CN106326567A - Valuing method of plastic constitutive parameters of steel-polypropylene hybrid fiber concrete in ABAQUS - Google Patents

Abstract

The invention discloses a valuing method of plastic constitutive parameters of steel-polypropylene hybrid fiber concrete in ABAQUS. The method sufficiently considers influences on mechanical properties of concrete, caused by factors including different fiber types, volume fractions, long-diameter ratios and the like, and related parameters of a built-in concrete damage plasticity model (CDPM) in the ABAQUS are properly revised, so that the related parameters can be more accurately matched with a yield criterion, a hardening rule and a flowing law of the steel-polypropylene hybrid fiber concrete, and a very good reference is provided or refined non-linear analysis of a fiber concrete structure under a complicated stress state.

Description

The value of steel-steel-polypropylene hybrid fiber concrete Plastic Constitutive parameter in ABAQUS Method

Technical field

The invention belongs to building material technical field, be specifically related to a kind of steel-steel-polypropylene hybrid fiber based on ABAQUS The obtaining value method of concrete plastic constitutive model parameter.

Background technology

Since this century, fiber concrete has obtained swift and violent development, in order to accurately determine its real constitutive model, state Inside and outside scholar has carried out substantial amounts of research, it is proposed that the stress-strain mathematic(al) representation under various loading conditions, and is used In the middle of Finite Element Simulation Analysis, but analog result tends not to reflect well the non-linear force row of fiber concrete For, as the change after fiber adds of the mechanical characteristics such as matrix multi-shaft strength, cubic deformation, hysteresis energy consumption cannot obtain preferably Embody.At present, large-scale general finite element software ABAQUS is widely used with its powerful copying, and wherein, it is built-in Damaged plasticity model for concrete (CDPM) in the mechanics property analysis of normal concrete structure, play pivotal role, but for Fiber concrete, especially hybrid fiber concrete, this model is the most applicable, needs further to be revised, but phase Close work and be not the most seen in any report, which greatly limits the depth of investigation of this field problem, unfavorable Further genralrlization in hybrid fiber concrete material is applied.

Summary of the invention

In order to solve above-mentioned technical problem, the invention provides a kind of suitable based on large-scale general finite element software ABAQUS Mould for steel-steel-polypropylene hybrid fiber concrete (hereinafter as without doing specified otherwise, being all referred to as " hybrid fiber concrete ") The obtaining value method of property Parameters of constitutive model.

The obtaining value method of steel-steel-polypropylene hybrid fiber concrete Plastic Constitutive parameter in ABAQUS, comprises the following steps:

Step 1: the general form of proposition yield criterion correction:

The yield criterion of described steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is:

$F=\frac{1}{1-{\mathrm{\&alpha;}}^{hf}}(\stackrel{\&OverBar;}{q}-3{\mathrm{\&alpha;}}^{hf}\stackrel{\&OverBar;}{p}+{\mathrm{\&beta;}}^{hf}<{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_{max}>-{\mathrm{\&gamma;}}^{hf}<-{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_{max}>)-{\mathrm{\&sigma;}}_{c0}\&le;0---\left(1\right)$

Wherein, effective hydrostatic pressureMises equivalent stress": " represents the point of tensor Long-pending；Effectively deviatoric stress tensor For stress tensor；I is unit matrix；For maximum effective stress value；〈·〉 For taking plus sign,X represents a numerical value；Parameter alpha^hf, β^hf, γ^hfComputing formula as follows:

${\mathrm{\&alpha;}}^{hf}=\frac{{\mathrm{\&sigma;}}_{b0}^{hf}/{\mathrm{\&sigma;}}_{c0}-1}{2({\mathrm{\&sigma;}}_{b0}^{hf}/{\mathrm{\&sigma;}}_{c0})-1},{\mathrm{\&beta;}}^{hf}=\frac{{\mathrm{\&sigma;}}_{c0}}{{\mathrm{\&sigma;}}_{t0}}(1-{\mathrm{\&alpha;}}^{hf})-(1+{\mathrm{\&alpha;}}^{hf}),{\mathrm{\&gamma;}}^{hf}=\frac{3(1-K_c^{hf})}{2K_c^{hf}-1}---\left(2\right)$

In formula,For hybrid fiber concrete biaxial compression intensity, σ_c0For normal concrete uniaxial compressive strength,Define yield surface shape under plane stress state；σ_t0For normal concrete uniaxial tension test；Regulation Work as hydrostatic pressureTime the drawing of hybrid fiber concrete, the ratio of pressure radial

Step 2: correction Hardening Law:

The Hardening Law of described steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is defined as follows:

(1) steel-steel-polypropylene hybrid fiber concrete in uniaxial tension-strain stress relation is:

σ_hft=(1-d_t)E_hftε_hft (10)

$d_t=\left\{\begin{array}{cc}1-{\mathrm{\&rho;}}_t\&lsqb;{\mathrm{\&alpha;}}_1+(1.5-1.25{\mathrm{\&alpha;}}_1)x+(0.25{\mathrm{\&alpha;}}_1-0.5)x^5\&rsqb;& x\&le;1\\ 1-\frac{{\mathrm{\&rho;}}_t}{{\mathrm{\&alpha;}}_t{(x-1)}^{1.7}+x}& x>1\end{array}\right.---\left(11\right)$

α₁=1.2 (1+0.265 λ_sf+0.277λ_pf)1.2≤α₁≤2 (12)

${\mathrm{\&alpha;}}_t=\frac{0.312{\left(f_t^0\right)}^2}{1+3.366{\mathrm{\&lambda;}}_{sf}+3.858{\mathrm{\&lambda;}}_{pf}},0\&le;{\mathrm{\&alpha;}}_t\&le;1.5---\left(13\right)$

$f_{hft}^0=f_t^0(1+0.379{\mathrm{\&lambda;}}_{sf}+0.02{\mathrm{\&lambda;}}_{sf}{\mathrm{\&lambda;}}_{pf}),{\mathrm{\&epsiv;}}_{hft}^0={\mathrm{\&epsiv;}}_t^0(1+0.498{\mathrm{\&lambda;}}_{sf}+0.697{\mathrm{\&lambda;}}_{pf})---\left(14\right)$

$x={\mathrm{\&epsiv;}}_{hft}/{\mathrm{\&epsiv;}}_{hft}^0,{\mathrm{\&rho;}}_t=f_{hft}^0/\left(E_{hft}{\mathrm{\&epsiv;}}_{hft}^0\right)---\left(15\right)$

In formula, E_hft、σ_hft、ε_hftAnd d_tRepresent hybrid fiber concrete tension elastic modelling quantity, tension stress, tension respectively Strain and tension impairment value；f_t ⁰It is respectively hybrid fiber concrete and the uniaxial tension test of normal concrete； The then the most corresponding above two material peak strain under the conditions of single shaft tension, λ_sf, λ_pfRepresent steel, polypropylene fibre respectively Eigenvalue；α₁For hybrid fiber concrete uniaxial tensile stress-strain stress relation ascent stage coefficient, α_tFor hybrid fiber concrete list Relationships of tension stress with strain descending branch coefficient；ρ_tFor hybrid fiber concrete uniaxial tension test and peak strain and springform The ratio of amount；

(2) steel-steel-polypropylene hybrid fiber concrete in uniaxial compressive stress-strain stress relation is:

$\left\{\begin{array}{cc}y=ax+(3-2a)x^2+(a-2)x^3& 0\&le;x\&le;1\\ y=\frac{x}{b{(x-1)}^2+x}& x>1\end{array}\right.---\left(16\right)$

$a=28.2283-23.2771{\left(f_{hfc}^0\right)}^{0.0374}+0.4772{\mathrm{\&lambda;}}_{sf}-0.4917{\mathrm{\&lambda;}}_{pf}---\left(17\right)$

$b=1+0.3688{\left(f_{hfc}^0\right)}^{-0.2846}-{\mathrm{\&lambda;}}_{sf}-{\mathrm{\&lambda;}}_{pf}---\left(18\right)$

$f_{hfc}^0=f_c^0(1+0.206{\mathrm{\&lambda;}}_{sf}+0.388{\mathrm{\&lambda;}}_{pf}),{\mathrm{\&epsiv;}}_{hfc}^0=263.3\sqrt{f_{hfc}^0}\&times;{10}^{-6}---\left(19\right)$

