Hybrid fiber reinforced geopolymer concrete static and dynamic compression constitutive model construction method

Abstract

The invention discloses a hybrid fiber reinforced geopolymer concrete static and dynamic compression constitutive model construction method which is applied to the technical field of structural mechanics analysis. The method is based on an elastic-plastic theory, considers the influence of elastic-plastic and damage coupling, constructs a nonlinear constitutive model framework, combines fiber characteristics and a failure mechanism, regards a damage variable as a random variable, explains a physical mechanism of damage generation and evolution, and expands a deterministic constitutive model into a probabilistic constitutive model. And finally, an elastic-plastic random damage model of the HFGPC is established, plastic evolution is corrected by using a Perzyna model, a strain rate effect is introduced into damage evolution, and an HFGPC static and dynamic constitutive model considering the fiber failure mechanism and the strain rate effect at the same time is established.

Description

Technical Field

[0001] The present invention relates to the technical field of structural mechanics analysis, and more particularly to a method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete. Background Art

[0002] The mechanical analysis of all structures is based on three basic equations: the mechanical equilibrium equation, the deformation compatibility equation, and the constitutive relation equation. Among them, the constitutive relation equation describes the physical relationship between force and deformation. In classical theory, concrete is regarded as a homogeneous material, and its failure model is obtained through statistical analysis of macroscopic experiments. However, this statistical-based phenomenological constitutive model is difficult to explain the failure mechanism of concrete, especially for new materials such as fiber concrete, recycled concrete, and geopolymer concrete, lacking universality. Although geopolymer concrete is similar to ordinary Portland cement concrete in macroscopic mechanical properties, its reaction product has a more stable chemical structure and a denser matrix, so it is more brittle and the failure process is faster, and its compressive stress-strain curve also shows different characteristics. Therefore, the constitutive model of geopolymer concrete cannot simply apply the model of ordinary concrete. At present, most of the research on geopolymer concrete focuses on the influence of material mix ratio, admixtures, and fiber types on its mechanical properties, and there is less systematic research on its compressive constitutive model. Existing research mostly optimizes parameters based on the specification model or existing models, and the applicability is limited. Therefore, how to provide a method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete (HFGPC) is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0003] In view of this, the present invention provides a method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete, and establishes a static and dynamic compressive constitutive model applicable to HFGPC.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] A method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete, comprising the following steps:

[0006] S1. Under the framework of irreversible thermodynamics and elastoplastic mechanics, select the damage energy release rate as the damage variable, and deduce the elastoplastic damage constitutive model of HFGPC;

[0007] S2. Analyze the damage mechanism of the surface element under the concept of random damage, establish the random damage variable of HFGPC, and transform the elastoplastic damage constitutive model of HFGPC into an elastoplastic random damage constitutive model;

[0008] S3. Analyze the influence of fibers on the damage threshold of the element surface based on the fiber failure mechanism, and calculate the expectation and variance of the random function of the HFGPC damage threshold;

[0009] S4. Combine the influence of the strain rate on plastic evolution and damage evolution to modify the elastoplastic random damage constitutive model of HFGPC;

[0010] S5. Conduct static and dynamic uniaxial compression tests, and calibrate the fiber pull-out energy dissipation parameter and damage evolution parameter of the elastoplastic random damage constitutive model of HFGPC based on the test data.

[0011] Optionally, S1 is specifically:

[0012] S11. Take the rate of change of Helmholtz free energy as the damage variable D, and determine the Helmholtz free energy of HFGPC:

[0013] F(ε e , κ p , D ± ) = F e+ (ε e , D + ) + F e- (ε e , D - ) + F p- (κ p , D - )

[0014] In the formula, ε e is the elastic strain tensor, κ p is the plastic internal variable, D + is the tensile damage variable, and D - is the shear damage variable;

[0015] S12. Based on the definition formula of the damage variable D = 1 - F D / F 0 , obtain:

[0016]

[0017] In the formula, σ is the stress tensor, F D is the damage elastic free energy, F 0 is the initial elastic free energy, is the tensile part of the initial elastic free energy, is the shear part of the initial elastic free energy;

