JP6070277B2 - Apparatus, control method thereof, and control program thereof - Google Patents

Description

  The present invention relates to an apparatus for analysis by a finite element method, a control method thereof, and a control program thereof.

  In recent years, fracture analysis and the like using the finite element method (Finite Element Method, FEM) are increasing (for example, Patent Document 1).

  The finite element method is a numerical analysis method in which the object to be analyzed is regarded as a collection of small and simple elements, the whole is divided into each element, analysis is performed for each element, and an approximation of the overall behavior is obtained. It is a technique to seek. From such a method, it is generally known that the magnitude of the state variables (for example, stress, strain, etc.) calculated depends on the element size.

  FIG. 9 shows an example of the relationship between the element size and the calculated strain. Here, the horizontal axis indicates the element size, and the vertical axis indicates the magnitude of strain. As shown in FIG. 9, generally, as the element size increases, the calculated magnitude of the strain decreases.

  As described above, in the analysis by the finite element method, since the size of the state variable calculated according to the element size changes, the evaluation criteria must be changed according to the element size, and the analysis is performed. It was difficult.

  For such a problem, it has been proposed to correct the calculated state variable (for example, Non-Patent Document 1). Specifically, paying attention to the fact that the change in the average value is not so large even if the element size is changed, the calculated state variable is corrected to be averaged in a predetermined region. As a result, the element size dependency of the calculated state variable can be reduced.

Japanese Unexamined Patent Publication No. 2011-83813

Zdenek P. Bazant et al., "Nonlocal Continuum Damage, Localization Instability and Convergence", Journal of Applied Mechanics, (USA), ASME, June 1988, Vol. 55, pp. 287-293

  However, the method described in Non-Patent Document 1 is difficult to handle with a general-purpose code because the averaging area depends on the shape of the analysis target, and information on a large number of elements needs to be processed.

  The present invention has been made to solve such a problem, and in the analysis by the finite element method, an apparatus capable of more easily reducing the element size dependency of the calculated state variable, and its control It is an object to provide a method and a control program thereof.

  An apparatus according to the present invention is an apparatus for determining a state of a material based on a state variable generated inside the material according to deformation, and stores analysis data including at least analysis model data, material property data, and boundary condition data. A plurality of state variables in each element of the material at one time of deformation, which affects the determination result of the strain and the material state. State variable calculation unit that calculates a plurality of state variables including at least a strain gradient calculation unit that calculates a strain gradient based on strain, and a determination result of the material state so as to reduce the element size dependency based on the strain gradient Based on a number of state variables, including a state variable correction unit that corrects state variables that affect the condition, and a state variable that affects the determination result of the state of the corrected material Comprising a state determining state determination unit of the material, and an output unit for outputting a determination result of the state of the material.

  Further, in the apparatus according to the present invention, the state variable correction unit calculates the element size influence degree based on the strain gradient, and corrects the state variable affecting the determination result of the material state based on the element size influence degree. Is preferred.

  In the apparatus according to the present invention, the element size influence degree is preferably calculated based on the strain gradient and the increment from the strain gradient at the time immediately before the strain gradient.

ここで、ｆは要素サイズ影響度であり、δはひずみ勾配であり、Δδはひずみ勾配の増分であり、Ａ〜Ｃは材料に応じて定まる定数であることが好ましい。 Further, in the apparatus according to the present invention, the element size influence degree is calculated by the following equation:

Here, f is an element size influence degree, δ is a strain gradient, Δδ is an increment of the strain gradient, and A to C are preferably constants determined according to materials.

  In the apparatus according to the present invention, it is preferable that the state variable correcting unit corrects the state variable that affects the determination result of the material state by multiplying or dividing the element size influence degree.

  In the apparatus according to the present invention, the state variable that affects the determination result of the material state is the damage rate, and the state determination unit indicates that the cumulative value of the corrected damage rate up to one time exceeds the threshold value. It is preferable to determine that a break has occurred in the corresponding element of the material.

  An apparatus according to the present invention corrects a state variable generated in a material in accordance with deformation, and reduces the element size dependency of a state variable calculated using a finite element method based on a strain gradient. Is provided with a state variable correction unit.