$x={\mathrm{\&epsiv;}}_{hfc}/{\mathrm{\&epsiv;}}_{hfc}^0,y={\mathrm{\&sigma;}}_{hfc}/f_{hfc}^0---\left(20\right)$

In formula, σ_hfcAnd ε_hfcRepresent hybrid fiber concrete compression chord and compressive strain respectively；It is respectively mixed Miscellaneous fiber concrete and the uniaxial compressive strength of normal concrete；For hybrid fiber concrete under the conditions of uniaxial compression Peak strain, λ_sf, λ_pfRepresent the eigenvalue of steel, polypropylene fibre respectively；A is hybrid fiber concrete uniaxial compressive stress-strain Relation ascent stage coefficient, b is hybrid fiber concrete uniaxial compressive stress-strain stress relation descending branch coefficient；

It is pointed out that described (1), (2) step sets forth single shaft draw, press in the case of stress-strain complete Curve, strain therein includes elastic strain and plastic strain two parts, and is using ABAQUS software to carry out finite element fraction Stress-plastic strain full curve only need to be provided during analysis, therefore, then need when inputting strain value to deduct elastic strain in advance；

Step 3: correction flow rule:

The dilative angle of described steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is defined as follows:

${\mathrm{\&psi;}}^{hf}=\arctan \left(\sqrt{\frac{\left|\right({\mathrm{\&phi;}}_1^{hf}{\stackrel{\&OverBar;}{q}}_2-{\mathrm{\&phi;}}_2^{hf}{\stackrel{\&OverBar;}{q}}_1|}{\left|{\left({\mathrm{\&phi;}}_1^{hf}\right)}^2{\left({\mathrm{\&phi;}}_2^{hf}\right)}^2({\stackrel{\&OverBar;}{q}}_2^2-{\stackrel{\&OverBar;}{q}}_1^2)\right|}}\right)---\left(27\right)$

In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, φ^hfFor hybrid fiber concrete Plastic Flow angle, Mises Equivalent stressValue under each parameter subscript " 1 ", " 2 " the most corresponding two kinds of different stress；

According to the definition of formula (27), can be calculated between the dilative angle of hybrid fiber concrete and fiber characteristic value Corresponding relation.

And, in formula (2), the ratio of described hybrid fiber concrete tension and compression meridianComputational methods be:

$K_c^{hf}=\frac{\stackrel{\&OverBar;}{q}{\left(TM\right)}^{hf}}{\stackrel{\&OverBar;}{q}{\left(CM\right)}^{hf}}=\frac{\stackrel{\&OverBar;}{q}\left(TM\right)\&CenterDot;k_t}{\stackrel{\&OverBar;}{q}\left(CM\right)\&CenterDot;k_c}=K_c\&CenterDot;\frac{k_t}{k_c}---\left(3\right)$

In formula, K_cMeridian value is drawn for normal concreteWith pressure radial valueRatio, k_t、k_cIt is respectively Normal concrete is drawn by assorted fibre, pressure radial affect coefficient, computational methods are as follows:

k_t=1+0.08 λ_sf+0.132λ_pf, k_c=1+0.056 λ_sf (4)

In formula, λ_sf, λ_pfRepresent the eigenvalue of steel, polypropylene fibre respectively.

And, in formula (2), described hybrid fiber concrete biaxial compression intensity and normal concrete uniaxial compressive strength RatioComputational methods as follows:

(1) according to elastic plastic theory, isobaric biaxial compression hot spot is positioned at and draws on meridian, makes hybrid fiber concrete Biaxial compression intensity is(pressure is negative), stress state isσ₁, σ₂, σ₃Respectively x, Principal stress on y, z direction, this stress state hydrostatic pressing force value ξ of correspondence under Haigh-Westergaard coordinate system is answered with inclined Force valueIt is respectively as follows:

$\mathrm{\&xi;}=\frac{I_1}{\sqrt{3}}=\frac{-2{\mathrm{\&sigma;}}_{b0}^{hf}}{\sqrt{3}}---\left(5\right)$

${\mathrm{\&rho;}}_t^{hf}=\sqrt{2J_2}=\sqrt{2\&CenterDot;\frac{1}{6}\&CenterDot;\&lsqb;{(0+{\mathrm{\&sigma;}}_{b0}^{hf})}^2+{(0+{\mathrm{\&sigma;}}_{b0}^{hf})}^2+{(-{\mathrm{\&sigma;}}_{b0}^{hf}+{\mathrm{\&sigma;}}_{b0}^{hf})}^2\&rsqb;}=\sqrt{\frac{2}{3}}{\mathrm{\&sigma;}}_{b0}^{hf}---\left(6\right)$

In formula, I₁For principal stress tensor the first invariant, I₁=σ₁+σ₂+σ₃；J₂For deviatoric stress tensor the second invariant；

(2) the deviatoric stress value of hybrid fiber concrete on the different drop-down meridians of hydrostatic pressureAdvise as follows:

${\mathrm{\&rho;}}_t^{hf}=\frac{-a_1-\sqrt{a_1^2-4a_2(a_0-\frac{\mathrm{\&xi;}}{{\mathrm{\&sigma;}}_{c0}})}}{2a_2}\&CenterDot;{\mathrm{\&sigma;}}_{c0}\&CenterDot;k_t---\left(7\right)$

In formula, a₀、a₁、a₂It is respectively fitting coefficient, formula (5) is brought into formula (7), connection solution formula (6) and (7), can obtain:

$\frac{8{a_2}^2}{3{k_t}^2}\&CenterDot;{\left(\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}\right)}^2+\left(\frac{4\sqrt{2}{a}_1{a}_2+8a_2{k}_t}{\sqrt{3}{k}_t}\right)\&CenterDot;\left(\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}\right)+4a_2{a}_0=0---\left(8\right)$

Each fitting coefficient a in formula₀、a₁、a₂Value suggestion be respectively a₀=0.1775, a₁=-1.4554, a₂=- 0.1576, they are substituted in formula (8), arrangement obtains

$\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}=\frac{-(0.749/k_t-0.728)+\sqrt{{(0.749/k_t-0.728)}^2+0.03/{k_t}^2}}{0.132/{k_t}^2}---\left(9\right)$

In formula, k_tFor assorted fibre, normal concrete being drawn the meridianal coefficient that affects, computational methods are as follows: k_t=1+ 0.08λ_sf+0.132λ_pf, in formula, λ_sf, λ_pfRepresent the eigenvalue of steel, polypropylene fibre respectively.

And, in step 2, for single shaft pulled condition, the strain of elastic limit point takes hybrid fiber concrete and reaches peak value Strain value corresponding during intensity, therefore, its plastic strain computing formula is as follows:

$\left\{\begin{array}{cc}{\widetilde{\mathrm{\&epsiv;}}}_t^{pl}=0& {\mathrm{\&sigma;}}_t\&le;f_{hft}^0\\ {\widetilde{\mathrm{\&epsiv;}}}_t^{pl}={\mathrm{\&epsiv;}}_t-{\mathrm{\&sigma;}}_t/E_{hft}& {\mathrm{\&sigma;}}_t>f_{hft}^0\end{array}\right.---\left(21\right)$

For uniaxial compression situation, elastic limit point strains and takes strain value corresponding at the 1/3 of peak strength, therefore, and its Plastic strain computing formula is:

$\left\{\begin{array}{cc}{\widetilde{\mathrm{\&epsiv;}}}_c^{pl}=0& {\mathrm{\&sigma;}}_c\&le;f_{hfc}^0/3\\ {\widetilde{\mathrm{\&epsiv;}}}_c^{pl}={\mathrm{\&epsiv;}}_c-{\mathrm{\&sigma;}}_c/E_{hfc}& {\mathrm{\&sigma;}}_c>f_{hfc}^0/3\end{array}\right.---\left(22\right)$

In formula,For under single shaft pulled condition by tensile plastic strain,For in the case of uniaxial compression by compressive plastic strain；ε_t For tension overall strain, ε under single shaft pulled condition_cFor pressurized overall strain in the case of uniaxial compression；σ_tAnswer for single shaft pulled condition is drop-down Power, σ_cCompressive stress under single shaft pulled condition；E_hfcFor hybrid fiber concrete pressurized elastic modelling quantity.

