments, artificial roots, dentures), building materials, mechanical materials, etc. are used by conducting various tests using a material testing machine. It is possible to perform a test according to the above (for example, see Non-Patent Document 1).
[0004]
[Non-Patent Document 1]
Takado, Shino Himei, Hiroshi Arita, etc., Prceeding of 6th Symposium on "Microjoining and Assembly Technology in Electronics", 85-90
[0005]
[Problems to be solved by the invention]
The conventional material testing machine described above performs quantitative measurement of stress and strain using a load sensor that measures the load applied to the DUT and a displacement sensor that measures the displacement of the DUT. ing.
That is, the conventional material test is performed in each part by calculating the deformation state of the material from the measured values of the load sensor and the displacement sensor and performing a predetermined calculation by a computer based on the deformation state and the shape / material of the device under test. To evaluate stress and strain.
[0006]
However, the material test using the above-mentioned material testing machine is limited to materials with uniform specimens and simple shapes, and when the materials are non-uniform (mixed with different materials) In addition, when the DUT has a complex shape, the displacement-strain and strain-stress relationship corresponding to the applied load is calculated by a computer or the like at each part of the DUT (including the inside of the DUT). Can not be determined from.
In addition, the above-mentioned material testing machine is used for a material to be used in a sealed state in another material, such as an artificial organ embedded (implanted) in a human body, and then sealed and tested. It is not possible to measure the load applied to the body (eg, an artificial organ) from other surrounding materials.
[0007]
The present invention has been made under such a background, and is deformed by a load of each part (including the inside) of the DUT that is embedded in another material and has a heterogeneous material and a complicated shape. An object of the present invention is to provide a material analysis system capable of evaluating in three dimensions including the mechanical characteristics of surrounding structural members and quantitatively measuring strain and stress in each part.
In addition, the present invention evaluates the deformation caused by the load in three dimensions in each part (including the inside) of the DUT having a heterogeneous material and a complicated shape, and quantitatively measures the stress and strain in each part. It is to provide a material testing system that can do this.
[0008]
[Means for Solving the Problems]
The material analysis system of the present invention includes an X-ray CT apparatus (X-ray CT apparatus 1) that has an X-ray source and a plurality of X-ray detectors and collects X-ray data relating to a cross section of a test object, and the X An image processing unit (image processing unit 2) that generates a three-dimensional perspective image of the test object based on the line data; a first three-dimensional fluoroscopic image of the test object in a state where no load is applied; An image storage unit (image storage unit 3) that stores a second three-dimensional perspective image of the DUT in a state where a load is applied, and each pixel of the first three-dimensional perspective image is moved by a predetermined calculation. A displacement amount calculation unit (displacement amount calculation unit 4) for obtaining a displacement amount due to a load of each pixel by matching the shapes of the first three-dimensional perspective image and the second three-dimensional perspective image, and the displacement From the amount, strain and stress in each part of the DUT due to load And having a computation for dynamics calculating unit (dynamics calculating unit 5).
[0009]
In the material analysis system of the present invention, the displacement calculation unit moves each pixel while sequentially changing the coefficient and constant of the predetermined calculation formula, so that the first three-dimensional perspective image and the second It is characterized by matching the shape with the three-dimensional perspective image.
[0010]
In the material analysis system of the present invention, the displacement amount calculation unit associates each pixel in the second three-dimensional perspective image and the first three-dimensional perspective image after movement based on each gradation, It is characterized by determining the coincidence of the shapes of the three-dimensional perspective image and the second three-dimensional perspective image.
[0011]
In the material analysis system of the present invention, when the mechanical calculation unit is based on the amount of displacement and the deformation of the material is minute, an equation corresponding to the strain of the minute deformation (expression (7): displacement-strain relational expression) is obtained. When the deformation of the material is large, an arithmetic expression corresponding to the large deformation strain (formula (5): displacement-strain relational expression) is used, and the strain is calculated based on the amount of displacement.
In the material analysis system of the present invention, when the dynamic calculation unit is based on the amount of displacement and the material is a linear material (a material exhibiting linearity in deformation), the first calculation formula (formula (8)) based on the linear constitutive law ), The first configuration matrix (matrix relating stress and strain, [D ^e ]), And based on the first configuration matrix, the stress is calculated by the first calculation formula. When the calculation material is a nonlinear material (a material showing nonlinearity in deformation), a nonlinear / incremental constitutive law Is used to calculate the second configuration matrix ([D ^p ]) And the stress is calculated by the second calculation formula based on the second configuration matrix.
[0012]
The material testing method of the present invention includes a data collection process for collecting X-ray data relating to a cross section of a test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors. An image processing process for generating a three-dimensional perspective image of the test object, a first three-dimensional fluoroscopic image of the test object in a state where no load is applied, and a state where a predetermined load is applied An image storage process in which a second three-dimensional perspective image of the object to be tested is stored in an image storage unit, and each pixel of the first three-dimensional perspective image is moved by a predetermined calculation, whereby the first three-dimensional By matching the shapes of the fluoroscopic image and the second three-dimensional fluoroscopic image, a displacement amount calculating process for obtaining a displacement amount due to the load of each pixel, and a strain in each part of the DUT due to the load from the displacement amount, It has a mechanical calculation process for calculating stress. And wherein the Rukoto.
[0013]
In the material test method of the present invention, in the displacement amount calculation process, each pixel is moved while sequentially changing the coefficient and constant of the predetermined calculation formula, so that the first three-dimensional perspective image and the second It is characterized by matching the shape with the three-dimensional perspective image.
[0014]
According to the material test method of the present invention, in the displacement amount calculation process, each pixel in the second three-dimensional perspective image and the first three-dimensional perspective image after movement is associated with each other based on each gradation, It is characterized by determining the coincidence of the shapes of the three-dimensional perspective image and the second three-dimensional perspective image.
[0015]
The material testing method according to the present invention uses an arithmetic expression (displacement-strain relational expression) corresponding to the strain of the minute deformation when the deformation of the material is minute based on the amount of displacement in the mechanical calculation process. Is large, the strain is calculated based on the amount of displacement using an arithmetic expression (displacement-strain relational expression) corresponding to the large deformation strain.
In the material test method of the present invention, when the material is a linear material in the mechanical calculation process, the first configuration matrix is obtained using the first calculation formula based on the linear constitutive law, and the first configuration matrix is obtained. On the basis of the configuration matrix, the stress is calculated by the first calculation formula, and when the calculation material is a nonlinear material, the second configuration matrix is obtained using the second calculation formula based on the non-linear / increment type constitutive law. The stress is calculated by the second calculation formula based on the second configuration matrix.
[0016]
A material analysis program according to the present invention is a material analysis program for operating the material analysis system, wherein an X-ray relating to a cross section of a test object is obtained from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors. Data collection processing for collecting data, image processing for generating a three-dimensional perspective image of the test object based on the X-ray data, and a first 3 of the test object in a state where no load is applied An image storage process in which a two-dimensional perspective image and a second three-dimensional perspective image of the test object in a state where a predetermined load is applied are stored in an image storage unit, and each pixel of the first three-dimensional perspective image Is moved by a predetermined calculation, and the first three-dimensional perspective image and the second three-dimensional perspective image are made to coincide with each other to obtain a displacement amount calculation process for obtaining a displacement amount due to the load of each pixel. The test under load Characterized in that to execute the dynamics calculation process of calculating the strain and stress in each part of the body to the computer.
[0017]
A computer-readable recording medium of the present invention is a recording medium that records a material analysis program for operating the material analysis system, and includes an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors. A data collection process for collecting X-ray data relating to a cross section of the test object, an image process for generating a three-dimensional perspective image of the test object based on the X-ray data, and the state in which no load is applied An image storage process in which a first three-dimensional perspective image of the test object and a second three-dimensional perspective image of the test object in a state where a predetermined load is applied are stored in the image storage unit; Displacement for obtaining a displacement amount due to a load of each pixel by moving each pixel of the three-dimensional perspective image by a predetermined calculation and matching the shapes of the first three-dimensional perspective image and the second three-dimensional perspective image. Quantity calculation processing, From serial displacement records the material analysis program for executing the dynamics calculation process of calculating the strain and stress in each part of the due to the load device to be tested on a computer.
[0018]
The material test system according to the present invention grips the upper and lower parts of a device under test with opposing grips (grips 21 and 22), generates a load between the grips, and this device under test (device under test). 14) An X-ray CT apparatus (collecting apparatus 20) for applying a load, an X-ray source and a plurality of X-ray detectors, and collecting X-ray data relating to a cross section of the test object An X-ray CT apparatus 1), an image processing unit (image processing unit 2) for generating a three-dimensional perspective image of the test object based on the X-ray data, and a first of the test object in a state where no load is applied. An image storage unit (image storage unit 3) for storing a first three-dimensional perspective image and a second three-dimensional perspective image of the test body in a state in which a predetermined load is applied, and the first three-dimensional perspective image Are moved by a predetermined calculation, and the first three-dimensional perspective image and the second A displacement amount calculation unit (displacement amount calculation unit 4) for obtaining a displacement amount due to the load of each pixel by matching the shape with the three-dimensional perspective image, and stress and strain in each part of the specimen by the load from the coefficient. And a dynamics calculation unit (dynamics calculation unit 5).
In the material testing system according to the present invention, the sample fixing unit includes a drive unit, a spline shaft to which rotation is given by the drive unit, and a rotation transmission mechanism that transmits the rotation of the spline shaft to each gripping tool. The drive side element of the rotation transmission mechanism of the upper gripper is splined to the spline shaft. In the material test system of the present invention, the displacement amount calculation unit moves each pixel while sequentially changing the coefficient and constant of the predetermined calculation formula, so that the first three-dimensional perspective image and the second It is characterized by matching the shape with the three-dimensional perspective image.