  An apparatus control method according to the present invention includes a storage unit that stores analysis data including at least analysis model data, material property data, and boundary condition data, and is based on a state variable generated in the material according to deformation. A device control method for determining a state, wherein the device performs analysis by a finite element method based on analysis data, and is a plurality of state variables in each element of the material at one time of deformation, including strain and material Calculates multiple state variables including at least state variables that affect state determination results, calculates strain gradient based on strain, and material state determination results to reduce element size dependency based on strain gradient The state variable that affects the material is corrected, the material state is determined based on multiple state variables including the state variable that affects the determination result of the corrected material state, and the material And it outputs the determination result of the state.

  A device control method according to the present invention is a device control method for correcting a state variable generated inside a material in accordance with deformation, wherein the device is based on a strain gradient based on a state variable calculated using a finite element method. To reduce the element size dependency.

  A control program for an apparatus according to the present invention includes a storage unit that stores analysis data including at least analysis model data, material property data, and boundary condition data, and is based on a state variable generated in the material according to deformation. A control program for a device for determining a state, wherein the device is analyzed by a finite element method based on analysis data, and is a plurality of state variables in each element of the material at one time of deformation, including strain and material Calculates multiple state variables including at least state variables that affect state determination results, calculates strain gradient based on strain, and material state determination results to reduce element size dependency based on strain gradient The state of the material based on multiple state variables, including state variables that modify state variables that affect the modified material state determination results Determined to execute outputting the determination result of the state of the material.

  A device control program according to the present invention is a device control program for correcting a state variable generated inside a material in accordance with deformation, and the state variable calculated using the finite element method is applied to the device based on a strain gradient. To correct the element size dependency.

  An apparatus, a control method thereof, and a control program thereof according to the present invention provide an element size dependency of a calculated state variable by correcting the calculated state variable based on a strain gradient in an analysis by a finite element method. It can be reduced more easily.

It is a figure which shows an example of the processing flow of a fracture analysis. It is a figure which shows an example of the relationship between a strain gradient and its increment. It is a figure which shows an example of the data structure of various data. It is a figure which shows an example of a test piece. It is a figure which shows another example of the data structure of various data. It is a figure which shows an example of an analysis result. It is a figure which shows another example of an analysis result. It is a figure which shows an example of schematic structure of a fracture analysis apparatus. It is a figure which shows an example of the relationship between element size and the distortion calculated.

  Hereinafter, various embodiments of the present invention will be described with reference to the drawings. However, it should be noted that the technical scope of the present invention is not limited to these embodiments, and extends to the invention described in the claims and equivalents thereof.

  In the present embodiment, the fracture analysis based on the continuum damage mechanics is performed using the finite element method, and the present invention is applied at that time.

ここで、Ｄ’は損傷変数Ｄの変化率（損傷速度）、Ｙは損傷同伴変数、Ｓは材料定数、ｐは累積塑性ひずみ、ｐ’は累積塑性ひずみｐの変化率、ｐ_Dはしきい値、Ｈ（）はHeaviside関数である。そして、損傷変数Ｄが増大して臨界値Ｄ_Cに達したとき、即ち、式２が成立したときに、き裂の発生あるいは破壊が生じるものと考える。

Continuum damage mechanics is a dynamic theory for analyzing the progress of material damage and fracture from the standpoint of continuum mechanics. In continuum damage mechanics, the damage state is modeled using appropriate macromechanical damage variables, and the damage variables are used to describe the mechanical behavior of the damaged material and the development of damage. Damage development is described, for example, as in Equation 1.

Here, D ′ is the rate of change of the damage variable D (damage rate), Y is the damage accompanying variable, S is the material constant, p is the cumulative plastic strain, p ′ is the rate of change of the cumulative plastic strain p, and p _D is the threshold. The value H () is the Heaviside function. Then, it is considered that when the damage variable D increases and reaches the critical value D _C , that is, when Equation 2 is satisfied, the generation or fracture of a crack occurs.