And, in step 3, the derivation of formula (27) is:

(1) flow rule uses non-associated flow lawWherein, Plastic Flow potential function g^hfUse D- P Hyperbolic Equation

$g^{hf}=\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{\stackrel{\&OverBar;}{q}}^2}-\stackrel{\&OverBar;}{p}{\mathrm{tan\&psi;}}^{hf}=0---\left(23\right)$

In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, describe the yield surface of this material in meridional plane with quiet The angle of water pressure axle；e^hfFor the eccentricity of hybrid fiber concrete plastic potential function, define and linear Drucker- The progressive degree of Prager plastic potential function, e in this method^hfTake 0.1；e^hfσ_t0Then represent this plastic potential hyperbola and Asymptote distance between hydrostatic pressure y-intercept；

(2) Plastic Flow of supposition hybrid fiber concrete direction at inclined plane arbitrfary point is consistent, and total plastic property should Become flow direction identical with plastic strain increment flow direction, i.e. hybrid fiber concrete Plastic Flow angle φ^hfWith Lode angle not Relevant；

By the most right for flow potential formula (23) both sidesSeek local derviation:

${\mathrm{\&phi;}}^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{\stackrel{\&OverBar;}{q}}^2}=-\stackrel{\&OverBar;}{q}---\left(24\right)$

Take two kinds of different stress to plastic potential parameter ψ^hfDemarcate:

${\mathrm{\&phi;}}_1^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{(e^{hf}{\mathrm{\&sigma;}}_{t0}\&CenterDot;{\mathrm{tan\&psi;}}^{hf})}^2+{{\stackrel{\&OverBar;}{q}}_1}^2}=-{\stackrel{\&OverBar;}{q}}_1---\left(25\right)$

${\mathrm{\&phi;}}_2^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{{\stackrel{\&OverBar;}{q}}_2}^2}=-{\stackrel{\&OverBar;}{q}}_2---\left(26\right)$

In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, e^hfBias for hybrid fiber concrete plastic potential function Rate, φ^hfFor hybrid fiber concrete Plastic Flow angle, Mises equivalent stressEach parameter subscript " 1 ", " 2 " point Value under not corresponding two kinds of different stress；

Simultaneous Equations (25) and (26), eliminate e^hfAnd solve ψ^hfAvailable:

${\mathrm{\&psi;}}^{hf}=\arctan \left(\sqrt{\frac{\left|\right({\mathrm{\&phi;}}_1^{hf}{\stackrel{\&OverBar;}{q}}_2-{\mathrm{\&phi;}}_2^{hf}{\stackrel{\&OverBar;}{q}}_1|}{\left|{\left({\mathrm{\&phi;}}_1^{hf}\right)}^2{\left({\mathrm{\&phi;}}_2^{hf}\right)}^2({\stackrel{\&OverBar;}{q}}_2^2-{\stackrel{\&OverBar;}{q}}_1^2)\right|}}\right)---\left(27\right)$

In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, φ^hfFor hybrid fiber concrete Plastic Flow angle, Mises Equivalent stressValue under each parameter subscript " 1 ", " 2 " the most corresponding two kinds of different stress.

And, in formula (27)

${\mathrm{\&phi;}}^{hf}=\sqrt{\frac{1}{2}\&CenterDot;\&lsqb;{({\mathrm{\&epsiv;}}_1^{pl}-{\mathrm{\&epsiv;}}_2^{pl})}^2+{({\mathrm{\&epsiv;}}_1^{pl}-{\mathrm{\&epsiv;}}_3^{pl})}^2+{({\mathrm{\&epsiv;}}_2^{pl}-{\mathrm{\&epsiv;}}_3^{pl})}^2\&rsqb;}/\frac{{\mathrm{\&epsiv;}}_1^{pl}+{\mathrm{\&epsiv;}}_2^{pl}+{\mathrm{\&epsiv;}}_3^{pl}}{3}---\left(28\right)$

In formula,It is respectively the plastic strain of x, y, z direction；

By under two kinds of different stressValue substitutes into formula (28) respectively, i.e. available correspondenceWithValue.In formulaComputing formula as follows:

$\begin{array}{c}{\mathrm{\&epsiv;}}_1^{pl}={\mathrm{\&epsiv;}}_1-\&lsqb;{\mathrm{\&sigma;}}_1-v({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_3)\&rsqb;/E\\ {\mathrm{\&epsiv;}}_2^{pl}={\mathrm{\&epsiv;}}_2-\&lsqb;{\mathrm{\&sigma;}}_2-v({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_3)\&rsqb;/E\\ {\mathrm{\&epsiv;}}_3^{pl}={\mathrm{\&epsiv;}}_3-\&lsqb;{\mathrm{\&sigma;}}_3-v({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_2)\&rsqb;/E\end{array}---\left(29\right)$

In formula, ε₁, ε₂, ε₃It is respectively the overall strain of x, y, z direction；σ₁, σ₂, σ₃It is respectively principal stress on x, y, z direction；V is Poisson's ratio；E is elastic modelling quantity.

And, according to change between dilative angle and the fiber characteristic value of hybrid fiber concrete in formula (24)～(29) Rule, it is proposed that a succinct computing formula

ψ^hf=ψ₀(1-0.89λ_sf-0.196λ_pf) (30)

Wherein, ψ₀For the dilative angle of normal concrete, span is between 30 °～40 °.

And, the eigenvalue λ of steel fibre_sf=V_sf(l_sf/d_sf), the eigenvalue λ of polypropylene fibre_pf=V_pf(l_pf/d_pf)； V_sf, V_pfIt is respectively steel, the volume parameter of polypropylene fibre；l_sf, l_pfIt is respectively steel, the length of polypropylene fibre；d_sf, d_pfRespectively For steel, the diameter of polypropylene fibre.

Present invention have an advantage that the present invention is based on interior in now widely used large-scale general finite element software ABAQUS The damaged plasticity model for concrete (CDPM) put, has taken into full account the factors pair such as different fiber type, volume volume and draw ratio The impact of mechanical performance of concrete, has carried out suitably revising to the relevant parameter of model so that it is the steel-polypropylene that coincide mixes fibre The dimension yield criterion of concrete, Hardening Law and flow rule such that it is able to prediction hybrid fiber concrete material the most accurately The mechanical properties such as the multi-shaft strength of material, cubic deformation, and the bearing capacity of respective members, hysteretic energy, tie for fiber concrete The structure nonlinear analysis that becomes more meticulous under complex stress condition provides a good reference.

Accompanying drawing explanation

The method overview flow chart of Fig. 1: the embodiment of the present invention；

The testing of materials compressive stress of Fig. 2: the embodiment of the present invention-inelastic strain relation comparison diagram；

The testing of materials tension of Fig. 3: the embodiment of the present invention-cracking strain stress relation comparison diagram；

The testing of materials uniaxial compression cyclic loading and unloading curve comparison figure of Fig. 4: the embodiment of the present invention；

The component test pillar hysteresis loop comparison diagram comparison diagram of Fig. 5: the embodiment of the present invention；

The component test pillar crack actual distribution comparison diagram of Fig. 6: the embodiment of the present invention；

The component test pillar stress simulation Comparative result figure of Fig. 7: the embodiment of the present invention.

Detailed description of the invention

Understand and implement the present invention for the ease of those of ordinary skill in the art, below in conjunction with the accompanying drawings and embodiment is to this Bright it is described in further detail, it will be appreciated that enforcement example described herein is merely to illustrate and explains the present invention, not For limiting the present invention.