In the material test system of the present invention, the displacement amount calculation unit associates each pixel in the second three-dimensional perspective image and the first three-dimensional perspective image after movement based on each gradation, It is characterized by determining the coincidence of the shapes of the three-dimensional perspective image and the second three-dimensional perspective image.
The material testing method of the present invention includes a sample fixing process in which an upper part and a lower part of a test object are respectively gripped by opposing grips, a load is generated between the grips, and a load is applied to the test object. A data collection process for collecting X-ray data relating to a cross section of a test object from an X-ray CT apparatus having a radiation source and a plurality of X-ray detectors, and a three-dimensional test object based on the X-ray data An image processing process in which a fluoroscopic image is generated, a first three-dimensional fluoroscopic image of the test object in a state where no load is applied, and a second 3 of the test object in a state where a predetermined load is applied An image storage process in which the three-dimensional perspective image is stored in the image storage unit, and each pixel of the first three-dimensional perspective image is moved by a predetermined calculation, and the first three-dimensional perspective image and the second three-dimensional perspective image By matching the shape with A displacement calculating step for obtaining the displacement amount from the displacement amount, stress and strain at each part of the test body by the load is characterized by having a dynamic calculation process is calculated.
In the material test method of the present invention, in the displacement amount calculation process, each pixel is moved while sequentially changing the coefficient and constant of the predetermined calculation formula, so that the first three-dimensional perspective image and the second It is characterized by matching the shape with the three-dimensional perspective image.
In the material test method of the present invention, the displacement amount calculation unit associates each pixel in the second three-dimensional perspective image and the first three-dimensional perspective image after movement based on each gradation, The material test method according to claim 17 or 18, wherein a match between the shapes of the three-dimensional perspective image and the second three-dimensional perspective image is determined.
The material test program according to the present invention is a material test program for operating the material test system described above, wherein the upper and lower parts of the device under test are each gripped by opposing grips, and a load is generated between the grips. A sample fixing process for applying a load to the test object, an X-ray source and a plurality of X-ray detectors, and an X-ray data collection process for collecting X-ray data relating to a cross section of the test object; Image processing for generating a three-dimensional perspective image of the test object based on the X-ray data, a first three-dimensional fluoroscopic image of the test object in a state where no load is applied, and a predetermined load are applied An image storage process for storing the second three-dimensional fluoroscopic image of the test specimen in a state, and each pixel of the first three-dimensional fluoroscopic image is moved by a predetermined calculation, so that the first three-dimensional fluoroscopic image and the second The shape of the 3D perspective image By causing the computer to perform a displacement amount calculation process for obtaining a displacement amount due to the load of each pixel, and causing a computer to execute a mechanical calculation process for calculating the stress and strain in each part of the specimen by the load from the displacement amount. Features.
The computer-readable recording medium of the present invention is a recording medium for recording a material test program for operating the above-described material test system, and grips the upper and lower portions of the device under test with opposing grippers. Collects X-ray data related to the cross-section of the DUT with a specimen fixing process that generates a load between the gripping tools and applies the load to the DUT, an X-ray source, and a plurality of X-ray detectors. X-ray data collection processing, image processing for generating a three-dimensional perspective image of the test object based on the X-ray data, a first three-dimensional perspective image of the test object in a state where no load is applied, And an image storage process for storing the second three-dimensional perspective image of the specimen in a state where a predetermined load is applied, and each pixel of the first three-dimensional perspective image is moved by a predetermined calculation, 3D perspective And the second three-dimensional perspective image are made to coincide with each other to calculate the amount of displacement due to the load of each pixel, and from the amount of displacement, calculate the stress and strain at each part of the specimen using the load A material test program is recorded that causes a computer to execute a mechanical calculation process.
[0019]
DETAILED DESCRIPTION OF THE INVENTION
The present invention provides a three-dimensional perspective image of a test object in a state where no load is applied (hereinafter referred to as a non-load fluoroscopic image), and a three-dimensional perspective image of the test object in a state where a predetermined load is applied ( Hereinafter, a load fluoroscopic image) is generated from X-ray data based on the X-ray transmission intensity from the X-ray CT apparatus.
Hereinafter, the material analysis system of the present invention will be described with a three-dimensional image obtained by using an X-ray CT apparatus.
However, the present invention is not limited to the X-ray CT apparatus, and it is also possible to use a three-dimensional fluoroscopic image obtained by MRI (magnetic resonance image) or an ultrasonic apparatus.
Then, the displacement amount calculation unit 4 described later moves each pixel of the non-load fluoroscopic image three-dimensionally (spatially) using a predetermined calculation formula.
[0020]
At this time, the simulation is performed while sequentially changing the coefficient and the constant value of the arithmetic expression until the shape of the unloaded perspective image after the movement matches the shape of the loaded perspective image.
That is, the displacement amount calculation unit 4 sets the load fluoroscopic image and each pixel when the distribution shape of pixels having the same gradation degree in the non-load fluoroscopic image after movement and the load fluoroscopic image substantially match. Assume that the shape matches the moved non-load fluoroscopic image.
[0021]
At this time, the displacement amount calculation unit 4 extracts the coefficients of the calculation formula used to move each pixel, and obtains the displacement amount of each pixel in the load fluoroscopic image based on this coefficient. Based on this displacement, the mechanics calculation unit 5 calculates quantitative numerical values of stress and strain applied to each part of the DUT from a predetermined calculation formula. As a result, quantitative analysis of strain and stress applied to each part of the test object (structure with a mechanically heterogeneous structure inside) such as an artificial bone embedded in the human body Can be performed.
[0022]
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
<First Embodiment: Material Testing System>
FIG. 1 is a block diagram showing a configuration example of a material analysis system according to the first embodiment of the present invention. In this figure, the material analysis system of the present invention has at least an X-ray CT apparatus 1, an image processing unit 2, an image storage unit 3, a displacement calculation unit 4, and a dynamics calculation unit 5.
The X-ray CT apparatus 1 irradiates a test object with X-rays, and outputs X-ray data based on the intensity of X-rays transmitted through the test object, that is, transmission intensity.
[0023]
Next, the configuration of the X-ray CT apparatus 1 will be briefly described with reference to FIG. FIG. 2 is a conceptual diagram showing a configuration example of the X-ray CT apparatus.
The X-ray CT apparatus 1 has an X-ray tube 11 that emits X-rays and an X-ray detector 13 that detects the intensity of the X-rays at positions facing each other. It is fixed between the X-ray detector 13 by a fixing device (not shown).
The fixing device fixes the upper and lower portions of the DUT 14 in the drawing with a gripping tool or the like, and applies a load such as tension / compression / twisting to the DUT 14.
[0024]
The fixing device can rotate the device under test along the body axis of the device under test 14 in the R direction within an angle range of 360 ° with the load applied.
Here, since the X-ray tube 11 radiates the X-ray 12 that spreads in a fan shape, the fixing device uses the X-ray tube 11 and the X-ray so that the X-ray 12 spread in a fan shape becomes the lateral width of the DUT 14. The position of the detector 13 is adjusted.
Then, the X-ray detector 13 measures the X-ray intensity of the X-ray 12 after passing through the device under test 14, for example, at the section 14 n of the device under test 14.
[0025]
Further, the fixing device is movable in the Z1 direction or the Z2 direction along the body axis.
The X-ray CT apparatus 1 controls the rotation and vertical movement of the fixing device, and measures the X-ray intensity of the X-ray 12 transmitted through the DUT 14 while rotating and moving the DUT 14. Do.
At this time, the X-ray CT apparatus 1 measures the X-ray intensity of the X-ray 12 transmitted through the DUT 14 in both the state where the load is applied to the DUT 14 and the state where the load is not applied. I do.
The X-ray CT apparatus may have any configuration as long as a three-dimensional perspective image can be obtained.
[0026]
Returning to FIG. 1, the X-ray CT apparatus 1 outputs the X-ray data of the cross section of the device under test (the device under test 14 in FIG. 2) with the above-described configuration.
Then, the image processing unit 2 accumulates the X-ray data (X-ray fluoroscopic image) output from the X-ray CT apparatus 1 while the object to be tested is rotated 360 °, and re-assembles the accumulated X-ray data. By performing the configuration calculation, a cross section of the test object, that is, a tomographic image of the test object perpendicular to the body axis is generated.
[0027]
Further, the image processing unit 2 superimposes the tomographic images obtained by moving in the Z1 direction or the Z2 direction synchronously along the body axis at a minute interval in the body axis direction, and 3 A three-dimensional perspective image (that is, an unloaded perspective image and a loaded perspective image) is generated.
At this time, the X-ray CT apparatus causes the image processing unit 2 to generate a non-load fluoroscopic image to which no load is applied and a load fluoroscopic image in a state where a predetermined load is applied by the above-described processing.
Further, the image processing unit 2 stores the obtained non-load fluoroscopic image and the load fluoroscopic image in the image storage unit 3, and displays the non-load fluoroscopic image and the load fluoroscopic image on a display screen of an image display device (not shown). To display.
[0028]
Hereinafter, the calculation formulas and algorithms of the calculations performed by the displacement calculation unit 4 and the dynamics calculation unit 5 will be described with reference to FIG. FIG. 3 is a flowchart showing an operation example of the displacement amount calculation of the displacement amount calculation unit 4.
In step S1, the image processing unit 2 reads out the non-load fluoroscopic image and the load fluoroscopic image from the image storage unit 3, and converts each three-dimensional fluoroscopic image to a predetermined image size (for example, to correspond to the subsequent calculation). The gradation of each pixel is extracted with a resolution expressed by “number of pixels / unit volume”, and a three-dimensional image (three-dimensional voxel model) composed of a distribution of pixel values indicating the gradation of each pixel is generated. To do.
Here, in a three-dimensional voxel model generated from an unloaded perspective image (hereinafter referred to as an unloaded voxel model), the gradation of each pixel at the position indicated by the coordinates of x, y, and z is expressed as a pixel value p (x, y , Z), and in the three-dimensional voxel model generated from the load perspective image (hereinafter referred to as load voxel model), the gradation of each pixel at the position indicated by the coordinates of x, y, and z is expressed as a pixel value P (x, y, z).
[0029]
Next, in step S2, the displacement amount calculation unit 4 uses the following equations (1), (2), and (3), so that the displacement amount u of each pixel in the x, y, and z directions, respectively. (X, y, z), v (x, y, z), w (x, y, z) are obtained.
At this time, the coefficient a used in each of the equations (1), (2), and (3) _un ~ J _wm , Constant p _u ~ R _w Is a provisional value.
Here, the provisional value is a coefficient a of a material that is considered to be close to the material under test that has already been analyzed. _un ~ J _wm , Constant p _u ~ R _w This is a value substituted for.
[Expression 1]