In this embodiment, the damage rate D ′ is corrected based on the strain gradient. Specifically, the damage size D ′ is corrected by calculating the element size influence f based on the strain gradient and multiplying or dividing the element size influence f. This is based on the assumption that the element size dependency can be reduced or offset by using a numerical value based on the strain gradient because the magnitude of the strain changes according to the element size and the magnitude of the strain gradient also changes. Is. Therefore, Equation 2 is modified as Equation 3.

ここで、ｆは要素サイズ影響度、δはひずみ勾配、Δδはその増分、Ａ〜Ｃは材料定数である。 The element size influence degree f is calculated based on, for example, the strain gradient and its increment (from the strain gradient at the previous time). Specifically, it is calculated according to Equation 4.

Here, f is an element size influence degree, δ is a strain gradient, Δδ is an increment thereof, and A to C are material constants.

FIG. 2 shows an example of the relationship between the strain gradient and its increment. Here, e _i is an element, p _i is an evaluation point in element e _i , ε _{t, i} is a strain at time t and evaluation point p _i , δ _{t, i} is a strain gradient at time t and evaluation point p _i , Δδ _{t, i} indicates the increment of the strain gradient δ _{t, i from} the strain gradient δ _{t-1, i} . As shown in FIG. 2, at each time t, the strain gradient δ _{t, i} and the increment Δδ _{t, i at} each evaluation point p _i are calculated, and the element size influence f is calculated.

  FIG. 1 shows an example of the processing flow of such a fracture analysis. This processing flow is based on a program stored in advance in the storage unit 12 of the fracture analysis apparatus 1 shown in FIG. Worked and executed. The hardware configuration of the breakage analysis apparatus 1 will be described later.

  It is assumed that analysis data is stored in the storage unit 12 in advance. The analysis data includes, for example, analysis model data indicating the shape of the material, material property data indicating the material constant, boundary condition data indicating the boundary condition, analysis control parameters related to analysis control, and the like. The analysis data may be manually input by the user via the operation unit 13 or may be automatically generated based on an application program for generating the analysis data by the processing unit 15.

  The analysis model data is data indicating the shape of the material. For example, element configuration data indicating the node of each element of the material (FIG. 3A), node coordinate data indicating the coordinates of each node (FIG. 3B). ) Etc. are included.

  FIG. 3A shows an example of the data structure of element configuration data. The element configuration data includes, for each element, the element number, the node number of the element, and the like.

  FIG. 3B shows an example of the data structure of node coordinate data. The node coordinate data includes, for each node, the node number, the X coordinate, the Y coordinate, and the Z coordinate of the node.

  FIG. 4 shows an example of a test piece displayed based on the analysis model data. FIG. 4 is a plan view of a JIS (Japanese Industrial Standards) No. 5 test piece modeled using hexahedral elements.

を用いる場合に、密度、ヤング率、ポアソン比、Ｋ、ε₀、ｎ等が含まれ、また、損傷関連定数として、ε₀、式１におけるＳ、式３におけるＤ_C、式４におけるＡ、Ｂ、及びＣ等が含まれる。 The material property data is data indicating a material constant, for example, the Swift law.

Is used, density, Young's modulus, Poisson's ratio, K, ε ₀ , n, etc. are included, and as damage-related constants, ε ₀ , S in Equation 1, D _C in Equation 3, A in Equation 4, B, C, etc. are included.

These material constants are determined so that the analysis result of the test (for example, uniaxial tensile test) matches the experimental result. In order to consider the element size dependency, the test is analyzed with two or more single element sizes, and the material constants are adjusted so that each result matches the experimental result.
Specifically, (1) the initial value of the material constant is determined, (2) the analysis of the test is performed with two or more single element sizes, the fracture strain and the stress-strain relationship are calculated, and (3) each It is determined whether or not the breaking strain and stress-strain relationship of the material match those obtained by experiments. (4) If any of the breaking strain does not match or the stress-strain relationship does not match, the material constant The material constant is adjusted by repeating the steps (2) to (4) until the breaking strain and the stress-strain relationship coincide with each other. However, since the accuracy of the stress-strain relationship decreases particularly due to the element size around the fracture strain, the comparison is performed before the maximum stress point at which no damage occurs.