[0018] S13. Based on the relationship between the effective stress tensor and the elastic free energy, obtain the double-scalar elastoplastic damage constitutive relationship of HFGPC;

[0019] S14. Select the Lee-Fenves-Lubiner model as the yield criterion for the monotonic compression of HFGPC;

[0020] S15. By defining the damage potential function G D (Y, Ω Y ), establish the damage criterion for HFGPC:

[0021] G D (Y, Ω Y ) = g D (Y) - g D (Ω Y ) ≤ 0

[0022]

[0023] In the formula, Y is the damage energy release rate at time n, Ω Y represents the damage threshold, Ω 0 is the initial damage threshold, and g D (·) represents a monotonically increasing scalar function;

[0024] S16. Establish the damage criterion, obtain the evolution equation of the damage variable according to the associated flow rule of classical plasticity mechanics, combine the damage criterion to obtain the damage surface equation through the consistency condition, and differentiate and integrate the damage surface equation to obtain the general expression form of the damage variable:

[0025] D = g(Ω Y )

[0026] The damage variable D can be obtained from the damage threshold Ω Y through the monotonically increasing function g(·). As long as the function of the damage variable D with respect to the damage threshold Ω Y is determined, the specific form of the damage evolution function can be obtained.

[0027] Optionally, S2 is specifically:

[0028] S21. Quantify the damage degree of HFGPC with the loss rate of Helmholtz free energy, and define the damage variable D:

[0029]

[0030] In the formula, ΔF represents the loss of Helmholtz free energy caused by damage to the surface element, F i represents the Helmholtz free energy of the surface element when it is not damaged. When the surface element is completely damaged, the damage variable D reaches the limit, and Y i = -F i represents the damage energy release rate, is the damage threshold of the i-th surface element, and H(·) is the Heaviside step function;

[0031] S22. Consider HFGPC as being composed of a number of surface elements. Assume that an external load acts on HFGPC and each surface element is uniformly loaded. When the number of surface elements N→∞, the damage variable D of HFGPC is expressed as:

[0032]

[0033] In the formula, x represents the position coordinate along the arrangement direction of the surface elements;

[0034] S23. Calculate the expectation and variance of the damage variable D, and establish the stochastic damage variable D of HFGPC:

[0035]

[0036] In the formula, E(D) is the expectation of the damage variable D, and Ω Y represents the damage threshold, and f(Ω Y ) represents the probability density function of the damage threshold;

[0037] S24. Assume that the stochastic damage variable of HFGPC follows a lognormal distribution. Let the random variable γ = ln(Ω Y ). Calculate the expectation 2 and variance Y of the damage threshold Ω through the expectation ξ and variance δ

[0038]

[0039] S25. Represent the expectation E(D) of the stochastic damage variable D with the cumulative distribution function Φ of the standard normal distribution:

[0040]

[0041] The expectation E(D) of the stochastic damage variable D is the value of the cumulative distribution function of the random variable γ at γ = ln(Y).

[0042] Optionally, S3 is specifically as follows:

[0043] S31. Calculate the damage threshold considering the fiber reinforcement factor

[0044]

[0045] In the formula, Ω Y is the damage threshold, Λ is the fiber characteristic parameter, W represents the energy consumption during the fiber pull - out or pull - break process, L is the length of the fiber, d is the diameter of the fiber, and V f is the volume fraction of the fiber;

[0046] S32. Analyze the pull-out energy dissipation of hooked-end steel fibers, straight steel fiber copper-coated microfilaments, and PVA fibers respectively;

[0047] S33. Calculate the ξ of the damage threshold random function when hooked-end steel fibers and PVA fibers are doped based on the pull-out energy dissipation HP and variance The ξ of the damage threshold random function when straight steel fiber copper-coated microfilaments and PVA fibers are doped MP and variance

[0048] Optionally, the ξ of the damage threshold random function when hooked-end steel fibers and PVA fibers are doped in S33 HP and variance The ξ of the damage threshold random function when straight steel fiber copper-coated microfilaments and PVA fibers are doped MP and variance Specifically:

[0049]