[Expression 2]

[Equation 3]

[0030]
In each of these formulas, the first term (the curly bracket term) in each square bracket is a Fourier series indicating the periodicity of the displacement, the second term indicates the amount of power displacement, The term is the above constant.
As the provisional values of the coefficients and constants described above, values that are considered to be close to actuality to some extent, such as values obtained experimentally and values obtained by analysis of similar materials before, are used.
[0031]
Next, in step S3, the displacement amount calculation unit 4 calculates the displacement amounts u (x, y, z), v (x, y, z) obtained from the equations (1), (2), and (3), Each pixel is moved based on w (x, y, z).
That is, by moving p (x, y, z) based on the displacements u, v, w, the pixel at the position (x, y, z) becomes (x + u, y + v, z + w). It moves to a position, that is, p (x, y, z) becomes p (x + u, y + v, z + w).
[0032]
This pixel value p (x + u, y + v, z + w) is used as the pixel value p. ^* (X, Y, Z). Here, X = x + u, Y = y + v, and Z = z + w.
And the displacement amount calculating part 4 performs the process of the movement in the three-dimensional coordinate of the pixel mentioned above with respect to each pixel which comprises a non-loading voxel model.
Where the pixel value p ^* (X, Y, Z) is a load voxel model of a sample in a virtual load state obtained by the displacement amount calculation unit 4, that is, a load voxel model (simulation voxel model) as a simulation result.
[0033]
Next, in step S4, the displacement amount calculation unit 4 determines the pixel value P (X, Y, Z) in the coordinate value (X, Y, Z) in the load voxel model and the pixel value p. ^* Comparison of numerical values with (X, Y, Z) is performed at each coordinate value in the load voxel model.
That is, the displacement amount calculation unit 4 calculates the numerical value of the pixel value P (X, Y, Z) at each coordinate value of the load voxel model and the pixel value p at each coordinate value of the non-load voxel model after movement. ^* It is determined whether or not the numerical values of (X, Y, Z) match (or include a case where they have a predetermined range and substantially match).
[0034]
Here, the displacement amount calculation unit 4 calculates the pixel value P (X, Y, Z) at each coordinate value of the load voxel model and the pixel value p at each coordinate value of the non-load voxel model after movement. ^* When the values of (X, Y, Z) match, each coefficient a _un ~ J _wm And the constant p _u ~ R _w Is output and the process ends, but if they do not match, the process proceeds to step S5.
At this time, the displacement amount calculation unit 4 uses the following equation (4) to calculate the pixel value P (X, Y) obtained by moving the pixel value P (x, y, z) with respect to the pixel value of the entire voxel model. , Z) and p ^* The differences from (X, Y, Z) are summed, normalized by 255 (gradation) × M, and output as f.
[Expression 4]

Here, M is the total number of voxels, and Σ represents the summation over all voxels in the image.
Then, each time the error function value of the error function f is obtained, the displacement amount calculation unit 4 sequentially compares the previous f value with the valley of the error function value (the point with the smallest error function value, that is, the minimum value). Value) is detected, and this point is determined as a point where the gradation of each pixel value of the entire voxel model is matched.
[0035]
Next, in step S5, the displacement amount calculation unit 4 calculates each coefficient a _un ~ J _wm And the constant p _u ~ R _w The numerical values of the coefficients and constants are sequentially changed by an operation according to this algorithm by an optimization method such as nonlinear programming.
Then, the displacement amount calculation unit 4 calculates the changed coefficient a _un ~ J _wm And the constant p _u ~ R _w Thus, in order to obtain new displacement amounts u (x, y, z), v (x, y, z), and w (x, y, z), the process returns to step S2.
[0036]
As described above, the displacement amount calculation unit 4 calculates the pixel value P (X, Y, Z) at each coordinate value of the load voxel model and the pixel value p at each coordinate value of the non-load voxel model after movement. ^* The processes from step S2 to step S5 are repeated until the numerical values of (X, Y, Z) match.
Then, the displacement amount calculation unit 4 finally calculates the pixel value P (X, Y, Z) at each coordinate value of the load voxel model and the pixel value p at each coordinate value of the non-load voxel model after movement. ^* When the numerical values of (X, Y, Z) match (the gradations match), each coefficient a at this time _un ~ J _wm And the constant p _u ~ R _w Is output.
[0037]
Next, the mechanics calculation unit 5 uses the coefficients a _un ~ J _wm And the constant p _u ~ R _w , And based on these, displacements u (x, y, z), v (x, y, z), w (x, y, z) are obtained from equations (1), (2), and (3). Ask for.
Then, the mechanics calculation unit 5 calculates the strain ε from the displacement strain equation based on the displacements u, v, and w. _ij The operation for obtaining is performed.
[0038]
At this time, if the mechanical calculation unit 5 is a material that must be supported by a large deformation theory with geometrical nonlinearity, the strain ε is expressed by using the following equation (5), which is a relational expression of displacement-strain. _ij Ask for.
[Equation 5]

Then, the mechanics calculation unit 5 gives a constitutive law (configuration matrix) between the strain and the stress in the formula (6) which is a calculation formula showing the stress-strain relationship shown below, and the force per unit area Some stress σ _ij Is calculated by load increment analysis.
[0039]
That is, when the material has nonlinearity, a matrix that changes depending on the stress state, that is, a configuration matrix [D ^p ] Is given by the equation (6) in incremental form, and the calculation is started from the state of stress “0”, the amount of change in stress is calculated sequentially, and the total stress is obtained by adding the obtained stresses. Ask for.
[Formula 6]

Here, the equation (5) is used as a displacement-strain relational equation corresponding to the large deformation theory, and the equation (6) is a nonlinear / incremental arithmetic equation, which is used when obtaining stress of the nonlinear material.
[0040]
On the other hand, if the mechanical calculation unit 5 is a material corresponding to a geometrically linear micro-deformation theory, the strain ε is calculated using the following equation (7), which is a displacement-strain calculation formula. _ij Ask for.
[Expression 7]

The mechanical calculation unit 5 gives a constitutive law between strain and stress in the following equation (8) which is a stress-strain relational expression, and stress σ which is a force per unit area _ij The operation for obtaining is performed.
For example, in the case of a linear material, a constant matrix, that is, a configuration matrix [D ^e ] Can be obtained by equation (8) using
[Equation 8]

Here, the expression (7) is used as a displacement-strain relational expression corresponding to the microdeformation theory, and the expression (8) is used when obtaining the stress of the linear material.
[0041]
That is, when the deformation of the material (test object 14) is very small, the mechanical calculation unit 5 uses the equation (7) corresponding to the displacement-strain relational expression based on the micro deformation theory, and when the deformation of the material is large, Strain is calculated using equation (5) corresponding to the displacement-strain relationship based on the large deformation theory.
Then, when the material (test object 14) is a linear material, the mechanical calculation unit 5 calculates the stress of each part of the test object 14 based on the applied load using the equation (8) based on the linear constitutive law. When the material is a nonlinear material, the stress of each part of the DUT 14 based on the applied load is calculated using the nonlinear / incremental constitutive law (6).
[0042]
Here, in a normal material test, a test piece with a simple shape that can easily calculate stress or strain is used, the relationship between the load and displacement is measured by a simple load, and then the stress is converted from the load, and the displacement The strain is converted from the structure matrix [D ^p ] Or [D ^e ] Is demanded.
In the above description, in the flow for obtaining the configuration matrix, the micro-deformation theory and the linear constitutive law of the linear material are associated with each other, and the large deformation theory and the non-linear material are associated with each other. Depending on the material, calculation may be performed by a combination of a small deformation theory and a nonlinear material, or a combination of a large deformation theory and a linear material.
[0043]
However, the configuration matrix [D in equations (6) and (8) ^p ] And [D ^e ] Is a relationship corresponding to a material with a non-uniform interior, and as described above, the stress-strain relationship cannot be simply calculated from the load and the displacement.
For this reason, a method for obtaining a stress-strain relationship corresponding to a DUT whose material is not uniform and whose shape is not simple will be described below with reference to FIGS.
FIG. 4 is a flowchart for explaining an example of the operation of calculating the stress-strain relationship of the mechanical calculation unit 5.
In step S <b> 11, the dynamic calculation unit 5 receives the displacement amounts u (x, y, z), v (x, y, z), w of each part of the DUT 14 corresponding to a predetermined load from the displacement amount calculation unit 4. Enter (x, y, z).
[0044]
Next, in step S12, a model of this material is temporarily set for the dynamics operation unit 5 by taking as an example a material that seems to be close to past experimental examples.
If the DUT 14 is a linear material that can be handled by the micro-deformation theory, the stress-strain relational expression is assumed to be the expression (8) as a model used for the calculation.
On the other hand, if the DUT 14 is a nonlinear material, the stress-strain relational expression is assumed to be an incremental expression (6) as a model used for the calculation.
This setting is set by inputting data indicating whether the DUT 14 is a linear material or a nonlinear material from an input device (not shown).
[0045]
Further, when the DUT 14 is a non-linear material, a configuration matrix [D ^p ] Is modeled in a timely manner, and a calculation method is set. For example, in the case of an elastoplastic material, it is set based on the coupled flow law.
Next, in step S13, the configuration matrix [D corresponding to the DUT 14 to be analyzed is selected. ^e ] Or [D ^p ] Are temporarily set as unknown variables, such as material parameters (Young's modulus, Poisson's ratio, etc. of each material) included in
[0046]
Next, in step S <b> 14, the mechanics calculation unit 5 sets the configuration matrix [D ^e ] Or [D ^p ] To perform a finite element analysis.
At this time, if the DUT 14 to be tested is a linear material, the element stiffness matrix [K _e ] Is calculated.
Then, the mechanics calculation unit 5 sets the configuration matrix [D ^e ] The element stiffness matrix [K _e ], The relationship between the applied load and the amount of displacement of each part of the DUT 14 (hereinafter, calculated displacement amount) is obtained.
[0047]
As this applied load, a numerical value equivalent to the predetermined load input in step S11 is used.
[Equation 9]