  The boundary condition data is data indicating boundary conditions, and includes, for example, displacement condition data indicating displacement conditions (FIG. 3C), load condition data indicating load conditions (FIG. 3D), and the like.

  FIG. 3C shows an example of the data structure of the displacement condition data. The displacement condition data includes, for each node, the node number, the X displacement, the Y displacement, and the Z displacement of the node.

  FIG. 3D shows an example of the data structure of the load condition data. The load condition data includes, for each node, the node number, the X load, the Y load, and the Z load of the node.

  When the execution of an application program for performing fracture analysis is instructed by the user via the operation unit 13, the processing unit 15 starts processing based on the program.

  First, the processing unit 15 initializes data (step S100). That is, the processing unit 15 acquires analytical model data from the storage unit 12, and determines a predetermined number (for example, 8) of evaluation points for each element of the material based on the analytical model data. Then, the processing unit 15 creates evaluation point data (FIG. 5A) indicating the determined evaluation point, and stores the evaluation point data in the storage unit 12. Further, the processing unit 15 secures an area in the storage unit 12 for storing a time counter indicating the current time and damage degree data (FIG. 5B) indicating the damage degree at the current time. Initialize the counter and data to zero.

  FIG. 5A shows an example of the data structure of the evaluation point data. The evaluation point data includes, for each element, the element number, the evaluation point number of the element, and the like.

  FIG. 5B shows an example of the data structure of the damage degree data. The damage degree data includes, for each evaluation point, the number of the evaluation point, the damage degree at the evaluation point, and the like.

  Next, the processing unit 15 calculates state variables (for example, stress, strain, damage rate, etc.) (step S102). That is, the processing unit 15 acquires analysis data and evaluation point data from the storage unit 12, proceeds with fracture analysis based on the analysis data and evaluation point data, and calculates node coordinates and state variables at the current time. Then, the processing unit 15 creates node coordinate data indicating the calculated node coordinates and state variable data (FIG. 5C) indicating the state variables, and stores the node coordinate data and the state variable data in the storage unit 12. . The break analysis uses Abaqus (registered trademark), which is a commercial application program. However, other application programs (for example, OpenFOAM (registered trademark)) can also be used.

  FIG. 5C shows an example of the data structure of the state variable data. The state variable data includes, for each evaluation point, the number of the evaluation point, stress, strain, damage rate, and the like at the evaluation point.

を材料全体について重ね合わせることにより、材料全体に対する運動方程式が求められる。ここで、Ｍは質量マトリクス、ｕは変位、Ｐは等価節点力ベクトル、Ｆは節点外力ベクトルである。次に、求められた運動方程式を解くことにより、変位ｕが求められる。そして、変位−ひずみ関係等に基づいて、求められた変位ｕから状態変数が求められる。なお、運動方程式を解くには、格子点法の一つである中央差分法を用いる。しかしながら、他の解法（前方差分法、後方差分法、ラグランジュ法、スペクトル法等）を用いることも可能である。 In Abacus (registered trademark), state variables are obtained based on a dynamic explicit method. The dynamic explicit method is a method for solving a dynamic balance equation (motion equation) in consideration of an acceleration term without iterative calculation. First, the equation of motion for one element

Is superposed on the entire material to obtain the equation of motion for the entire material. Here, M is a mass matrix, u is displacement, P is an equivalent nodal force vector, and F is a nodal external force vector. Next, the displacement u is obtained by solving the obtained equation of motion. Then, based on the displacement-strain relationship or the like, a state variable is obtained from the obtained displacement u. In order to solve the equation of motion, a central difference method, which is one of lattice point methods, is used. However, other solution methods (forward difference method, backward difference method, Lagrangian method, spectrum method, etc.) can also be used.

  Next, the processing unit 15 calculates a strain gradient (step S104). That is, the processing unit 15 acquires strain at each evaluation point with reference to the state variable data stored in the storage unit 12, and calculates a strain gradient at each evaluation point based on the strain. The strain gradient at one evaluation point is the difference between the strain at the one evaluation point and the strain at another evaluation point adjacent to the one evaluation point, between the one evaluation point and the other evaluation point. It can be calculated by dividing by the distance. Then, the processing unit 15 creates strain gradient data (FIG. 5D) indicating the calculated strain gradient, and stores the strain gradient data in the storage unit 12 in association with the current time.