The obtaining value method of steel-steel-polypropylene hybrid fiber concrete Plastic Constitutive parameter in a kind of ABAQUS, including following step Rapid:

The yield criterion of step 1 steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is:

$F=\frac{1}{1-{\mathrm{\&alpha;}}^{hf}}(\stackrel{\&OverBar;}{q}-3{\mathrm{\&alpha;}}^{hf}\stackrel{\&OverBar;}{p}+{\mathrm{\&beta;}}^{hf}<{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_{max}>-{\mathrm{\&gamma;}}^{hf}<-{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_{max}>)-{\mathrm{\&sigma;}}_{c0}\&le;0---\left(1\right)$

Wherein, effective hydrostatic pressureMises equivalent stress": " represents the point of tensor Long-pending；Effectively deviatoric stress tensor For stress tensor；I is unit matrix；For maximum effective stress value；<·> For taking plus sign, i.e.X represents a numerical value；Parameter alpha^hf, β^hf, γ^hfComputing formula as follows:

${\mathrm{\&alpha;}}^{hf}=\frac{{\mathrm{\&sigma;}}_{b0}^{hf}/{\mathrm{\&sigma;}}_{c0}-1}{2({\mathrm{\&sigma;}}_{b0}^{hf}/{\mathrm{\&sigma;}}_{c0})-1},{\mathrm{\&beta;}}^{hf}=\frac{{\mathrm{\&sigma;}}_{c0}}{{\mathrm{\&sigma;}}_{t0}}(1-{\mathrm{\&alpha;}}^{hf})-(1+{\mathrm{\&alpha;}}^{hf}),{\mathrm{\&gamma;}}^{hf}=\frac{3(1-K_c^{hf})}{2K_c^{hf}-1}---\left(2\right)$

In formula,For hybrid fiber concrete biaxial compression intensity, σ_c0For normal concrete uniaxial compressive strength,Define yield surface shape under plane stress state；σ_t0For normal concrete uniaxial tension test；Regulation Work as hydrostatic pressureTime the drawing of hybrid fiber concrete, the ratio of pressure radial

The ratio of step 1.1 hybrid fiber concrete tension and compression meridianComputational methods be:

$K_c^{hf}=\frac{\stackrel{\&OverBar;}{q}{\left(TM\right)}^{hf}}{\stackrel{\&OverBar;}{q}{\left(CM\right)}^{hf}}=\frac{\stackrel{\&OverBar;}{q}\left(TM\right)\&CenterDot;k_t}{\stackrel{\&OverBar;}{q}\left(CM\right)\&CenterDot;k_c}=K_c\&CenterDot;\frac{k_t}{k_c}---\left(3\right)$

In formula, K_cMeridian value is drawn for normal concreteWith pressure radial valueRatio, k_t、k_cIt is respectively Normal concrete is drawn by assorted fibre, pressure radial affect coefficient, computational methods are as follows:

k_t=1+0.08 λ_sf+0.132λ_pf, k_c=1+0.056 λ_sf (4)

In formula, λ_sf=V_sf(l_sf/d_sf), λ_pf=V_pf(l_pf/d_pf) represent the eigenvalue of steel, polypropylene fibre respectively；V_sf, V_pfIt is respectively steel, the volume parameter of polypropylene fibre；l_f, l_fIt is respectively steel, the length of polypropylene fibre, d_f, d_fBe respectively steel, The diameter of polypropylene fibre.

The ratio of step 1.2 hybrid fiber concrete biaxial compression intensity and normal concrete uniaxial compressive strength Computational methods as follows:

(1) according to elastic plastic theory, isobaric biaxial compression hot spot is positioned at and draws on meridian, makes hybrid fiber concrete Biaxial compression intensity is(pressure is negative), stress state isσ₁, σ₂, σ₃Respectively x, Principal stress on y, z direction, this stress state hydrostatic pressing force value ξ of correspondence under Haigh-Westergaard coordinate system is answered with inclined Force valueIt is respectively as follows:

$\mathrm{\&xi;}=\frac{I_1}{\sqrt{3}}=\frac{-2{\mathrm{\&sigma;}}_{b0}^{hf}}{\sqrt{3}}---\left(5\right)$

${\mathrm{\&rho;}}_t^{hf}=\sqrt{2J_2}=\sqrt{2\&CenterDot;\frac{1}{6}\&CenterDot;\&lsqb;{(0+{\mathrm{\&sigma;}}_{b0}^{hf})}^2+{(0+{\mathrm{\&sigma;}}_{b0}^{hf})}^2+{(-{\mathrm{\&sigma;}}_{b0}^{hf}+{\mathrm{\&sigma;}}_{b0}^{hf})}^2\&rsqb;}=\sqrt{\frac{2}{3}}{\mathrm{\&sigma;}}_{b0}^{hf}---\left(6\right)$

In formula, I₁For principal stress tensor the first invariant, I₁=σ₁+σ₂+σ₃；J₂For deviatoric stress tensor the second invariant；

(2) the deviatoric stress value of hybrid fiber concrete on the different drop-down meridians of hydrostatic pressureAdvise as follows:

${\mathrm{\&rho;}}_t^{hf}=\frac{-a_1-\sqrt{a_1^2-4a_2(a_0-\frac{\mathrm{\&xi;}}{{\mathrm{\&sigma;}}_{c0}})}}{2a_2}\&CenterDot;{\mathrm{\&sigma;}}_{c0}\&CenterDot;k_t---\left(7\right)$

In formula, a₀、a₁、a₂It is respectively fitting coefficient；

Formula (5) is brought into formula (7), connection solution formula (6) and (7), can obtain:

$\frac{8{a_2}^2}{3{k_t}^2}\&CenterDot;{\left(\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}\right)}^2+\left(\frac{4\sqrt{2}{a}_1{a}_2+8a_2{k}_t}{\sqrt{3}{k}_t}\right)\&CenterDot;\left(\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}\right)+4a_2{a}_0=0---\left(8\right)$

Each fitting coefficient a in formula₀、a₁、a₂Value suggestion be respectively a₀=0.1775, a₁=-1.4554, a₂=- 0.1576, they are substituted in formula (8), arrangement obtains

$\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}=\frac{-(0.749/k_t-0.728)+\sqrt{{(0.749/k_t-0.728)}^2+0.03/{k_t}^2}}{0.132/{k_t}^2}---\left(9\right)$

It should be noted that and work as k_tWhen=1, the most do not consider that assorted fibre is to yield surface shape under plane stress state Impact, this formula then deteriorates toResult of calculation isIdentical with the suggestion value of normal concrete, show these public affairs The suitability of formula is strong, also sets up normal concrete.

The Hardening Law of step 2 steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is defined as follows:

(1) steel-steel-polypropylene hybrid fiber concrete in uniaxial tension-strain stress relation is:

σ_hft=(1-d_t)E_hftε_hft (10)

$d_t=\left\{\begin{array}{cc}1-{\mathrm{\&rho;}}_t\&lsqb;{\mathrm{\&alpha;}}_1+(1.5-1.25{\mathrm{\&alpha;}}_1)x+(0.25{\mathrm{\&alpha;}}_1-0.5)x^5\&rsqb;& x\&le;1\\ 1-\frac{{\mathrm{\&rho;}}_t}{{\mathrm{\&alpha;}}_t{(x-1)}^{1.7}+x}& x>1\end{array}\right.---\left(11\right)$

α₁=1.2 (1+0.265 λ_sf+0.277λ_pf)1.2≤α₁≤2 (12)

${\mathrm{\&alpha;}}_t=\frac{0.312{\left(f_t^0\right)}^2}{1+3.366{\mathrm{\&lambda;}}_{sf}+3.858{\mathrm{\&lambda;}}_{pf}},0\&le;{\mathrm{\&alpha;}}_t\&le;1.5---\left(13\right)$

$f_{hft}^0=f_t^0(1+0.379{\mathrm{\&lambda;}}_{sf}+0.02{\mathrm{\&lambda;}}_{sf}{\mathrm{\&lambda;}}_{pf}),{\mathrm{\&epsiv;}}_{hft}^0={\mathrm{\&epsiv;}}_t^0(1+0.498{\mathrm{\&lambda;}}_{sf}+0.697{\mathrm{\&lambda;}}_{pf})---\left(14\right)$

$x={\mathrm{\&epsiv;}}_{hft}/{\mathrm{\&epsiv;}}_{hft}^0,{\mathrm{\&rho;}}_t=f_{hft}^0/\left(E_{hft}{\mathrm{\&epsiv;}}_{hft}^0\right)---\left(15\right)$

In formula, E_hft、σ_hft、ε_hftAnd d_tRepresent hybrid fiber concrete tension elastic modelling quantity, tension stress, tension respectively Strain and tension impairment value；f_t ⁰It is respectively hybrid fiber concrete and the uniaxial tension test of normal concrete； The then the most corresponding above two material peak strain under the conditions of single shaft tension, λ_sf, λ_pfRepresent steel, polypropylene fibre respectively Eigenvalue；α₁For hybrid fiber concrete uniaxial tensile stress-strain stress relation ascent stage coefficient, α_tFor hybrid fiber concrete list Relationships of tension stress with strain descending branch coefficient；ρ_tFor hybrid fiber concrete uniaxial tension test and peak strain and springform The ratio of amount；The physical significance of other parameters is with the most identical.