In this equation (9), matrix [B] is a displacement-strain matrix, and _ve dv represents a volume integral relating to one element of analysis in the finite element method.
Next, the mechanics calculation unit 5 calculates an element stiffness matrix [K depending on the stress state or the like from the calculation according to the following expression (10) for the DUT 14 to be tested. _p ] Is calculated.
[0048]
That is, the mechanics calculation unit 5 sets the provisional matrix [D ^p ] The element stiffness matrix [K _p ], The relationship between the applied load and the amount of displacement of each part of the DUT 14 (hereinafter, calculated displacement amount) is obtained by incremental analysis.
[Expression 10]

Further, when it is necessary to consider large deformation (geometric non-linearity), the tangential stiffness matrix is calculated with the definition of strain as the following equation (11), and incremental analysis is performed.
[Expression 11]

[0049]
Next, in step S15, the mechanics calculation unit 5 determines whether the calculated displacement amount of each part of the DUT 14 obtained by the finite element method matches the displacement amount of each part of the DUT 14 input in step S11. Determine whether or not.
At this time, if the calculated displacement amount obtained from the finite element method and the input displacement amount do not match, the dynamics operation unit 5 advances the process to step S16.
[0050]
Next, in step S <b> 16, the mechanics calculation unit 5 performs a configuration matrix [D for the material by a predetermined optimization method. ^e ] Or [D ^p ], A new parameter is set, the process proceeds to step S14, and the calculated displacement is obtained again by the finite element method.
In step S15, when the calculated displacement amount obtained from the finite element method matches the input displacement amount, the dynamics calculation unit 5 determines that the configuration matrix [D ^e ] Or [D ^p ] Is output to an output device (not shown), and the processing for determining the configuration relationship is terminated.
[0051]
Then, the mechanics calculation unit 5 obtains the obtained configuration matrix [D ^e ] Or [D ^p ] Is used to calculate the stress applied to each part of the DUT 14 according to the equation (8) or (6).
That is, when the material (test object 14) is a linear material, the mechanics calculation unit 5 obtains the configuration relationship using the equation (8) based on the linear constitutive law from the displacement obtained by the displacement calculation unit 4. Based on the constitutive relationship of the linear material, the stress of each part of the device under test 14 is calculated by the above formula (8). And the stress of each part of the DUT 14 is calculated according to the equation (6) based on this nonlinear material.
[0052]
In step S3, each pixel value P performed by the displacement amount calculation unit 4 ^* A method for obtaining the value of (X, Y, Z) will be described below.
First, the displacement amount calculation unit 4 creates a spatial grid corresponding to each pixel in the voxel model shown in FIG. 7A, and each pixel value is assigned to the corresponding grid as shown in FIG. 7B. Assign each to the center of gravity.
Then, the displacement amount calculation unit 4 moves the center of gravity in FIG. 7 (c) by the calculated “u, v, w” (move the center of gravity by deformation mapping (Mapping, x = D (X)) ).
The center of gravity after movement (hereinafter referred to as “Mapped Points”: black circle) and the center of gravity of the spatially fixed grid constituting the deformed image (hereinafter referred to as “Fixed Points”: white circle) can be seen in FIG. 7C. So generally do not match.
Next, the displacement amount calculation unit 4 finally assigns the pixel value of the moving point (: deformation map) to the corresponding point for each space fixed grid, as shown in FIG. Generate a simulation voxel model.
[0053]
For this reason, the pixel value of the corresponding point of each space fixed grid is determined from the pixel value of each moving point under the following conditions.
Basically, in the present embodiment, an 8-neighbor nearest neighbor based on nearest neighbor interpolation, in which the pixel value of the moving point nearest to each corresponding point is the pixel value of this corresponding point. An approximation method is used.
That is, when the moving point moves into the space fixed grid including the corresponding point, the displacement amount calculating unit 4 determines the pixel value of the moving point as the pixel value of the corresponding point when there is one moving point in the space fixed grid. When there are a plurality of moving points in the space fixed grid, the average value of the pixel values of these moving points is calculated, and this average value is set as the pixel value of the corresponding point.
[0054]
If there is no moving point in the space fixed grid of the corresponding point, the search is performed in the 8-neighboring grid in the surrounding 3 × 3 grid.
At this time, if there is no moving point in the surrounding 3 × 3 grid, the pixel value is set to “0”, and if there is a moving point, the moving point nearest to the position of the corresponding point from among the moving points is displayed. Let the pixel value be the pixel value of this corresponding point.
The above description has been made in two dimensions to simplify the description, but in the case of three dimensions, if there are no moving points in the space-fixed grid, there are 26 grids in the 3 × 3 × 3 grid surrounding the neighboring grid. Then, the moving point is searched, and the lattice point of the corresponding point is determined by the same method as in the case of the 8-neighbor lattice.
[0055]
Next, how to obtain the numerical values of the coefficients and constants in step S5 will be described.
As described above, in step S5, the displacement amount calculation unit 4 determines each coefficient a as described above. _un ~ J _wm And the constant p _u ~ R _w The numerical values of the coefficients and constants are sequentially changed by an operation according to this algorithm by an optimization method such as nonlinear programming.
Here, since the voxel value is a discrete value, and because discrete image processing is performed based on the nearest neighbor approximation, the sensitivity information of the objective function (the degree of change in the numerical value f corresponding to the amount of change in each coefficient and constant) ) Can not get.
[0056]
For this reason, in the present embodiment, the displacement amount calculation unit 4 performs error minimization processing by a discrete optimization method such as a genetic algorithm (Genetic Algorithm) or the like (the algorithms of a) and b) described below.
a) When using genetic algorithms
For example, it is assumed that the displacement amount calculation unit 4 assigns 8-bit binary data as variable and constant data capacities, and has 256-step numerical values for each variable and constant.
These 256-step numerical values are obtained by dividing a predetermined range (such as the number of pixels and dimensions of a voxel model) that is assumed in advance as a range of deformation (as a search range).
As a condition for the simulation of the genetic algorithm, each individual is selected from the numerical values of the variables and constants in the displacement amount calculation unit 4 and configured as 1000 combinations.
As genetic manipulation to change the combination of each individual, uniform crossover (crossover rate 75%), linear ranking selection, elite strategy, mutation (mutation rate 1.0%) and the like were used.
[0057]
b) SCE-UA (Shuffled Complex Evolution Method developed at the University Arizona) method
This SCE-UA method adopts an evolutionary method similar to genetic algorithm, can set a search area for solutions with physical meaning, and evolves independently in multiple populations in the middle of the calculation. When obtaining a solution, it is characterized by the fact that a solution is always obtained without incompatibilities or divergence.
[0058]
In other words, the SCE-UA method is an optimization method based on band search that combines the concepts of competitive evolution and population mixing. The calculation procedure is briefly shown below.
(1) Decision variable (coefficient a in equations (1) to (3) _un ~ J _wm And the constant p _u ~ R _w Or the variable a in the expressions (1 ′) to (3 ′) _u13 (K ₁ , k ₂ , k ₃ ), Etc.) n, the number of groups p, and the number of individuals m (= 2n + 1) in each group are set, and each individual is regarded as a point on an n-dimensional space having a decision variable as a coordinate value.
For example, when there are a total of n coefficients and constants, “2n + 1” individual groups are allocated to p groups.
{Circle around (2)} As the initial generation, each decision variable value is given at random, and, for example, the individuals are arranged in ascending order of the error function value of the error function of equation (4).
[0059]
(3) In the order arranged in (2), from the first individual, the first individual is included in the first group, the second individual to the second group, ..., the pth individual to the pth group, p + 1 Individuals are assigned to all groups in order, the 1st individual to the first group, the 2p (ie, p + p) th individual to the pth group, and so on.
That is, in this distribution method, p (X, Y, Z) and p calculated by combining each coefficient and constant corresponding to this pixel value are selected. ^* Based on (X, Y, Z), an error function f is obtained and assigned to each of the p groups in order of increasing error function value.
For example, when there are a total of n coefficients and constants, “2n + 1” individual groups are allocated to p groups.
[0060]
(4) The population is evolved by a CCE (Conditional Class Entropy) algorithm independently for each group.
In the CCE algorithm, each individual is evolved by changing coefficients and constants so that an individual with a high error function value of the error function f becomes an individual with a lower error function value.
(5) Eventually, p populations, that is, all populations are combined into one, and all individuals included in all populations are rearranged again in the order of low error function values. Whether the error function value of the best individual among the above is within the range of a preset convergence judgment value, or whether the number of iterations of coefficient and constant optimization processing is a preset iteration setting value Until it corresponds to any of the above, (3) to (5) are repeated to optimize the coefficients and constants.
[0061]
As described above, the material analysis system of the present invention can take a three-dimensional perspective image, and if the pixel values of the pixels are distributed at different values (non-uniform structure), By obtaining a non-load fluoroscopic image and a load fluoroscopic image, it is possible to analyze each non-uniform strain and stress three-dimensionally.
[0062]
Next, as an example of the evaluation of stress and strain between an actual non-load fluoroscopic image and a load fluoroscopic image using FIGS. 5 and 6, an eight-strand rope (material shape is used as a textile material) on the specimen. The flow of evaluation for stress and strain in the test subject in a load application state using a three-dimensional perspective image will be described below by taking a complicated and non-uniform material as an example.
For example, a rope having a diameter of 10 mm is used, the X-ray irradiation conditions are a voltage of 85 kV, a current of 50 μA, a state where 1 N (Newton) of the rope's own weight is applied (hereinafter referred to as an unloaded state), Imaging with an X-ray CT apparatus was evaluated in an applied state (hereinafter referred to as a load state).
[0063]
FIG. 5B is a tomographic image in a state where no load is applied (the above-described unloaded state), and FIG. 5A is a three-dimensional voxel model in a non-loaded state, that is, a non-load perspective image. FIG. 6B is a tomographic image in a state where a load is applied (the above-described load state), and FIG. 6A is a three-dimensional voxel model in a loaded state, that is, a load perspective image.
Both of FIGS. 5 and 6 are displayed as white as the amount of X-ray transmission is small, and even from these figures, the octopus rope is pulled in the opposite direction by applying a load in the vertical direction. It can be confirmed that the rope fibers are clogged.
[0064]
In this example, the tomographic images in FIGS. 5B and 6B are set to 1024 × 1024 pixels (the pixel gradation is 256), and the tomographic images are spaced by 0.2 mm (in the direction of the body axis). The image is taken in the range of the upper and lower score intervals of about 17 mm. 5 (a) and 6 (a) show a plurality of tomographic images shown in FIGS. 5 (b) and 6 (b), which are captured in the above-described range of the evaluation interval, with the axial resolution (axial direction). This is a three-dimensional voxel model obtained by averaging data of gradations of a plurality of pixels and converting the data from 1024 × 1024 pixels to 100 × 100 pixels while reducing the resolution of the image.
Here, FIG. 5A shows an unloaded voxel model, and FIG. 6A shows a loaded voxel model.
That is, the image processing unit 2 reads the unloaded perspective image and the loaded perspective image from the image storage unit 3, changes each three-dimensional perspective image to a resolution of 100 × 100 pixels of a predetermined image size, The gradation is extracted, and each three-dimensional voxel model configured by the distribution of pixel values indicating the gradation of each pixel is generated.
[0065]
Then, the displacement amount calculation unit 4 performs a simulation (based on each step of the flowchart of FIG. 3) using the already described equations (1) to (3) at each pixel in the unloaded voxel model of FIG. The displacement amounts u, v, and w are obtained from the above.
Next, since the eight-strike rope is greatly deformed, the mechanics calculation unit 5 calculates the load voxel corresponding to the non-load voxel model from the displacements u, v, and w by the equation (5) based on the large deformation theory. Find the strain in the model.
Then, since the eight-strike rope is a non-linear material, the mechanical calculation unit 5 uses the equation (6) to calculate the structural relationship (stress and stress) in the load voxel model corresponding to the non-load voxel model based on the displacements u, v, and w. The relationship with strain is determined according to the steps of the flowchart of FIG. 4 already described.
[0066]
Next, the equations (1), (2), and (3) used by the displacement amount calculation unit 4 for calculating the displacement amounts u, v, and w are respectively expressed as (1 ′), (2 ′), and A case where the displacement amounts u, v, and w are calculated instead of (3 ′) will be described.
[Expression 12]