[0050] In the formula, ξC is the expectation of the damage threshold random function when no fibers are doped, is the variance of the damage threshold random function when no fibers are doped, V H , V M are the volume fractions of hooked-end steel fibers and straight steel fiber copper-coated microfilaments respectively, Λ p is the characteristic parameter of PVA fibers, W θH , W θM , W p are the pull-out energy dissipations of hooked-end steel fibers, straight steel fiber copper-coated microfilaments, and PVA fibers respectively, E(W θH ), E(W θM ), E(W p ) are the expectations of W θH , W θM , W p respectively, Var(W θH ), Var(W θM ), Var(W p ) are the variances of W θH , W θM , W p respectively, τ H , τ M represent the energy dissipation parameters of hooked-end steel fibers and straight steel fiber copper-coated microfilaments respectively, l H , l M represent the lengths of hooked-end steel fibers and straight steel fiber copper-coated microfilaments respectively, d H , d Mrespectively represent the diameters of hooked steel fibers and straight steel fiber copper-coated microfilaments.

[0051] Optionally, S4 is specifically as follows:

[0052] S41. The elastic strain tensor at time t n is assigned; elastic scalar E 0 , plastic strain plastic internal variable damage variable D n , damage threshold Ω Y，n , strain increment Δε n+1 is assigned;

[0053] S42. Predict the predicted value of the effective stress tensor at time t n+1 through elastic trial calculation; predicted value of elastic strain tensor predicted value of plastic strain predicted value of plastic internal variable

[0054] S43. Trial calculate the yield condition If it indicates that no new plastic flow occurs within the increment step [t n , t n+1 , enter S45; if then enter S44;

[0055] S44. Take the result predicted by elastic trial calculation as the initial variable and calculate the plastic correction through an iterative algorithm;

[0056] S45. Calculate the damage energy release rate Y at time t n+1 , correct the damage threshold Ω n+1 and the damage variable D Y，n+1 . n+1 .

[0057] Optionally, S44 is specifically as follows:

[0058] S441. Set the initial value Δλp (1) = 0;

[0059] S442. Solve for the state variable increment Δx through the Newton - Raphson iterative algorithm;

[0060] S443. Judge whether ||Δx|| is less than the convergence value Thd;

[0061] S444. If ||Δx|| ≥ Thd, then re - iterate according to the updated state variable ;

[0062] S445. If ||Δx|| < Thd, update the state variables

[0063] Optionally, S45 is specifically as follows:

[0064] S451. Calculate the damage energy release rate Y at time t n+1 ; n+1 ;

[0065] S452. When Y n+1 > Ω Y，n , it indicates that new damage has occurred within the increment step [t n , t n+1 , enter S453, otherwise enter S454;

[0066] S453. Modify the damage threshold Ω Y , n+1 and the damage variable D n+1 ;

[0067] S454. Update σ n+1 , the damage threshold Ω Y，n+1 and the damage variable D n+1 .

[0068] Optionally, S5 is specifically as follows: Conduct static and dynamic uniaxial compressive tests, obtain the relationship between the damage variable D and the damage energy release rate Y by test fitting, combine with the cumulative distribution function of the random variable γ, make the damage value of the static and dynamic uniaxial compressive test equal to the theoretical damage value, and obtain the normal distribution parameter expectation ξ and variance δ Y of the random variable γ = ln(Ω 2 ), and then determine the expectation Y and variance of the damage threshold Ω Calibrate the energy dissipation parameters τ H , τ M of the hooked-end steel fiber and the straight steel fiber copper-plated microfilament, the expectation E(W p ) of the pull-out energy dissipation of the PVA fiber and the variance Var(W p ), fit the relationship between the damage variable D and the damage energy release rate Y at different strain rates, and obtain the expressions of the expectation Y and variance of the damage threshold Ω at different strain rates with respect to the fiber eigenvalue.

[0069] From the above technical solutions, it can be seen that compared with the prior art, the present invention provides a method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete, having the following beneficial effects:

[0070] The present invention takes into account the randomness of damage development, introduces a random damage variable based on the fiber failure mechanism, and makes a viscoplastic extension to the constitutive model, considering the strain rate effects of plastic evolution and damage evolution. A static and dynamic compressive constitutive model applicable to HFGPC is established, and the constructed model has good simulation effects in both the mean value and random fluctuations of the simulation curve. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the provided drawings.