(2) steel-steel-polypropylene hybrid fiber concrete in uniaxial compressive stress-strain stress relation is:

$\left\{\begin{array}{cc}y=ax+(3-2a)x^2+(a-2)x^3& 0\&le;x\&le;1\\ y=\frac{x}{b{(x-1)}^2+x}& x>1\end{array}\right.---\left(16\right)$

$a=28.2283-23.2771{\left(f_{hfc}^0\right)}^{0.0374}+0.4772{\mathrm{\&lambda;}}_{sf}-0.4917{\mathrm{\&lambda;}}_{pf}---\left(17\right)$

$b=1+0.3688{\left(f_{hfc}^0\right)}^{-0.2846}-{\mathrm{\&lambda;}}_{sf}-{\mathrm{\&lambda;}}_{pf}---\left(18\right)$

$f_{hfc}^0=f_c^0(1+0.206{\mathrm{\&lambda;}}_{sf}+0.388{\mathrm{\&lambda;}}_{pf}),{\mathrm{\&epsiv;}}_{hfc}^0=263.3\sqrt{f_{hfc}^0}\&times;{10}^{-6}---\left(19\right)$

$x={\mathrm{\&epsiv;}}_{hfc}/{\mathrm{\&epsiv;}}_{hfc}^0,y={\mathrm{\&sigma;}}_{hfc}/f_{hfc}^0---\left(20\right)$

In formula, σ_hfcAnd ε_hfcRepresent hybrid fiber concrete compression chord and compressive strain respectively；It is respectively mixed Miscellaneous fiber concrete and the uniaxial compressive strength of normal concrete；For hybrid fiber concrete under the conditions of uniaxial compression Peak strain；λ_sf, λ_pfRepresent the eigenvalue of steel, polypropylene fibre respectively；A is hybrid fiber concrete uniaxial compressive stress-strain Relation ascent stage coefficient, b is hybrid fiber concrete uniaxial compressive stress-strain stress relation descending branch coefficient；The physics of other parameters Meaning is with the most identical.

It is pointed out that above-mentioned (1), (2) step sets forth single shaft draw, press in the case of stress-strain complete Curve, strain therein includes elastic strain and plastic strain two parts, and is using ABAQUS software to carry out finite element fraction Stress-plastic strain full curve only need to be provided during analysis, therefore, then need when inputting strain value to deduct elastic strain in advance.

(3) for single shaft pulled condition, the strain of elastic limit point takes hybrid fiber concrete and reaches corresponding during peak strength Strain value, therefore, its plastic strain computing formula is as follows:

$\left\{\begin{array}{cc}{\widetilde{\mathrm{\&epsiv;}}}_t^{pl}=0& {\mathrm{\&sigma;}}_t\&le;f_{hft}^0\\ {\widetilde{\mathrm{\&epsiv;}}}_t^{pl}={\mathrm{\&epsiv;}}_t-{\mathrm{\&sigma;}}_t/E_{hft}& {\mathrm{\&sigma;}}_t>f_{hft}^0\end{array}\right.---\left(21\right)$

For uniaxial compression situation, elastic limit point strains and takes strain value corresponding at the 1/3 of peak strength, therefore, and its Plastic strain computing formula is:

$\left\{\begin{array}{cc}{\widetilde{\mathrm{\&epsiv;}}}_c^{pl}=0& {\mathrm{\&sigma;}}_c\&le;f_{hfc}^0/3\\ {\widetilde{\mathrm{\&epsiv;}}}_c^{pl}={\mathrm{\&epsiv;}}_c-{\mathrm{\&sigma;}}_c/E_{hfc}& {\mathrm{\&sigma;}}_c>f_{hfc}^0/3\end{array}\right.---\left(22\right)$

In formula,For under single shaft pulled condition by tensile plastic strain,For in the case of uniaxial compression by compressive plastic strain；ε_t For tension overall strain, ε under single shaft pulled condition_cFor pressurized overall strain in the case of uniaxial compression；σ_tAnswer for single shaft pulled condition is drop-down Power, σ_cCompressive stress under single shaft pulled condition；E_hfcFor hybrid fiber concrete pressurized elastic modelling quantity.

The dilative angle of step 3 steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is defined as follows:

(1) this flow rule uses non-associated flow lawWherein, Plastic Flow potential function g^hfUse D-P Hyperbolic Equation, i.e.

$g^{hf}=\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{\stackrel{\&OverBar;}{q}}^2}-\stackrel{\&OverBar;}{p}{\mathrm{tan\&psi;}}^{hf}=0---\left(23\right)$

In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, describe the yield surface of this material in meridional plane with quiet The angle of water pressure axle；e^hfFor the eccentricity of hybrid fiber concrete plastic potential function, define and linear Drucker- The progressive degree of Prager plastic potential function, e in this method^hfTake 0.1；e^hfσ_t0Then represent this plastic potential hyperbola and Asymptote distance between hydrostatic pressure y-intercept.

(2) method assumes that the Plastic Flow of the hybrid fiber concrete direction at inclined plane arbitrfary point is consistent, and always Plastic strain flow direction is identical with plastic strain increment flow direction, i.e. hybrid fiber concrete Plastic Flow angle φ^hfWith Lode angle is uncorrelated.

By the most right for flow potential formula (23) both sidesSeek local derviation:

${\mathrm{\&phi;}}^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{\stackrel{\&OverBar;}{q}}^2}=-\stackrel{\&OverBar;}{q}---\left(24\right)$

Take two kinds of different stress to plastic potential parameter ψ^hfDemarcate:

${\mathrm{\&phi;}}_1^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{(e^{hf}{\mathrm{\&sigma;}}_{t0}\&CenterDot;{\mathrm{tan\&psi;}}^{hf})}^2+{{\stackrel{\&OverBar;}{q}}_1}^2}=-{\stackrel{\&OverBar;}{q}}_1---\left(25\right)$

${\mathrm{\&phi;}}_2^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{{\stackrel{\&OverBar;}{q}}_2}^2}=-{\stackrel{\&OverBar;}{q}}_2---\left(26\right)$

Value in formula, under each parameter subscript " 1 ", " 2 " the most corresponding two kinds of different stress.

Simultaneous Equations (25) and (26), eliminate e^hfAnd solve ψ^hfAvailable:

${\mathrm{\&psi;}}^{hf}=\arctan \left(\sqrt{\frac{\left|\right({\mathrm{\&phi;}}_1^{hf}{\stackrel{\&OverBar;}{q}}_2-{\mathrm{\&phi;}}_2^{hf}{\stackrel{\&OverBar;}{q}}_1|}{\left|{\left({\mathrm{\&phi;}}_1^{hf}\right)}^2{\left({\mathrm{\&phi;}}_2^{hf}\right)}^2({\stackrel{\&OverBar;}{q}}_2^2-{\stackrel{\&OverBar;}{q}}_1^2)\right|}}\right)---\left(27\right)$

In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, φ^hfFor hybrid fiber concrete Plastic Flow angle, Mises Equivalent stressValue under each parameter subscript " 1 ", " 2 " the most corresponding two kinds of different stress；

Wherein

${\mathrm{\&phi;}}^{hf}=\sqrt{\frac{1}{2}\&CenterDot;\&lsqb;{({\mathrm{\&epsiv;}}_1^{pl}-{\mathrm{\&epsiv;}}_2^{pl})}^2+{({\mathrm{\&epsiv;}}_1^{pl}-{\mathrm{\&epsiv;}}_3^{pl})}^2+{({\mathrm{\&epsiv;}}_2^{pl}-{\mathrm{\&epsiv;}}_3^{pl})}^2\&rsqb;}/\frac{{\mathrm{\&epsiv;}}_1^{pl}+{\mathrm{\&epsiv;}}_2^{pl}+{\mathrm{\&epsiv;}}_3^{pl}}{3}---\left(28\right)$

In formula,It is respectively the plastic strain of x, y, z direction；

By under two kinds of different stressValue substitutes into formula (28) respectively, i.e. available correspondenceWithValue.In formulaComputing formula as follows:

$\begin{array}{c}{\mathrm{\&epsiv;}}_1^{pl}={\mathrm{\&epsiv;}}_1-\&lsqb;{\mathrm{\&sigma;}}_1-v({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_3)\&rsqb;/E\\ {\mathrm{\&epsiv;}}_2^{pl}={\mathrm{\&epsiv;}}_2-\&lsqb;{\mathrm{\&sigma;}}_2-v({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_3)\&rsqb;/E\\ {\mathrm{\&epsiv;}}_3^{pl}={\mathrm{\&epsiv;}}_3-\&lsqb;{\mathrm{\&sigma;}}_3-v({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_2)\&rsqb;/E\end{array}---\left(29\right)$

In formula, ε₁, ε₂, ε₃It is respectively the overall strain of x, y, z direction；σ₁, σ₂, σ₃It is respectively principal stress on x, y, z direction；V is Poisson's ratio；E is elastic modelling quantity.