  FIG. 5D shows an example of the data structure of strain gradient data. The strain gradient data includes, for each evaluation point, the number of the evaluation point, the strain gradient at the evaluation point, and the like.

  Next, the processing unit 15 corrects the damage speed (step S106). That is, the processing unit 15 refers to the strain gradient data stored in the storage unit 12 in association with the current time, and acquires the strain gradient at each evaluation point. In addition, the processing unit 15 refers to the strain gradient data stored in the storage unit 12 in association with the immediately preceding time, acquires the strain gradient at each evaluation point, and subtracts it from the corresponding strain gradient, so that each evaluation is performed. Calculate the strain gradient increment at the point. Furthermore, the processing unit 15 refers to the material property data stored in the storage unit 12 to obtain damage-related constants A to C, the damage-related constants A to C, strain gradients at each evaluation point, and increments thereof. Is used to calculate the element size influence degree at each evaluation point. Then, the processing unit 15 refers to the state variable data stored in the storage unit 12, acquires the damage rate at each evaluation point, and corrects the damage rate by dividing by the corresponding element size influence degree. . The processing unit 15 refers to the state variable data stored in the storage unit 12 and stores the corrected damage rate.

  Next, the processing unit 15 updates the damage degree (step S108). That is, the processing unit 15 refers to the state variable data stored in the storage unit 12 and acquires the damage rate at each evaluation point. Then, the processing unit 15 refers to the damage level data stored in the storage unit 12, acquires the damage level at each evaluation point, and updates the damage level by adding the corresponding damage speed. The processing unit 15 refers to the damage level data stored in the storage unit 12 and stores the updated damage level.

  Next, the processing unit 15 refers to the damage level data stored in the storage unit 12 to acquire the damage level at each evaluation point, and whether or not the damage level exceeds a threshold value at any of the evaluation points. Is determined (step S110).

  Then, when the damage degree exceeds the threshold value at any of the evaluation points (step S110—Yes), the processing unit 15 outputs the analysis result (step S112). That is, the processing unit 15 refers to the damage degree data stored in the storage unit 12 to obtain the number of each evaluation point, and specifies the number of the evaluation point whose damage degree exceeds the threshold value. Further, the processing unit 15 refers to the state variable data stored in the storage unit 12 using the identified number as a key, and acquires the corresponding state variable. Then, the processing unit 15 outputs the specified number, the acquired state variable, and the like to the display unit 14.

  On the other hand, when the degree of damage does not exceed the threshold value at any evaluation point (step S110-No), the processing unit 15 advances the current time by one (step S114). That is, the processing unit 15 refers to the time counter stored in the storage unit 12, acquires the current time, and increments (+1) to advance the time by one. Then, the processing unit 15 refers to the time counter stored in the storage unit 12 and stores the advanced time.

  Then, the processing unit 15 returns to the state variable calculation process (step S102).

FIG. 6 shows an example of analysis results obtained by the conventional methods and the methods of the present invention. FIG. 6 shows an analysis result when the test piece (JIS No. 5 test piece) shown in FIG. 4 is pulled in the direction of the arrow at a constant speed. Here, the material is mild steel. As constants, the plate thickness is 2 mm, the density is 7.89 × 10 ⁻⁶ kg / mm ³ , the Young's modulus is 206000 MPa, the Poisson's ratio is 0.333, K is 643 MPa, and ε ₀ is 0.0152 and n were set to 0.258. As damage-related constants, ε ₀ is 0.229, S is 60 MPa, D _C is 4.24 × 10 ⁻³ , A is 1.0 × 10 ⁵ , B is 1.0, and C is −1.0. It was. Furthermore, as an analysis model, the type of element was an 8-node perfect integration hexahedron element, the size was 0.5 mm to 8 mm, and the thickness was 0.4 mm. Note that the fracture criterion (threshold value for damage value) was determined so that the analysis results at the element sizes of 4 mm and 1 mm (only the method of the present invention) coincided with the experimental results.