[Formula 13]

[Expression 14]

[0067]
These equations (1 ′), (2 ′), and (3 ′) include the influence of displacement in a plurality of coordinate axes in the Fourier series terms for each of equations (1), (2), and (3). It is not.
In each of the equations (1 ′), (2 ′) and (3 ′), Mu, Mv, Mw and Nu, Nv, Nw are integer values, which are constants that are appropriately set according to the problem, ω is the fundamental frequency, Similarly, it is a constant set appropriately depending on the problem.
Α _ijk , Β _ijk , Γ _ijk Is a variable that is defined as a different variable if i, j, and k are different, and is determined by an optimization algorithm such as GA so that the error function value obtained from the error function is minimized.
And a _u13 (k1, k2, k3), a _v13 (k1, k2, k3), a _w13 (k1, k2, k3), etc. are also defined as different variables if k1, k2, k3 are different, and are determined by an optimization algorithm such as GA so that the error function value obtained from the error function is minimized. Is a variable.
[0068]
For this reason, by using the equations (1 ′), (2 ′), and (3 ′), the displacement in each coordinate axis direction includes the influence from the other coordinate axis directions, that is, the correction amount. Compared with the cases where the equations (1), (2), and (3) are used, a more accurate simulation can be performed when calculating the displacements u, v, and w.
For example, a sample for material analysis is a small tomato, and in a non-loading state in which no load is applied, the X-ray CT apparatus 1 sets the length of one side of one voxel to 0.4 mm, thereby taking a non-loading. A fluoroscopic image is obtained.
Then, the image processing unit 2 performs a non-loading fluoroscopic image obtained by the X-ray CT apparatus 1 on the unloaded sample (petit tomato) from FIG. 8 (FIG. 8A: half of the whole). A three-dimensional voxel model (unloaded voxel model: one voxel side length of 0.4 mm) of the initial image shown in FIG. 8B (part 1/8 of the whole) is generated.
[0069]
Next, the top and bottom of the sample cherry tomato were sandwiched between parallel plates, and a 400 mN load was applied perpendicularly to the plates to compress them, and the X-ray CT apparatus 1 reduced the length of one side of one voxel to 0. By taking a fluoroscopic image as 4 mm, a load fluoroscopic image is obtained.
Then, the image processing unit 2 performs, for the sample in the loaded state, from the load fluoroscopic image obtained by the X-ray CT apparatus 1, FIG. 9 (FIG. 9 (a): half of the whole, FIG. b): 1/8 part of the whole) 3D voxel model (load voxel model, voxel size: length of one side of voxel is 0.4 mm) is generated.
Then, the displacement amount calculation unit 4 calculates the p obtained by displacing the pixels of the unloaded voxel model according to the flowchart of FIG. ^* A comparison is made between (X, Y, Z) and p (X, Y, Z) obtained from the load voxel model (FIG. 9), and a point where the error function of equation (4) is minimized is searched. Each coefficient and constant at the minimum point is output as an optimum value.
[0070]
A simulation voxel model (voxel size: one voxel side length of 0.4 mm) of the simulation result obtained at this time is shown in FIG. 10 (FIG. 10 (a): half of the whole, FIG. 10 (b). : 1/8 part of the whole)
Also, FIG. 11 (1/2 part of the whole) shows a difference voxel model indicating a difference in pixel values at each position between the load voxel model of FIG. 9 and the simulation voxel model of FIG.
In FIG. 11, the gradation level of the portion with a large difference is increased, and as a result, there is almost no portion with a high gradation level. Therefore, (1 ′), (2 ′), and (3 It can be seen that the simulation voxel model obtained by each calculation is in good agreement with the actual load voxel model based on the formula ') and the flowchart of FIG.
In particular, in FIGS. 9 and 10, it can be confirmed that the “toe” and “core” portions of the cherry tomatoes shown surrounded by an ellipse are very voxel models.
[0071]
Next, the mechanics calculation unit 5 obtains α obtained as an optimum value. _ijk , Β _ijk , Γ _ijk And a _u13 (k1, k2, k3), a _v13 (k1, k2, k3), a _w13 By inputting (k1, k2, k3), etc., the displacements u, v, w are obtained respectively.
Then, the mechanics calculation unit 5 uses the calculated displacements u, v, and w to calculate the strain ε using the equation (5) or (7). _ij Is calculated.
Thereafter, the displacement-strain matrix, the element stiffness matrix [K, which were performed using the equations (1) to (3) already described. _p ], Configuration matrix [D ^p ], Which is the same as the calculation for calculating the tangential stiffness matrix, the description thereof will be omitted.
[0072]
As described above, by using the material analysis system of the present invention, conventionally, the material is not homogeneous, the shape is complicated, and the overall behavior is only known in the material test, and the local state is unknown. Since the distribution of stress and strain generated in each part inside the DUT can be obtained quantitatively by applying a load to the DUT, the structure of the structure using the DUT as a structural member Design can be performed with high accuracy according to the intended use.
[0073]
In addition, the configuration of the present invention has been described using the X-ray CT apparatus 1 configured to include a device for applying a load to a test object. However, according to the present invention, for example, an artificial organ (artificial bone) implanted in a human body. Etc.), the load applied to the surrounding human body tissue (considered as a structural member) can be evaluated.
In this case, first, the image processing unit 2 uses a non-load voxel model such as a muscular tissue in which a prosthetic organ is to be embedded in a state in which the artificial organ is not to be deformed from a tomographic image captured by an X-ray CT apparatus used for normal medical use. That is, a non-load fluoroscopic image is created by the method described above and stored in the image storage unit 3.
[0074]
Next, the image processing unit 2 applies a load voxel model such as a muscular tissue in which a prosthetic organ is to be implanted in a state in which a predetermined load is applied and deformed from a tomographic image captured by a medical X-ray CT apparatus, That is, the load fluoroscopic image is created by the method described above and stored in the image storage unit 3.
At this time, the unloaded voxel model of the muscle tissue or the like to be tested and the loaded voxel model are tomographic images captured at the same resolution, have the same scale, and have the same number of pixel configurations. For example, both are 100 × 100 pixels.
[0075]
As for the load fluoroscopic image, a load fluoroscopic image is created for each state where different loads are applied to the muscle tissue or the like while changing the body shape of the site such as the muscle tissue to which a predetermined load is applied.
Then, the image processing unit 2 stores the image data of the unloaded voxel model and the plurality of loaded voxel models in the image storage unit 3.
Next, the displacement amount calculation unit 4 calculates the displacement amounts u, v, and (1), (2), (3), or (1 ′), (2 ′), (3 ′) according to the above-described equations. w is obtained for each load voxel model of each body shape.
[0076]
Next, when the muscular tissue or the like to which the load is applied is used as a test object, the mechanics calculation unit 5 is a large deformation as a deformation, and therefore, based on the displacement amounts u, v, and w according to Equation (5), The strain in the load voxel model corresponding to the load voxel model is obtained according to each step of the flowchart of FIG.
Since the muscular tissue or the like is a non-linear material, the mechanics calculation unit 5 has already explained the structural relationship in the load voxel model corresponding to the non-load voxel model based on the displacement amounts u, v, and w using the equation (6). It calculates | requires according to each step of the flowchart of FIG.
[0077]
Here, the mechanics calculation part 5 calculates | requires the distortion and stress concerning a muscle tissue etc. for every body shape of a to-be-tested person by a finite element method.
That is, the mechanics calculation unit 5 assumes a load applied to surrounding muscular tissues and the like by artificial organs embedded in the human body in each of the plurality of body shapes of the test subject, and the muscular tissues and the like (including blood vessels and nerves). The stress and strain generated in
By the above-described calculation, the characteristics of the mechanical structure of the living tissue for each patient, that is, the relationship between stress and strain, is obtained, and the artificial organ to be implanted and the object to be tested (muscle tissue in the above case) are structured. The structural design of the structural body (here, the human body) as a member can be performed with high accuracy.
[0078]
Then, based on the relationship between the stress and strain of the surrounding muscular tissue and the like, the structure of the implanted artificial organ is designed, and an artificial organ having a size, stress and strain relationship corresponding to the muscular tissue is created.
Then, when the created artificial organ is embedded in the human body, a test similar to the above-described test performed on the muscle tissue is performed on the artificial organ.
[0079]
That is, the image processing unit 2 creates an unloaded voxel model of an artificial bone before embedding, that is, an unloaded fluoroscopic image, from the tomographic image captured by an X-ray CT apparatus used for normal medical use by the method described above. And stored in the image storage unit 3.