(3) according to formula (24)～the definition of (29), dilative angle and the fiber of hybrid fiber concrete can be calculated Corresponding relation between eigenvalue.For facilitating the application of this method further, according to above-mentioned Changing Pattern between the two, we Method suggested a succinct computing formula, i.e.

ψ^hf=ψ₀(1-0.89λ_sf-0.196λ_pf) (30)

Wherein, ψ₀For the dilative angle of normal concrete, span is between 30 °～40 °.

Testing of materials result verification: in each parameter input ABAQUS software that will be obtained by above-mentioned modification method, calculate Hybrid fiber concrete is the response of material under single shaft dullness tension, pressurized, circulation tension and compression load action, and by itself and test knot Fruit contrast, as shown in accompanying drawing 2,3,4, comparing result shows that numerical result and result of the test are coincide good.

Component test result verification: in each parameter input ABAQUS software that will be obtained by above-mentioned modification method, calculate Hybrid fiber concrete post component response under Frequency Cyclic Static Loading, and by itself and comparison of test results, as accompanying drawing 5, 6, shown in 7, comparing result shows that numerical result and result of the test are coincide good.

The present invention moulds based on built-in concrete damage in now widely used large-scale general finite element software ABAQUS Property model (CDPM), has taken into full account that the factors such as different fiber type, volume volume and draw ratio are to mechanical performance of concrete Impact, has carried out suitably revising to the relevant parameter of model so that it is the surrender of the steel-steel-polypropylene hybrid fiber concrete that coincide is accurate Then, Hardening Law and flow rule such that it is able to the prediction multi-shaft strength of hybrid fiber concrete material, volume the most accurately Deformation, and the mechanical property such as the bearing capacity of respective members, hysteretic energy, for fiber concrete structure under complex stress condition The nonlinear analysis that becomes more meticulous provide a good reference.

It should be appreciated that the part that this specification does not elaborates belongs to prior art.

It should be appreciated that the above-mentioned description for preferred embodiment is more detailed, can not therefore be considered this The restriction of invention patent protection scope, those of ordinary skill in the art, under the enlightenment of the present invention, is weighing without departing from the present invention Profit requires under the ambit protected, it is also possible to make replacement or deformation, within each falling within protection scope of the present invention, this The bright scope that is claimed should be as the criterion with claims.

Claims (8)

1. The obtaining value method of steel-steel-polypropylene hybrid fiber concrete Plastic Constitutive parameter in 1.ABAQUS, it is characterised in that include with Lower step:

   Step 1: the general form of proposition yield criterion correction:

   The yield criterion of described steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is:

   $F=\frac{1}{1-{\mathrm{\&alpha;}}^{hf}}(\stackrel{\&OverBar;}{q}-3{\mathrm{\&alpha;}}^{hf}\stackrel{\&OverBar;}{p}+{\mathrm{\&beta;}}^{hf}<{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_{\max }>-{\mathrm{\&gamma;}}^{hf}<{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}}_{max}>)-{\mathrm{\&sigma;}}_{c0}\&le;0---\left(1\right)$

   Wherein, effective hydrostatic pressureMises equivalent stress": " represents the dot product of tensor；Have Effect deviatoric stress tensor For stress tensor；I is unit matrix；For maximum effective stress value；<>is for just taking Symbol,X represents a numerical value；Parameter alpha^hf, β^hf, γ^hfComputing formula as follows:

   ${\mathrm{\&alpha;}}^{hf}=\frac{{\mathrm{\&sigma;}}_{b0}^{hf}/{\mathrm{\&sigma;}}_{c0}-1}{2({\mathrm{\&sigma;}}_{b0}^{hf}/{\mathrm{\&sigma;}}_{c0})-1},{\mathrm{\&beta;}}^{hf}=\frac{{\mathrm{\&sigma;}}_{c0}}{{\mathrm{\&sigma;}}_{t0}}(1-{\mathrm{\&alpha;}}^{hf})-(1+{\mathrm{\&alpha;}}^{hf}),{\mathrm{\&gamma;}}^{hf}=\frac{3(1-K_c^{hf})}{2K_c^{hf}-1}---\left(2\right)$

   In formula,For hybrid fiber concrete biaxial compression intensity, σ_c0For normal concrete uniaxial compressive strength,Fixed Justice yield surface shape under plane stress state；σ_t0For normal concrete uniaxial tension test；Define and work as hydrostatic PressureTime the drawing of hybrid fiber concrete, the ratio of pressure radial

   Step 2: correction Hardening Law:

   The Hardening Law of described steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is defined as follows:

   (1) steel-steel-polypropylene hybrid fiber concrete in uniaxial tension-strain stress relation is:

   σ_hft=(1-d_t)E_hftε_hft (10)

   $d_t=\left\{\begin{array}{cc}1-{\mathrm{\&rho;}}_t\&lsqb;{\mathrm{\&alpha;}}_1+(1.5-1.25{\mathrm{\&alpha;}}_1)x+(0.25{\mathrm{\&alpha;}}_1-0.5)x^5\&rsqb;& x\&le;1\\ 1-\frac{{\mathrm{\&rho;}}_t}{{\mathrm{\&alpha;}}_t{(x-1)}^{1.7}+x}& x>1\end{array}\right.---\left(11\right)$

   α₁=1.2 (1+0.265 λ_sf+0.277λ_pf) 1.2≤α₁≤2 (12)

   $\begin{array}{cc}{\mathrm{\&alpha;}}_t=\frac{0.312{\left(f_t^0\right)}^2}{1+3.366{\mathrm{\&lambda;}}_{sf}+3.858{\mathrm{\&lambda;}}_{pf}}& 0\&le;{\mathrm{\&alpha;}}_t\&le;1.5\end{array}---\left(13\right)$

   $f_{hft}^0=f_t^0(1+0.379{\mathrm{\&lambda;}}_{sf}+0.02{\mathrm{\&lambda;}}_{sf}{\mathrm{\&lambda;}}_{pf}),{\mathrm{\&epsiv;}}_{hft}^0={\mathrm{\&epsiv;}}_t^0(1+0.498{\mathrm{\&lambda;}}_{sf}+0.697{\mathrm{\&lambda;}}_{pf})---\left(14\right)$

   $x={\mathrm{\&epsiv;}}_{hft}/{\mathrm{\&epsiv;}}_{hft}^0,{\mathrm{\&rho;}}_t=f_{hft}^0/\left(E_{hft}{\mathrm{\&epsiv;}}_{hft}^0\right)---\left(15\right)$

   In formula, E_hft、σ_hft、ε_hftAnd d_tRespectively represent hybrid fiber concrete tension elastic modelling quantity, tension stress, tensile strain and Tension impairment value；f_t ⁰It is respectively hybrid fiber concrete and the uniaxial tension test of normal concrete；Then distinguish Corresponding above two material peak strain under the conditions of single shaft tension, λ_sf, λ_pfRepresent the feature of steel, polypropylene fibre respectively Value；α¹For hybrid fiber concrete uniaxial tensile stress-strain stress relation ascent stage coefficient, α_tDrawing for hybrid fiber concrete single shaft should Power-strain stress relation descending branch coefficient；ρ_tFor hybrid fiber concrete uniaxial tension test and peak strain and the ratio of elastic modelling quantity Value；