  FIG. 6A shows an example of an analysis result (relationship between element size and calculated fracture strain) by a conventional method. Here, the horizontal axis indicates the element size, and the vertical axis indicates the magnitude of the breaking strain. Moreover, the straight line 600 shows the magnitude | size of the fracture | rupture distortion obtained by experiment. As shown in FIG. 6 (a), the calculated fracture strain does not match the experimentally obtained size for element sizes other than 4 mm as a reference.

  On the other hand, FIG. 6B shows an example of an analysis result (relationship between element size and calculated fracture strain) by the method of the present invention. Similar to FIG. 6A, the horizontal axis indicates the element size, and the vertical axis indicates the magnitude of the breaking strain. Moreover, the straight line 600 shows the magnitude | size of the fracture | rupture distortion obtained by experiment. As shown in FIG. 6 (b), with the element sizes other than the standard 4 mm and 1 mm, the magnitude of the fracture strain calculated still does not match that obtained by the experiment, but there is a difference between these differences. Is smaller than that shown in FIG. That is, the element size dependency of the calculated breaking strain is reduced.

  FIG. 7 shows another example of the analysis results obtained by the conventional methods and the methods of the present invention. The analysis results when the test piece (H15A12.5 test piece) shown in FIG. 7A is pulled at a constant speed in the direction of the arrow are shown in FIGS. 7B and 7C. Here, the material was mild steel, and the characteristics thereof were the same as those shown in FIGS. In addition, as an analysis model, the type of element was an 8-node perfect integration hexahedral element, the size was 1 mm to 4 mm, and the thickness was 0.25 mm.

  FIG. 7B shows an example of an analysis result (relationship between element size and calculated aperture ratio) by a conventional method. Here, the horizontal axis indicates the element size, and the vertical axis indicates the aperture ratio. A straight line 700 indicates the aperture ratio obtained by experiments. The opening ratio is calculated by (opening width at break / original opening width) × 100. As shown in FIG. 7B, the calculated aperture ratio does not coincide with that obtained by experiment for any element size.

  On the other hand, FIG. 7C shows an example of an analysis result (relationship between element size and calculated aperture ratio) according to the method of the present invention. Similar to FIG. 7B, the horizontal axis indicates the element size, and the vertical axis indicates the aperture ratio. A straight line 700 indicates the aperture ratio obtained by experiments. As shown in FIG. 7 (c), the aperture ratio calculated for any element size is still not consistent with that obtained by experiment, but the difference between the element sizes is shown in FIG. 7 (b). Compared to what is shown in. That is, the element size dependency of the calculated aperture ratio is reduced.

  Hereinafter, the hardware configuration of the fracture analysis apparatus 1 will be described. FIG. 8 shows an example of a schematic configuration of the fracture analysis apparatus 1.

  The fracture analysis device 1 refers to data stored in the storage unit 12 and / or data stored in another device (not shown) based on a program stored in the storage unit 12 in advance. Execute the process. The fracture analysis apparatus 1 executes various processes in accordance with instructions input via the operation unit 13 by the user and outputs the results to the display unit 14. For this purpose, the fracture analysis device 1 includes a communication unit 11, a storage unit 12, an operation unit 13, a display unit 14, and a processing unit 15.

  The communication unit 11 includes a communication interface circuit for connecting the fracture analysis device 1 to a network (not shown). Then, the communication unit 11 supplies data received from another device (not shown) via the network to the processing unit 15. In addition, the communication unit 11 transmits the data supplied from the processing unit 15 to another device via the network.