Next, the image processing unit 2 creates a load voxel model of an artificial bone after being embedded in a human body from a tomographic image captured by a medical X-ray CT apparatus, that is, a load fluoroscopic image, by the method described above. Store in the image storage unit 3.
[0080]
At this time, the unloaded voxel model and the loaded voxel model of the artificial bone which is the test object are tomographic images captured at the same resolution, are the same scale, and have the same number of pixel configurations, For example, both are 100 × 100 pixels.
As for the load fluoroscopic image, a load fluoroscopic image is created for each state in which different loads are applied to the artificial bone while changing the body shape of the part of the human body in which the artificial bone is embedded.
[0081]
Then, the image processing unit 2 stores the image data of the unloaded voxel model and the plurality of loaded voxel models in the image storage unit 3.
Next, the displacement amount calculation unit 4 obtains the displacement amounts u, v, and w for each load voxel model of each body by the equations (1), (2), and (3) already described.
Next, when the artificial bone embedded in the human body is used as the test object, the mechanics calculation unit 5 is a very small deformation, and therefore, based on the displacement amounts u, v, and w according to the equation (6), The strain in the load voxel model corresponding to the load voxel model is obtained according to each step of the flowchart of FIG.
Then, since the artificial bone is a linear material, the mechanics calculation unit 5 has already explained the stress in the load voxel model corresponding to the non-load voxel model based on the displacement amounts u, v, and w according to the equation (7). 4 is obtained according to each step of the flowchart of FIG.
[0082]
Here, the mechanics calculation unit 5 obtains strain and stress applied to the artificial bone for each body shape of the person under test based on the displacement amount of each pixel for each load voxel model with respect to each pixel of the non-load voxel model.
That is, the mechanics calculation unit 5 calculates the stress and strain generated in each part (including the inside) of the artificial bone by the load applied to the artificial bone from other living tissue of the human body in each of the plurality of body shapes of the test subject. .
Then, it is determined whether or not the relationship between the stress and strain of the muscular tissue already calculated, that is, whether or not an unfavorable load is applied to the muscular tissue, etc. Examine the validity of structural design.
Thus, by using the material analysis system of the invention, the structural design of the artificial organ that matches the individual differences of each patient's human body is improved, and the compatibility with other structural members (for example, muscular tissue) is improved with high accuracy. It becomes possible to design with.
[0083]
By using the material analysis system of the present invention described above, in the evaluation of the artificial organ embedded in the human body that could not be evaluated conventionally, before the artificial organ is embedded, the stress and strain applied to the surrounding biological tissue by implanting the artificial organ And structural design for the strength of biological tissue and artificial organs as structural members by quantitatively obtaining in three dimensions the stress and strain applied to each part of this artificial organ by the load applied from the surrounding biological tissue In addition, material design can be performed in accordance with individual differences of human bodies and usage environments, and it is possible to manufacture artificial organs that are highly compatible with individual differences of human bodies to be embedded.
[0084]
Further, by using the material analysis system of the present invention, a load is applied from the outside to an organ of a healthy person, for example, a bone, or the load is changed by changing the body shape, and each of the three-dimensional voxel models is used. The stress and strain generated in each part of this bone based on the state load are quantitatively calculated in three dimensions, and the evaluation results are fed back to the structural design and material design of the artificial bone, making it closer to the actual bone It is possible to develop and manufacture artificial bones.
[0085]
<Second Embodiment: Material Testing System>
The material test system according to the second embodiment of the present invention uses the configuration of the material analysis system according to the first embodiment, and a different part is that the fixing device 20 is not included in the first embodiment. is there.
The present invention relates to a three-dimensional perspective image of a test object in a state where no load is applied (hereinafter referred to as a loaded fluoroscopic image), and a three-dimensional perspective image of the test object in a state where a predetermined load is applied ( Hereinafter, a load fluoroscopic image) is generated from X-ray data based on the X-ray transmission intensity from the X-ray CT apparatus.
However, the present invention is not limited to the X-ray CT apparatus, and it is also possible to use a three-dimensional fluoroscopic image obtained by MRI (magnetic resonance image) or an ultrasonic apparatus.
Then, the displacement amount calculation unit 4 described later moves each pixel of the non-load fluoroscopic image three-dimensionally (spatially) using a predetermined calculation formula.
[0086]
At this time, the material test system of the second embodiment is similar to the material analysis system of the first embodiment until the shapes of the unloaded fluoroscopic image after movement and the loaded fluoroscopic image coincide with each other. The simulation is performed while sequentially changing the coefficients and constants, and the quantitative analysis of the stress and strain applied to each part of the DUT embedded in the other material (structure whose internal structure is mechanically heterogeneous) Can be done.
[0087]
Hereinafter, a second embodiment will be described with reference to the drawings. FIG. 12 is a block diagram showing a configuration example of a material testing system according to the second embodiment of the present invention. In this figure, the material testing system of the present invention has at least an X-ray CT apparatus 1, an image processing unit 2, an image storage unit 3, a displacement calculation unit 4, a dynamic calculation unit 5, and a fixing device 20.
The X-ray CT apparatus 1, the image processing unit 2, the image storage unit 3, the displacement amount calculation unit 4, and the dynamics calculation unit 5 are the same as those in FIG. 1 of the first embodiment (similar processing is performed). For this purpose, the same reference numerals are given and the description is omitted.
[0088]
Next, the configuration of the X-ray CT apparatus 1 will be briefly described with reference to FIG. FIG. 2 is a conceptual diagram showing a configuration example of the X-ray CT apparatus.
The X-ray CT apparatus 1 has an X-ray tube 11 that emits X-rays and an X-ray detector 13 that detects the intensity of the X-rays at positions facing each other. It is fixed between the X-ray detector 13 by a fixing device 20 (not shown).
The fixing device 20 fixes the upper and lower portions of the device under test 14 in the drawing with a gripping tool or the like, and applies a load such as tension / compression / twist to the device under test 14.
[0089]
The fixing device 20 can rotate the device under test along the body axis of the device under test 14 in the R direction within an angle range of 360 ° with the load applied.
Here, since the X-ray tube 11 radiates the X-ray 12 that spreads in a fan shape, the fixing device 20 causes the X-ray tube 11 and the X-ray tube 11 and the X-ray so that the X-ray 12 that spreads in the fan shape becomes the lateral width of the DUT 14. The position of the line detector 13 is adjusted.
Then, the X-ray detector 13 measures the X-ray intensity of the X-ray 12 after passing through the device under test 14, for example, at the section 14 n of the device under test 14.
[0090]
In addition, the fixing device 20 can move in the Z1 direction or the Z2 direction in synchronization with the body axis.
Then, the X-ray CT apparatus 1 measures the X-ray intensity of the X-ray 12 that passes through the device under test 14 while rotating and moving the fixing device 20.
At this time, the X-ray CT apparatus 1 has the X-ray intensity of the X-ray 12 transmitted through the device under test 14 in both the state where the load is applied to the device under test 14 and the state where the load is not applied. Measure.
[0091]
The above-described fixing device 20 will be described with reference to FIG. FIG. 13 is a conceptual diagram illustrating a configuration example of the fixing device 20.
The upper part of the DUT 14 is gripped by the gripping tool 21 and the lower part is gripped by the gripping tool 22.
The arm 23 has a gripping tool 21, and the arm 24 has a gripping tool 22, and the fixing device 20 moves the gripping tool 21 and the gripping tool 22 to a load axis along the opposing direction of the gripping tools. A load mechanism for driving up and down in parallel is provided inside.
Further, the gripping tools 21 and 22 are driven in synchronization by a drive unit in the fixing device 20, and the gripping sample is moved in the R direction in FIG. 2 with a central axis parallel to the load axis of the DUT 14. Rotated as center.
[0092]
Further, the fixing device 20 is provided with a spline shaft 25 that is rotated by the other driving unit.
The gripping tool 21 and the gripping tool 22 of the arm 23 and the arm 24 are provided with a rotation transmission mechanism that transmits the rotation of the spline shaft 25.
As a result, the gripping tool 21 and the gripping tool 22 rotate in the R direction synchronously while gripping the sample.