[0072] Figure 1 It is a flowchart of the construction method of the static and dynamic compressive constitutive model of the present invention;

[0073] Figure 2 It is a flowchart for correcting the elastoplastic random damage constitutive model of the present invention;

[0074] Figure 3 It is a schematic diagram of the operation output result at a strain rate of 10 -5 s -1 in an embodiment of the present invention;

[0075] Figure 4 It is a schematic diagram of the operation output result at a strain rate of 10 -4 s -1 in an embodiment of the present invention;

[0076] Figure 5 It is a schematic diagram of the operation output result at a strain rate of 10 -3 s -1 in an embodiment of the present invention;

[0077] Figure 6 It is a schematic diagram of the operation output result at a strain rate of 45 s -1 in an embodiment of the present invention;

[0078] Figure 7 It is a schematic diagram of the operation output result at a strain rate of 60 s -1 in an embodiment of the present invention;

[0079] Figure 8 It is a schematic diagram of the operation output result at a strain rate of 85 s -1 in an embodiment of the present invention;

[0080] Figure 9 It is a schematic diagram of the operation output result at a strain rate of 145 s- 1Schematic diagram of the operation output result at the strain rate;

[0081] Figure 10 It is a schematic diagram of the operation output result at the strain rate of 180 s-1 in the embodiment of the present invention;

[0082] Figure 11 It is for the schematic diagram of the operation output result at the strain rate of 220 s- 1 in the embodiment of the present invention. Detailed implementation manners

[0083] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0084] The embodiment of the present invention discloses a method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete, as Figure 1 shown, including the following steps:

[0085] S1. Under the framework of irreversible thermodynamics and elastoplastic mechanics, select the damage energy release rate as the damage variable, and deduce the elastoplastic damage constitutive model of HFGPC;

[0086] S2. Analyze the damage mechanism of the surface element under the concept of random damage, establish the random damage variable of HFGPC, and transform the elastoplastic damage constitutive model of HFGPC into an elastoplastic random damage constitutive model;

[0087] S3. Based on the fiber failure mechanism, analyze the influence of the fiber on the damage threshold of the surface element, and calculate the expectation and variance of the random function of the damage threshold of HFGPC;

[0088] S4. Combine the influence of the strain rate on the plastic evolution and damage evolution, and correct the elastoplastic random damage constitutive model of HFGPC;

[0089] S5. Conduct static and dynamic uniaxial compression tests, and calibrate the fiber pull-out energy dissipation parameter and damage evolution parameter of the elastoplastic random damage constitutive model of HFGPC based on the test data.

[0090] Further, S1 is specifically:

[0091] S11. Take the change rate of Helmholtz free energy as the damage variable D, and determine the Helmholtz free energy of HFGPC:

[0092] F(ε e ,κ p ,D± ) = F e+ (ε e , D + ) + F e- (ε e , D - ) + F p- (κ p , D - )

[0093] In the formula, ε e is the elastic strain tensor, κ p is the plastic internal variable, D + is the tensile damage variable, D - is the shear damage variable;

[0094] S12. Based on the definition formula of the damage variable D = 1 - F D / F 0 we get:

[0095]

[0096] In the formula, σ is the stress tensor, F D is the damaged elastic free energy, F 0 is the initial elastic free energy, is the tensile part of the initial elastic free energy, is the shear part of the initial elastic free energy;

[0097] S13. Based on the relationship between the effective stress tensor and the elastic free energy, the HFGPC double - scalar elasto - plastic damage constitutive relationship is obtained;

[0098] S14. Select the Lee - Fenves - Lubiner model as the yield criterion for HFGPC monotonic compression;

[0099] S15. By defining the damage potential function G D (Y, Ω Y ), the damage criterion of HFGPC is established:

[0100] G D (Y, Ω Y ) = g D (Y) - g D (Ω Y ) ≤ 0

[0101]

[0102] In the formula, Y is the damage energy release rate at time n, Ω Y represents the damage threshold, Ω 0 is the initial damage threshold, g D(·) represents a monotonically increasing scalar function;