  The storage unit 12 includes, for example, at least one of a semiconductor memory, a magnetic disk device, and an optical disk device. The storage unit 12 stores an operating system program, a driver program, an application program, data, and the like used for processing in the processing unit 15. For example, the storage unit 12 stores an input device driver program for controlling the operation unit 13 and an output device driver program for controlling the display unit 14 as driver programs. The storage unit 12 stores an application program for creating analysis data, an application program for performing fracture analysis, and the like as application programs. The storage unit 12 also includes, as data, analysis model data indicating the shape of the material (element configuration data indicating the nodes of each element of the material, node coordinate data indicating the coordinates of each node, etc.), and material property data indicating the material constants , Boundary condition data indicating boundary conditions (displacement condition data indicating displacement conditions, load condition data indicating load conditions, etc.), analysis control parameters relating to analysis control, and the like are stored. In addition, the storage unit 12 includes, as other data, evaluation point data indicating an evaluation point, a time counter indicating the current time, damage degree data indicating the degree of damage at the current time, state variable data indicating a state variable, each time The strain gradient data indicating the strain gradient at is stored. Furthermore, the storage unit 12 may temporarily store temporary data related to a predetermined process.

  The operation unit 13 may be any device as long as the operation of the fracture analysis apparatus 1 can be performed, such as a keyboard and a touch pad. The user can input characters, numbers, and the like via the operation unit 13. When operated by the user, the operation unit 13 generates a signal corresponding to the operation. The generated signal is supplied to the processing unit 15 as a user instruction.

  The display unit 14 may be any device as long as it can display images, images, and the like, and is, for example, a liquid crystal display, an organic EL (Electro-Luminescence) display, or the like. The display unit 14 displays a video corresponding to the video data supplied from the processing unit 15, an image corresponding to the image data, and the like.

  The processing unit 15 includes one or a plurality of processors and their peripheral circuits. The processing unit 15 comprehensively controls the overall operation of the fracture analysis apparatus 1 and is, for example, a CPU (Central Processing Unit). The processing unit 15 includes a communication unit 11, a display unit 14, and the like so that various processes of the fracture analysis apparatus 1 are executed according to a program stored in the storage unit 12, an operation of the operation unit 13, and the like. To control the operation. The processing unit 15 executes processing based on programs (operating system program, driver program, application program, etc.) stored in the storage unit 12. The processing unit 12 can execute a plurality of programs (such as application programs) in parallel.

  The processing unit 15 includes a control unit 151 that executes steps S100, S112, and S114 in FIG. 1, a state variable calculation unit 152 that executes step S102, and a strain gradient calculation unit that executes step S104. 153, a state variable correction unit 154 that executes the process of step S106, and a break determination unit 155 that executes the processes of steps S108 and S110. Each of these units is a functional module realized by a program executed by a processor included in the processing unit 15. Or these each part may be mounted in the fracture | rupture analysis apparatus 1 as firmware.

  As described above, in the fracture analysis based on continuum damage mechanics using the finite element method, the calculated damage rate is corrected based on the strain gradient, so that the calculated damage degree depends on the element size. It becomes possible to reduce more easily.

  Note that the present invention is not limited to this embodiment. For example, in the present embodiment, hexahedral elements are used for modeling the analysis target, but other types of elements (for example, a triangle, a tetragon, a tetrahedron, a triangle column, etc.) may be used.

  Further, in the present embodiment, mild steel is assumed as an analysis target, but other materials (for example, high tension, aluminum, magnesium, etc.) may be used.

  In the present embodiment, the present invention is applied to the fracture analysis based on the continuum damage mechanics, but any (rupture) analysis can be applied as long as it is based on the calculated state variables such as stress and strain. May be.

  Moreover, in this embodiment, although the fracture | rupture analysis apparatus 1 was provided with each part shown by FIG. 8, the server apparatus not shown may be provided about the one part. The server device includes, for example, a storage unit corresponding to the storage unit 12 of the fracture analysis device 1, transmits a program, data, and the like stored in the storage unit to the fracture analysis device 1, and performs processing on the fracture analysis device 1. It may be executed. Alternatively, the server device includes a storage unit and a processing unit corresponding to the storage unit 12 and the processing unit 15 of the fracture analysis device 1, and executes processing using a program, data, and the like stored in the storage unit, Only the result may be provided to the fracture analysis apparatus 1.

  Further, a computer program for causing a computer to realize each function included in the processing unit 15 may be provided in a form recorded on a computer-readable recording medium such as a magnetic recording medium or an optical recording medium.