Here, the drive side element of the rotation transmission mechanism of the gripping tool 21 at the upper part is splined to the spline shaft 25.
By doing so, the grippers 21 and 22 can be rotated in the R direction in a synchronized state while applying a load to the sample by a load mechanism provided in the fixing device 20.
[0093]
Therefore, when the gripping tool 21 is pulled with a predetermined force in the upper direction by the load mechanism, the gripping tool 22 is similarly pulled with the same force in the lower direction by the load mechanism, and a tensile load is applied to the DUT 14. Will be applied.
Further, when the gripping tool 21 is pushed downward by the load mechanism with a predetermined force, the gripping tool 22 is similarly pushed upward by the load mechanism, and a compressive load is applied to the DUT 14. Become.
[0094]
The load applied to the DUT 14 is measured by a load cell embedded in the gripping tool 21.
The drive control unit of the fixing device 20 controls the load function using the load detection result measured by the load cell so that the load applied to the device under test 14 becomes a preset numerical value.
[0095]
In addition, the gripping tools 21 and 22 change the angle for each minute angle while the drive unit in the fixing device 20 is synchronized in a state where a load is applied to the device under test 14. ° Can rotate.
As a result, the X-rays 12 emitted from the X-ray tube 11 pass through the test object 14 under a load and are detected by the X-ray detection device 13. Are output as X-ray data used for generating a layer image in the image processing unit 2.
[0096]
Returning to FIG. 12, with the above-described configuration, the X-ray CT apparatus 1 outputs X-ray data of a cross section of the device under test (the device under test 14 in FIG. 2).
Then, the image processing unit 2 accumulates the X-ray data (X-ray fluoroscopic image) output from the X-ray CT apparatus 1 while the object to be tested is rotated 360 °, and re-assembles the accumulated X-ray data. By performing the configuration calculation, a cross section of the test object, that is, a tomographic image of the test object perpendicular to the body axis is generated.
[0097]
Further, the image processing unit 2 superimposes the tomographic images obtained by moving in the Z1 direction or the Z2 direction synchronously along the body axis at a minute interval in the body axis direction, and 3 A three-dimensional perspective image (three-dimensional voxel model) is generated.
At this time, in the X-ray CT apparatus, an unloaded voxel model of a non-loaded fluoroscopic image to which no load is applied and a loaded voxel model of a loaded fluoroscopic image in a state where a predetermined load is applied are obtained by the above-described processing. The data is generated by the processing unit 2.
[0098]
Further, the image storage unit 2 stores the obtained non-load voxel model and load voxel model in the image storage unit 3 and displays the non-load voxel model and load voxel model on a display screen of an image display device (not shown). To display.
Hereinafter, the calculation formula and algorithm (the processing of the flowcharts of FIGS. 3 and 4) for calculating the displacement, stress and strain performed by the displacement calculation unit 4 and the dynamic calculation unit 5 will be described in the first embodiment. Since it is the same as the form (because the same reference numerals perform the same processing), the description is omitted.
[0099]
As described above, by using the material test system of the present invention, the specimen 14 in a loaded state is 360 ° with respect to the specimen in a loaded state, which could not be evaluated conventionally. The fixing device 20 that can be rotated makes it possible to generate a three-dimensional voxel model of the device under test 14 under a load, that is, a load perspective image. It is possible to detect the shape of the three-dimensional deformation caused by the load of the test object 14 which is homogeneous and has a complicated shape.
[0100]
In addition, by using the material testing system of the present invention, it is possible to test a test object whose material is not uniform and the shape is complicated and strength / ductility / toughness can be evaluated only by using a destructive test. Even when it is performed, the stress and strain distribution generated in each part inside the DUT can be quantitatively determined in three dimensions by applying a load without destroying the DUT. It becomes possible to carry out with high precision according to the application using the structural design and material design of the device under test.
[0101]
As described above, by using the material testing system of the present invention, conventionally, the material is not homogeneous, the shape is complicated, and only the overall behavior is known in the material test, and the local state is unknown. Since it is possible to quantitatively determine the stress and strain distribution generated in each part inside the DUT by applying a load to the DUT, the structural design of the structure using the DUT as a structural member Can be accurately performed according to the intended use.
[0102]
In the above-described embodiment of the present invention, the procedure executed in the material analysis system and the material test system is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read into the computer system. When executed, the material analysis system of the present invention is realized. The computer system referred to here includes an OS and hardware such as peripheral devices.
[0103]
Further, the “computer system” includes a homepage providing environment (or display environment) if the WWW system is used.
The “computer-readable recording medium” refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, and a CD-ROM, and a storage device such as a hard disk built in the computer system. Further, the “computer-readable recording medium” refers to a volatile memory (RAM) in a computer system that becomes a client or a system when a program is transmitted through a network such as the Internet or a communication line such as a telephone line. In addition, those holding programs for a certain period of time are also included.
[0104]
The program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line.
The program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, and what is called a difference file (difference program) may be sufficient.
[0105]
As described above, the first and second embodiments of the present invention have been described in detail with reference to the drawings, but the specific configuration is not limited to this embodiment, and the design does not depart from the gist of the present invention. Any changes and the like are included in the present invention.
[0106]
【The invention's effect】
According to the material analysis system of the present invention, each part (internal part) of a DUT having a non-uniform material and a complicated shape, such as an artificial organ embedded in another material (for example, an artificial organ embedded in a human body). (Including the deformation) can be evaluated by a three-dimensional voxel model, and the stress and strain in each part can be measured quantitatively, and the structural design corresponding to the environment to be used, that is, the load condition, and Material design can be performed.
[0107]
According to the material test system of the present invention, the deformation of each part (including the inside) of the DUT having a non-uniform material and a complicated shape can be evaluated by a three-dimensional voxel model, and the stress in each part In addition, it is possible to quantitatively measure the strain and the structural design and material design corresponding to the environment to be used, that is, the degree of load.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration example of a material analysis system according to a first embodiment of the present invention.
FIG. 2 is a conceptual diagram showing a configuration of the X-ray CT apparatus 1 of FIG.
FIG. 3 is a flowchart showing an operation example of displacement amount calculation of a displacement amount calculation unit 4 in FIG. 1;
FIG. 4 is a flowchart showing an example of stress calculation operation of the mechanics calculation unit 5 in FIG. 1;
FIG. 5 is a perspective image of an unloaded eight-pitch rope generated from a layer image captured by the X-ray CT apparatus 1 according to the present invention.
FIG. 6 is a perspective image of an eight-strike rope in a loaded state generated from a layer image captured by the X-ray CT apparatus 1 according to the present invention.
FIG. 7 shows each pixel value P in the displacement amount calculation unit 4. ^* It is a conceptual diagram explaining the calculation method of the value of (X, Y, Z).
FIG. 8 is a diagram of a three-dimensional voxel model (unloaded voxel model) in a non-loaded state of a sample (petit tomato) generated from a tomographic image captured by the X-ray CT apparatus 1;
FIG. 9 is a diagram of a three-dimensional voxel model (load voxel model) in a loaded state of a sample (petit tomato) generated from a tomographic image captured by the X-ray CT apparatus 1;
FIG. 10 is a diagram of a loaded voxel model (length of one side of one voxel is 0.4 mm) obtained by simulation from an unloaded voxel model.
11 is a diagram of a difference voxel model showing a difference in pixel values at each position in the load voxel model in FIG. 9 and the simulation voxel model in FIG. 10;
FIG. 12 is a block diagram showing a configuration example of a material testing system according to a second embodiment of the present invention.
13 is a conceptual diagram showing a configuration example of a fixing device 20 for fixing a test sample 14 in FIG.
[Explanation of symbols]
1 X-ray CT system
2 Image processing device
3 Image storage
4 Displacement calculation unit
5 Dynamics calculation part
11 X-ray tube
12 X-ray
13 X-ray detector
14 DUT
20 Fixing device
21 and 22
23, 24 arms
25 Spline shaft