[0103] S16. Establish a damage criterion, obtain the evolution equation of the damage variable according to the orthotropic flow rule of classical plasticity, combine the damage criterion to obtain the damage surface equation through the consistency condition, differentiate and integrate the damage surface equation to obtain the general expression form of the damage variable:

[0104] D = g(Ω Y )

[0105] The damage variable D can be obtained from the damage threshold Ω through the monotonically increasing function g(·) Y As long as the function of the damage variable D with respect to the damage threshold Ω is determined, the specific form of the damage evolution function can be obtained. Y

[0106] Furthermore, S2 is specifically as follows:

[0107] S21. Quantify the damage degree of HFGPC with the loss rate of Helmholtz free energy, and define the damage variable D:

[0108]

[0109]

[0110] In the formula, ΔF represents the loss of Helmholtz free energy caused by damage to the surface element, F i represents the Helmholtz free energy of the surface element when it is not damaged. When the surface element is completely damaged, the damage variable D reaches the limit, and Y i =-F i represents the damage energy release rate, is the damage threshold of the i-th surface element, and H(·) is the Heaviside step function;

[0111] S22. Consider HFGPC as composed of several surface elements. Assume that an external load acts on HFGPC, and each surface element is uniformly loaded. When the number of surface elements N→∞, the damage variable D of HFGPC is expressed as:

[0112]

[0113] In the formula, x represents the position coordinate along the arrangement direction of the surface elements;

[0114] S23. Calculate the expectation and variance of the damage variable D, and establish the stochastic damage variable D of HFGPC:

[0115]

[0116] In the formula, E(D) is the expectation of the damage variable D, and Ω Y ​denotes the damage threshold, and f(Ω Y ) represents the probability density function of the damage threshold;

[0117] S24. Assume that the random damage variable of HFGPC follows a lognormal distribution. Let the random variable γ = ln(Ω Y ). Calculate the expectation ξ and variance δ of the damage threshold Ω 2 through the expectation ξ and variance δ of the random variable γ Y of the random variable γ. and variance

[0118]

[0119] S25. Express the expectation E(D) of the random damage variable D using the cumulative distribution function Φ of the standard normal distribution:

[0120]

[0121] The expectation E(D) of the random damage variable D is the value of the cumulative distribution function of the random variable γ at γ = ln(Y).

[0122] Furthermore, S3 is specifically as follows:

[0123] S31. Calculate the damage threshold considering the fiber reinforcement factor In subsequent calculations, use the damage threshold considering the fiber reinforcement factor as the damage threshold Ω Y for calculation:

[0124]

[0125] In the formula, Ω Y is the damage threshold, Λ is the fiber characteristic parameter, W represents the energy consumption during fiber pull - out or breakage, L is the fiber length, d is the fiber diameter, and V f is the fiber volume fraction;

[0126] S32. Analyze the pull - out energy consumption of hooked - end steel fibers (HS), straight - type steel fiber - coated copper micro - wires (MS), and PVA fibers respectively;

[0127] S33. Calculate ξ HP and variance of the damage threshold random function when hooked - end steel fibers and PVA fibers are doped MP and variance

[0128] Furthermore, ξ of the damage threshold random function when hooked - end steel fibers and PVA fibers are doped in S33HP Sum of variances ξ of the random function of the damage threshold when straight steel fiber copper-plated microfilaments and PVA fibers are doped MP Sum of variances Specifically:

[0129]

[0130] In the formula, ξC is the expectation of the random function of the damage threshold when no fibers are doped, is the variance of the random function of the damage threshold when no fibers are doped, V H , V M are the volume fractions of hooked-end steel fibers and straight steel fiber copper-plated microfilaments respectively, Λ p is the characteristic parameter of PVA fiber, W θH , W θM , W p are the pull-out energy consumptions of hooked-end steel fibers, straight steel fiber copper-plated microfilaments, and PVA fibers respectively, E(W θH ), E(W θM ), E(W p ) are the expectations of W θH , W θM , W p respectively, Var(W θH ), Var(W θM ), Var(W p ) are the variances of W θH , W θM , W p respectively, τ H , τ M represent the energy consumption parameters of hooked-end steel fibers and straight steel fiber copper-plated microfilaments respectively, l H , l M represent the lengths of hooked-end steel fibers and straight steel fiber copper-plated microfilaments respectively, d H , d M represent the diameters of hooked-end steel fibers and straight steel fiber copper-plated microfilaments respectively.