   (2) steel-steel-polypropylene hybrid fiber concrete in uniaxial compressive stress-strain stress relation is:

   $\left\{\begin{array}{cc}y=ax+(3-2a)x^2+(a-2)x^3& 0\&le;x\&le;1\\ y=\frac{x}{b{(x-1)}^2+x}& x>1\end{array}\right.---\left(16\right)$

   $a=28.2283-23.2771{\left(f_{hfc}^0\right)}^{0.0374}+0.4772{\mathrm{\&lambda;}}_{sf}-0.4917{\mathrm{\&lambda;}}_{pf}---\left(17\right)$

   $b=1+0.3688{\left(f_{hfc}^0\right)}^{-0.2846}-{\mathrm{\&lambda;}}_{sf}-{\mathrm{\&lambda;}}_{pf}---\left(18\right)$

   $f_{hfc}^0=f_c^0(1+0.206{\mathrm{\&lambda;}}_{sf}+0.388{\mathrm{\&lambda;}}_{pf}),{\mathrm{\&epsiv;}}_{hfc}^0=263.3\sqrt{f_{hfc}^0}\&times;{10}^{-6}---\left(19\right)$

   $x={\mathrm{\&epsiv;}}_{hfc}/{\mathrm{\&epsiv;}}_{hfc}^0,y={\mathrm{\&sigma;}}_{hfc}/f_{hfc}^0---\left(20\right)$

   In formula, σ_hfcAnd ε_hfcRepresent hybrid fiber concrete compression chord and compressive strain respectively；Respectively mix fibre Dimension concrete and the uniaxial compressive strength of normal concrete；For hybrid fiber concrete peak value under the conditions of uniaxial compression Strain, λ_sf, λ_pfRepresent the eigenvalue of steel, polypropylene fibre respectively；A is hybrid fiber concrete uniaxial compressive stress-strain stress relation Ascent stage coefficient, b is hybrid fiber concrete uniaxial compressive stress-strain stress relation descending branch coefficient；

   It is pointed out that described (1), (2) step sets forth single shaft draw, press in the case of stress-strain curve, Strain therein includes elastic strain and plastic strain two parts, and when using ABAQUS software to carry out finite element analysis only Stress-plastic strain full curve need to be provided, therefore, then need when inputting strain value to deduct elastic strain in advance；

   Step 3: correction flow rule:

   The dilative angle of described steel-steel-polypropylene hybrid fiber concrete plastic constitutive model is defined as follows:

   ${\mathrm{\&psi;}}^{hf}=arctan\left(\sqrt{\frac{|{\mathrm{\&phi;}}_1^{hf}{\stackrel{\&OverBar;}{q}}_2-{\mathrm{\&phi;}}_2^{hf}{\stackrel{\&OverBar;}{q}}_1|}{\left|{\left({\mathrm{\&phi;}}_1^{hf}\right)}^2{\left({\mathrm{\&phi;}}_2^{hf}\right)}^2({\stackrel{\&OverBar;}{q}}_2^2-{\stackrel{\&OverBar;}{q}}_1^2)\right|}}\right)---\left(27\right)$

   In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, φ^hfFor effects such as hybrid fiber concrete Plastic Flow angle, Mises PowerValue under each parameter subscript " 1 ", " 2 " the most corresponding two kinds of different stress；

   According to the definition of formula (27), can be calculated between the dilative angle of hybrid fiber concrete and fiber characteristic value is right Should be related to.
2. Method the most according to claim 1, it is characterised in that:

   In formula (2), the ratio of described hybrid fiber concrete tension and compression meridianComputational methods be:

   $K_c^{hf}=\frac{\stackrel{\&OverBar;}{q}{\left(TM\right)}^{hf}}{\stackrel{\&OverBar;}{q}{\left(CM\right)}^{hf}}=\frac{\stackrel{\&OverBar;}{q}\left(TM\right)\&CenterDot;k_t}{\stackrel{\&OverBar;}{q}\left(CM\right)\&CenterDot;k_c}=K_c\&CenterDot;\frac{k_t}{k_c}---\left(3\right)$

   In formula, K_cMeridian value is drawn for normal concreteWith pressure radial valueRatio, k_t、k_cRespectively mix Normal concrete is drawn by fiber, pressure radial affect coefficient, computational methods are as follows:

   k_t=1+0.08 λ_sf+0.132λ_pf, k_c=1+0.056 λ_sf (4)

   In formula, λ_sf, λ_pfRepresent the eigenvalue of steel, polypropylene fibre respectively.
3. Method the most according to claim 1, it is characterised in that:

   In formula (2), the ratio of described hybrid fiber concrete biaxial compression intensity and normal concrete uniaxial compressive strengthComputational methods as follows:

   (1) according to elastic plastic theory, isobaric biaxial compression hot spot is positioned at and draws on meridian, makes the twin shaft of hybrid fiber concrete Comprcssive strength is(pressure is negative), stress state isσ₁, σ₂, σ₃It is respectively x, y, z side Upwards principal stress, this stress state is hydrostatic pressing force value ξ of correspondence and deviatoric stress value under Haigh-Westergaard coordinate systemIt is respectively as follows:

   $\mathrm{\&xi;}=\frac{I_1}{\sqrt{3}}=\frac{-2{\mathrm{\&sigma;}}_{b0}^{hf}}{\sqrt{3}}---\left(5\right)$

   ${\mathrm{\&rho;}}_t^{hf}=\sqrt{2J_2}=\sqrt{2\&CenterDot;\frac{1}{6}\&CenterDot;\&lsqb;{(0+{\mathrm{\&sigma;}}_{b0}^{hf})}^2+{(0+{\mathrm{\&sigma;}}_{b0}^{hf})}^2+{(-{\mathrm{\&sigma;}}_{b0}^{hf}+{\mathrm{\&sigma;}}_{b0}^{hf})}^2\&rsqb;}=\sqrt{\frac{2}{3}}{\mathrm{\&sigma;}}_{b0}^{hf}---\left(6\right)$

   In formula, I₁For principal stress tensor the first invariant, I₁=σ₁+σ₂+σ₃；J₂For deviatoric stress tensor the second invariant；

   (2) the deviatoric stress value of hybrid fiber concrete on the different drop-down meridians of hydrostatic pressureAdvise as follows:

   ${\mathrm{\&rho;}}_t^{hf}=\frac{-a_1-\sqrt{a_1^2-4a_2(a_0-\frac{\mathrm{\&xi;}}{{\mathrm{\&sigma;}}_{c0}})}}{2a_2}\&CenterDot;{\mathrm{\&sigma;}}_{c0}\&CenterDot;k_t---\left(7\right)$

   In formula, a₀、a₁、a₂It is respectively fitting coefficient, formula (5) is brought into formula (7), connection solution formula (6) and (7), can obtain:

   $\frac{8{a_2}^2}{3{k_t}^2}\&CenterDot;{\left(\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}\right)}^2+\left(\frac{4\sqrt{2}{a}_1{a}_2+8a_2{k}_t}{\sqrt{3}{k}_t}\right)\&CenterDot;\left(\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}\right)+4a_2{a}_2=0---\left(8\right)$

   Each fitting coefficient a in formula₀、a₁、a₂Value suggestion be respectively a₀=0.1775, a₁=-1.4554, a₂=-0.1576, will They substitute in formula (8), and arrangement obtains

   $\frac{{\mathrm{\&sigma;}}_{b0}^{hf}}{{\mathrm{\&sigma;}}_{c0}}=\frac{-(0.749/k_t-0.728)+\sqrt{{(0.749/k_t-0.728)}^2+0.03/{k_t}^2}}{0.132/{k_t}^2}---\left(9\right)$

   In formula, k_tFor assorted fibre, normal concrete being drawn the meridianal coefficient that affects, computational methods are as follows: k_t=1+0.08 λ_sf+ 0.132λ_pf, in formula, λ_sf, λ_pfRepresent the eigenvalue of steel, polypropylene fibre respectively.
4. Method the most according to claim 1, it is characterised in that:

   In step 2, for single shaft pulled condition, the strain of elastic limit point takes hybrid fiber concrete and reaches corresponding during peak strength Strain value, therefore, its plastic strain computing formula is as follows:

   $\left\{\begin{array}{cc}{\widetilde{\mathrm{\&epsiv;}}}_t^{pl}=0& {\mathrm{\&sigma;}}_t\&le;f_{hft}^0\\ {\widetilde{\mathrm{\&epsiv;}}}_t^{pl}={\mathrm{\&epsiv;}}_t-{\mathrm{\&sigma;}}_t/E_{hft}& {\mathrm{\&sigma;}}_t>f_{hft}^0\end{array}\right.---\left(21\right)$

   For uniaxial compression situation, the strain of elastic limit point takes strain value corresponding at the 1/3 of peak strength, therefore, its plasticity Strain calculation formula is:

   $\left\{\begin{array}{cc}{\widetilde{\mathrm{\&epsiv;}}}_c^{pl}=0& {\mathrm{\&sigma;}}_c\&le;f_{hfc}^0/3\\ {\widetilde{\mathrm{\&epsiv;}}}_c^{pl}={\mathrm{\&epsiv;}}_c-{\mathrm{\&sigma;}}_c/E_{hfc}& {\mathrm{\&sigma;}}_c>f_{hfc}^0/3\end{array}\right.---\left(22\right)$

   In formula,For under single shaft pulled condition by tensile plastic strain,For in the case of uniaxial compression by compressive plastic strain；ε_tFor list Tension overall strain, ε under axle pulled condition_cFor pressurized overall strain in the case of uniaxial compression；σ_tFor tension under single shaft pulled condition, σ_cCompressive stress under single shaft pulled condition；E_hfcFor hybrid fiber concrete pressurized elastic modelling quantity.
5. Method the most according to claim 1, it is characterised in that:

   In step 3, the derivation of formula (27) is:

   (1) flow rule uses non-associated flow lawWherein, Plastic Flow potential function g^hfUse D-P hyperbolic Line equation

   $g^{hf}=\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{\stackrel{\&OverBar;}{q}}^2}-\stackrel{\&OverBar;}{p}{\mathrm{tan\&psi;}}^{hf}=0---\left(23\right)$

   In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, describe the yield surface of this material in meridional plane and hydrostatic pressing The angle of power axle；e^hfFor the eccentricity of hybrid fiber concrete plastic potential function, define and linear Drucker-Prager The progressive degree of plastic potential function, e in this method^hfTake 0.1；e^hfσ_t0Then represent this plastic potential hyperbola and asymptote thereof Distance between hydrostatic pressure y-intercept；

   (2) Plastic Flow of supposition hybrid fiber concrete direction at inclined plane arbitrfary point is consistent, and total plastic property answers unsteady flow Dynamic direction is identical with plastic strain increment flow direction, i.e. hybrid fiber concrete Plastic Flow angle φ^hfUncorrelated with Lode angle；

   By the most right for flow potential formula (23) both sidesSeek local derviation:

   ${\mathrm{\&phi;}}^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{\stackrel{\&OverBar;}{q}}^2}=-\stackrel{\&OverBar;}{q}---\left(24\right)$

   Take two kinds of different stress to plastic potential parameter ψ^hfDemarcate:

   ${\mathrm{\&phi;}}_1^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{(e^{hf}{\mathrm{\&sigma;}}_{t0}\&CenterDot;{\mathrm{tan\&psi;}}^{hf})}^2+{{\stackrel{\&OverBar;}{q}}_1}^2}=-{\stackrel{\&OverBar;}{q}}_1---\left(25\right)$

   ${\mathrm{\&phi;}}_2^{hf}{\mathrm{tan\&psi;}}^{hf}\sqrt{{\left(e^{hf}{\mathrm{\&sigma;}}_{t0}{\mathrm{tan\&psi;}}^{hf}\right)}^2+{{\stackrel{\&OverBar;}{q}}_2}^2}=-{\stackrel{\&OverBar;}{q}}_2---\left(26\right)$

   In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, e^hfFor the eccentricity of hybrid fiber concrete plastic potential function, φ^hfFor hybrid fiber concrete Plastic Flow angle, Mises equivalent stressEach parameter subscript " 1 ", " 2 " are the most right Answer the value under two kinds of different stress；

   Simultaneous Equations (25) and (26), eliminate e^hfAnd solve ψ^hfAvailable:

   ${\mathrm{\&psi;}}^{hf}=\arctan \left(\sqrt{\frac{|{\mathrm{\&phi;}}_1^{hf}{\stackrel{\&OverBar;}{q}}_2-{\mathrm{\&phi;}}_2^{hf}{\stackrel{\&OverBar;}{q}}_1|}{\left|{\left({\mathrm{\&phi;}}_1^{hf}\right)}^2{\left({\mathrm{\&phi;}}_2^{hf}\right)}^2({\stackrel{\&OverBar;}{q}}_2^2-{\stackrel{\&OverBar;}{q}}_1^2)\right|}}\right)---\left(27\right)$

   In formula, ψ^hfFor the dilative angle of hybrid fiber concrete, φ^hfFor effects such as hybrid fiber concrete Plastic Flow angle, Mises PowerValue under each parameter subscript " 1 ", " 2 " the most corresponding two kinds of different stress.
6. Method the most according to claim 5, it is characterised in that:

   In formula (27)

   ${\mathrm{\&phi;}}^{hf}=\sqrt{\frac{1}{2}\&CenterDot;\&lsqb;{({\mathrm{\&epsiv;}}_1^{pl}-{\mathrm{\&epsiv;}}_2^{pl})}^2+{({\mathrm{\&epsiv;}}_1^{pl}-{\mathrm{\&epsiv;}}_3^{pl})}^2+{({\mathrm{\&epsiv;}}_2^{pl}-{\mathrm{\&epsiv;}}_3^{pl})}^2\&rsqb;}/\frac{{\mathrm{\&epsiv;}}_1^{pl}+{\mathrm{\&epsiv;}}_2^{pl}+{\mathrm{\&epsiv;}}_3^{pl}}{3}---\left(28\right)$

   In formula,It is respectively the plastic strain of x, y, z direction；

   By under two kinds of different stressValue substitutes into formula (28) respectively, i.e. available correspondenceWith Value.In formulaComputing formula as follows:

   $\begin{array}{c}{\mathrm{\&epsiv;}}_1^{pl}={\mathrm{\&epsiv;}}_1-\&lsqb;{\mathrm{\&sigma;}}_1-v({\mathrm{\&sigma;}}_2+{\mathrm{\&sigma;}}_3)\&rsqb;/E\\ {\mathrm{\&epsiv;}}_2^{pl}={\mathrm{\&epsiv;}}_2-\&lsqb;{\mathrm{\&sigma;}}_2-v({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_3)\&rsqb;/E\\ {\mathrm{\&epsiv;}}_3^{pl}={\mathrm{\&epsiv;}}_3-\&lsqb;{\mathrm{\&sigma;}}_3-v({\mathrm{\&sigma;}}_1+{\mathrm{\&sigma;}}_2)\&rsqb;/E\end{array}---\left(29\right)$

   In formula, ε₁, ε₂, ε₃It is respectively the overall strain of x, y, z direction；σ₁, σ₂, σ₃It is respectively principal stress on x, y, z direction；V is Poisson Ratio；E is elastic modelling quantity.
7. Method the most according to claim 6, it is characterised in that:

   According to Changing Pattern between dilative angle and the fiber characteristic value of hybrid fiber concrete in formula (24)～(29), it is proposed that One succinct computing formula

   ψ^hf=ψ₀(1-0.89λ_sf-0.196λ_pf) (30)

   Wherein, ψ₀For the dilative angle of normal concrete, span is between 30 °～40 °.
8. Method the most according to any one of claim 1 to 7, it is characterised in that:

   The eigenvalue λ of steel fibre_sf=V_sf(l_sf/d_sf), the eigenvalue λ of polypropylene fibre_pf=V_pf(l_pf/d_pf)；V_sf, V_pfRespectively For steel, the volume parameter of polypropylene fibre；l_sf, l_pfIt is respectively steel, the length of polypropylene fibre；d_sf, d_pfBe respectively steel, poly-third The diameter of alkene fiber.