Claims (21)

An X-ray CT apparatus that has an X-ray source and a plurality of X-ray detectors, and collects X-ray data relating to a cross section of the test object;
An image processing unit that generates a three-dimensional perspective image of the test object based on the X-ray data;
An image storage unit for storing a first three-dimensional fluoroscopic image of the test object in a state where no load is applied and a second three-dimensional fluoroscopic image of the test object in a state where a predetermined load is applied; ,
Each pixel of the first three-dimensional fluoroscopic image by a predetermined calculation is moved three-dimensionally, by matching the shape of the first three-dimensional perspective image and the second three-dimensional perspective images, each pixel A displacement amount calculation unit for obtaining a displacement amount due to a load;
A material analysis system, comprising: a mechanical calculation unit that calculates strain and stress in each part of the DUT due to a load from the displacement amount.   The displacement amount calculation unit moves each pixel while sequentially changing the coefficient and constant of the predetermined calculation formula, thereby changing the shapes of the first three-dimensional perspective image and the second three-dimensional perspective image. The material analysis system according to claim 1, wherein the materials are matched.   The displacement amount calculation unit associates each pixel in the second three-dimensional perspective image with the first three-dimensional perspective image after movement based on the respective degrees of gradation, and the second three-dimensional perspective image and the second three-dimensional perspective image. The material analysis system according to claim 1, wherein the coincidence of the shape with the three-dimensional perspective image is determined.   Based on the amount of displacement, the mechanical calculation unit uses an arithmetic expression corresponding to a small deformation strain when the material deformation is small, and uses an arithmetic expression corresponding to a large deformation strain when the material deformation is large. The material analysis system according to any one of claims 1 to 3, wherein a strain is calculated.   When the material is a linear material based on the amount of displacement, the mechanical calculation unit obtains a first configuration matrix using a first calculation formula based on a linear constitutive law, and based on the first configuration matrix, When the stress is calculated by the calculation formula 1 and the calculation material is a nonlinear material, the second calculation matrix is obtained using the second calculation formula based on the non-linear / incremental constitutive law. The material analysis system according to any one of claims 1 to 4, wherein a stress is calculated based on the second calculation formula. A data collection process for collecting X-ray data relating to a cross section of a test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors;
An image processing process in which a three-dimensional perspective image of the test object is generated based on the X-ray data;
A first three-dimensional fluoroscopic image of the test object in a state where no load is applied and a second three-dimensional fluoroscopic image of the test object in a state where a predetermined load is applied are stored in the image storage unit. Image storage process,
Each pixel of the first three-dimensional fluoroscopic image by a predetermined calculation is moved three-dimensionally, by matching the shape of the first three-dimensional perspective image and the second three-dimensional perspective images, each pixel Displacement amount calculation process for obtaining displacement amount due to load,
A material test method comprising: calculating a strain and a stress in each part of the DUT due to a load from the displacement amount.   In the displacement amount calculation process, the shape of the first three-dimensional perspective image and the second three-dimensional perspective image is changed by moving each pixel while sequentially changing the coefficient and constant of the predetermined arithmetic expression. The material testing method according to claim 6, wherein the materials are matched.   In the displacement amount calculation process, each pixel in the second three-dimensional perspective image and the first three-dimensional perspective image after movement is associated with each other based on each gradation, and the first three-dimensional perspective image and the second three-dimensional perspective image The material testing method according to claim 6, wherein the coincidence of the shape with the three-dimensional perspective image is determined.   In the mechanical calculation process, when the deformation of the material is very small, an arithmetic expression corresponding to the strain of the small deformation is used, and when the deformation of the material is large, an arithmetic expression corresponding to the distortion of the large deformation is used and based on the displacement amount. The material test method according to claim 6, wherein strain is calculated.   In the mechanical calculation process, when the material is a linear material based on the displacement amount, a first configuration matrix is obtained using a first calculation formula based on a linear constitutive law, and the first configuration matrix is used to determine the first configuration matrix. When the stress is calculated by the calculation formula 1 and the calculation material is a nonlinear material, the second calculation matrix is obtained using the second calculation formula based on the non-linear / incremental constitutive law. The material test method according to any one of claims 6 to 9, wherein a stress is calculated based on the second calculation formula based on the second calculation formula. A material analysis program for operating the material analysis system according to any one of claims 1 to 5,
A data collection process for collecting X-ray data relating to a cross section of a test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors;
Image processing for generating a three-dimensional perspective image of the test object based on the X-ray data;
A first three-dimensional fluoroscopic image of the test object in a state where no load is applied and a second three-dimensional fluoroscopic image of the test object in a state where a predetermined load is applied are stored in the image storage unit. Image storage processing
Each pixel of the first three-dimensional fluoroscopic image by a predetermined calculation is moved three-dimensionally, by matching the shape of the first three-dimensional perspective image and the second three-dimensional perspective images, each pixel A displacement amount calculation process for obtaining a displacement amount due to a load;
A material analysis program for causing a computer to execute a mechanical calculation process for calculating strain and stress in each part of the DUT due to a load from the displacement amount. A recording medium recording a material analysis program for operating the material analysis system according to any one of claims 1 to 5,
A data collection process for collecting X-ray data relating to a cross section of a test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors;
Image processing for generating a three-dimensional perspective image of the test object based on the X-ray data;
A first three-dimensional fluoroscopic image of the test object in a state where no load is applied and a second three-dimensional fluoroscopic image of the test object in a state where a predetermined load is applied are stored in the image storage unit. Image storage processing
Each pixel of the first three-dimensional fluoroscopic image by a predetermined calculation is moved three-dimensionally, by matching the shape of the first three-dimensional perspective image and the second three-dimensional perspective images, each pixel A displacement amount calculation process for obtaining a displacement amount due to a load;
A computer-readable recording medium having recorded thereon a material analysis program for causing a computer to execute a mechanical calculation process for calculating strain and stress in each part of the DUT due to a load from the displacement. A sample fixing unit for holding the upper and lower parts of the test object with opposing grips, generating a load between the grips, and applying a load to the test object;
An X-ray CT apparatus that has an X-ray source and a plurality of X-ray detectors, and collects X-ray data relating to a cross section of the device under test;
An image processing unit that generates a three-dimensional perspective image of the test object based on the X-ray data;
An image storage unit for storing a first three-dimensional fluoroscopic image of the test object in a state where no load is applied, and a second three-dimensional fluoroscopic image of the test object in a state where a predetermined load is applied;
Each pixel of the first three-dimensional fluoroscopic image by a predetermined calculation is moved three-dimensionally, by matching the shape of the first three-dimensional perspective image and the second three-dimensional perspective images, each pixel A displacement amount calculation unit for obtaining a displacement amount due to a load;
A material test system comprising: a mechanical calculation unit that calculates a stress and a strain in each part of the specimen by a load from the amount of displacement.   The sample fixing unit includes a drive unit, a spline shaft to which rotation is given by the drive unit, and a rotation transmission mechanism that transmits the rotation of the spline shaft to each gripping tool, and the rotation transmission mechanism of the upper gripping tool. The material testing system according to claim 13, wherein the drive side element is splined to the spline shaft.   The displacement amount calculation unit moves each pixel while sequentially changing the coefficient and constant of the predetermined calculation formula, thereby changing the shapes of the first three-dimensional perspective image and the second three-dimensional perspective image. 15. The material testing system according to claim 13, wherein the material testing system is matched.   The displacement amount calculation unit associates each pixel in the second three-dimensional perspective image with the first three-dimensional perspective image after movement based on the respective degrees of gradation, and the second three-dimensional perspective image and the second three-dimensional perspective image. The material test system according to any one of claims 13 to 15, wherein the coincidence of the shape with the three-dimensional perspective image is determined. A sample fixing process in which the upper and lower parts of the test object are respectively gripped by opposing grips, a load is generated between the grips, and a load is applied to the test object.
A data collection process for collecting X-ray data relating to a cross section of a test object from an X-ray CT apparatus having an X-ray source and a plurality of X-ray detectors;
An image processing process in which a three-dimensional perspective image of the test object is generated based on the X-ray data;
A first three-dimensional fluoroscopic image of the test object in a state where no load is applied and a second three-dimensional fluoroscopic image of the test object in a state where a predetermined load is applied are stored in the image storage unit. Image storage process,
Each pixel of the first three-dimensional fluoroscopic image by a predetermined calculation is moved three-dimensionally, by matching the shape of the first three-dimensional perspective image and the second three-dimensional perspective images, each pixel Displacement amount calculation process for obtaining displacement amount due to load,
And a mechanical calculation process in which stress and strain at each part of the test body are calculated by a load from the amount of displacement.   In the displacement amount calculation process, the shape of the first three-dimensional perspective image and the second three-dimensional perspective image is changed by moving each pixel while sequentially changing the coefficient and constant of the predetermined arithmetic expression. The material testing method according to claim 17, wherein the materials are matched.   The displacement amount calculating step associates each pixel in the second three-dimensional perspective image with the first three-dimensional perspective image after movement based on the respective degrees of gradation, and the second three-dimensional perspective image and the second three-dimensional perspective image. The material test method according to claim 17, wherein the coincidence of the shape with the three-dimensional perspective image is determined. A material test program for operating the material test system according to any one of claims 13 to 16,
A sample fixing process in which the upper and lower parts of the test object are respectively gripped by opposing grips, a load is generated between the grips, and a load is applied to the test object.
An X-ray data collection process having an X-ray source and a plurality of X-ray detectors, and collecting X-ray data relating to a cross section of the test object;
Image processing for generating a three-dimensional perspective image of the test object based on the X-ray data;
An image storage process for storing a first three-dimensional fluoroscopic image of the test object in a state where no load is applied, and a second three-dimensional fluoroscopic image of the test object in a state where a predetermined load is applied;
Each pixel of the first three-dimensional fluoroscopic image by a predetermined calculation is moved three-dimensionally, by matching the shape of the first three-dimensional perspective image and the second three-dimensional perspective images, each pixel A displacement amount calculation unit for obtaining a displacement amount due to a load;
A material test program for causing a computer to execute a mechanical calculation process for calculating a stress and a strain in each part of the specimen by a load from the displacement amount. A recording medium for recording a material test program for operating the material test system according to any one of claims 13 to 16,
A sample fixing process in which the upper and lower parts of the test object are respectively gripped by opposing grips, a load is generated between the grips, and a load is applied to the test object.
An X-ray data collection process having an X-ray source and a plurality of X-ray detectors, and collecting X-ray data relating to a cross section of the test object;
Image processing for generating a three-dimensional perspective image of the test object based on the X-ray data;
An image storage process for storing a first three-dimensional fluoroscopic image of the test object in a state where no load is applied, and a second three-dimensional fluoroscopic image of the test object in a state where a predetermined load is applied;
Each pixel of the first three-dimensional fluoroscopic image by a predetermined calculation is moved three-dimensionally, by matching the shape of the first three-dimensional perspective image and the second three-dimensional perspective images, each pixel A displacement amount calculation unit for obtaining a displacement amount due to a load;
A computer-readable recording medium recording a material test program for causing a computer to execute a mechanical calculation process for calculating a stress and a strain in each part of the specimen by a load from the displacement amount.

Images