  It should be understood by those skilled in the art that various changes, substitutions, and modifications can be made thereto without departing from the spirit and scope of the present invention.

DESCRIPTION OF SYMBOLS 1 Break analysis apparatus 11 Communication part 12 Memory | storage part 13 Operation part 14 Display part 15 Processing part 151 Control part 152 State variable calculation part 153 Strain gradient calculation part 154 State variable correction part 155 Break determination part

Claims (11)

An apparatus for determining a state of the material based on a state variable generated inside the material according to deformation,
A storage unit for storing analysis data including at least analysis model data, material property data, and boundary condition data;
Analysis is performed by the finite element method based on the analysis data, and includes a plurality of state variables in each element of the material at one time of deformation, which include at least a state variable that affects the determination result of strain and the state of the material A state variable calculator for calculating a plurality of state variables;
A strain gradient calculation unit for calculating a strain gradient based on the strain;
A state variable correction unit that corrects a state variable that affects the determination result of the state of the material so as to reduce the element size dependency based on the strain gradient;
A state determination unit that determines the state of the material based on the plurality of state variables including a state variable that affects the determination result of the state of the modified material;
An output unit for outputting a determination result of the state of the material;
A device comprising:   The said state variable correction part calculates element size influence degree based on the said strain gradient, and corrects the state variable which influences the determination result of the said material state based on the said element size influence degree. Equipment.   The apparatus according to claim 2, wherein the element size influence degree is calculated based on the strain gradient and an increment from the strain gradient at a time immediately before the strain gradient. The element size influence degree is calculated by the following equation:

Here, f is the element size influence degree, δ is the strain gradient, Δδ is an increment of the strain gradient, and A to C are constants determined according to the material. Equipment.   The apparatus according to any one of claims 2 to 4, wherein the state variable correction unit corrects a state variable that affects the determination result of the state of the material by multiplying or dividing the element size influence degree. The state variable that affects the determination result of the state of the material is the damage rate,
The said state determination part determines with the fracture | rupture having arisen in the corresponding element of the said material, when the cumulative value to the said one time of the said damage rate corrected exceeded the threshold value. The device according to any one of the above. An apparatus for correcting a state variable generated inside a material according to deformation,
A state variable correction unit for correcting the state variable calculated using the finite element method so as to reduce the element size dependency based on the strain gradient;
A device comprising: A control method for an apparatus that includes a storage unit that stores analysis data including at least analysis model data, material property data, and boundary condition data, and that determines a state of the material based on a state variable generated in the material according to deformation. And the device is
Analysis is performed by the finite element method based on the analysis data, and includes a plurality of state variables in each element of the material at one time of deformation, which include at least a state variable that affects the determination result of strain and the state of the material Calculate multiple state variables,
A strain gradient is calculated based on the strain;
Modify the state variables that affect the determination of the state of the material to reduce element size dependency based on the strain gradient;
Determining the state of the material based on the plurality of state variables including a state variable that affects the determination result of the state of the modified material;
Outputting the judgment result of the state of the material,
A control method characterized by that. A method for controlling an apparatus for correcting a state variable generated inside a material in response to deformation, wherein the apparatus comprises:
Modifying the state variables calculated using a finite element method to reduce element size dependence based on strain gradients;
A control method characterized by that. A control program for an apparatus that includes a storage unit that stores analysis data including at least analysis model data, material property data, and boundary condition data, and that determines a state of the material based on a state variable generated inside the material according to deformation. In the device,
Analysis is performed by the finite element method based on the analysis data, and includes a plurality of state variables in each element of the material at one time of deformation, which include at least a state variable that affects the determination result of strain and the state of the material Calculate multiple state variables,
A strain gradient is calculated based on the strain;
Modify the state variables that affect the determination of the state of the material to reduce element size dependency based on the strain gradient;
Determining the state of the material based on the plurality of state variables including a state variable that affects the determination result of the state of the modified material;
Outputting the judgment result of the state of the material,
A control program characterized by causing A control program for a device that corrects a state variable generated inside a material in accordance with deformation, the device including:
Modifying the state variables calculated using a finite element method to reduce element size dependence based on strain gradients;
A control program characterized by causing

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