[0131] Furthermore, as Figure 2 shown, S4 is specifically:

[0132] S41. For the elastic strain tensor n at time t elastic scalar E 0 , plastic strain plastic internal variable damage variable D n , damage threshold Ω Y，n , strain increment Δε n+1 are assigned values;

[0133] S42. Predict the effective stress tensor prediction value at time t through elastic trial calculation n+1 Elastic strain tensor prediction value Plastic strain prediction value Plastic internal variable prediction value

[0134] S43. Trial calculation of the yield condition If It indicates that no new plastic flow occurs during the increment step [t n , t n+1 , enter S45; if Then enter S44;

[0135] S44. Use the results predicted by elastic trial calculation as the initial variables and calculate plastic correction through an iterative algorithm;

[0136] S45. Calculate the damage energy release rate Y at time t n+1 , correct the damage threshold Ω n+1 and the damage variable D Y，n+1 . n+1

[0137] Furthermore, S44 is specifically as follows:

[0138] S441. Set the initial value Δλp(1) = 0;

[0139] S442. Solve for the state variable increment Δx through the Newton - Raphson iterative algorithm;

[0140] S443. Determine whether ||Δx|| is less than the convergence value Thd;

[0141] S444. If ||Δx|| ≥ Thd, then re - iterate according to the updated state variables ;

[0142] S445. If ||Δx|| < Thd, update the state variables

[0143] Furthermore, S45 is specifically as follows:

[0144] S451. Calculate the damage energy release rate Y at time t n+1 ; n+1

[0145] S452. When Y n+1 > Ω Y，n , it indicates that during the increment step [t n , t n+1 ​​​If new damage occurs, go to S453; otherwise, go to S454.

[0146] S453. Modify the damage threshold Ω Y，n+1 and the damage variable D n+1 ;

[0147] S454. Update σ n+1 , the damage threshold Ω Y，n+1 and the damage variable D n+1 .

[0148] In the embodiments of the present invention, the constitutive model includes strength parameters, fiber parameters, strain rate effect parameters, and damage evolution parameters. Among them, the strength parameters include compressive strength, elastic modulus, elastic proportional limit strain, and Poisson's ratio, which can be obtained from test data. The fiber parameters include fiber aspect ratio and fiber volume fraction. Specifically, for the three types of fibers HS, MS, and PVA, they are all known parameters. In addition, it also includes the fiber pull-out energy dissipation parameter. For HS and MS fibers, the corresponding τ H , τ M , and for PVA fibers, the expected value E(W p ) and variance Var(W p ) of the pull-out energy dissipation can be inversely calibrated through test data. The damage evolution parameters include the expected value ξ and variance δ Y of the random variable γ = ln(Ω 2 ), the expected value Y of the damage threshold Ω and variance of the dynamic damage variable parameter ξ d and Among the above four types of parameters, the fiber pull-out energy dissipation parameter and the damage evolution parameter cannot be directly obtained.

[0149] Furthermore, S5 is specifically as follows: Conduct static and dynamic uniaxial compressive tests. Obtain the relationship between the damage variable D and the damage energy release rate Y by fitting the test results. Combine with the cumulative distribution function of the random variable γ. Let the damage value of the static and dynamic uniaxial compressive tests be equal to the theoretical damage value, and obtain the normal distribution parameter expected value ξ and variance δ Y of the random variable γ = ln(Ω 2 ), and then determine the expected value Y of the damage threshold Ω and variance Calibrate the energy dissipation parameters τ H , τ M of the hooked-end steel fibers and straight steel fibers with copper-plated microfilaments, the expected value E(W p ) of the pull-out energy dissipation of PVA fibers and variance Var(W p) Fit the relationship between the damage variable D and the damage energy release rate Y at different strain rates to obtain the damage threshold Ω at different strain rates. Y expectation and variance expressions regarding the fiber eigenvalue.

[0150] In the embodiment of the present invention, several points are taken on the entire stress-strain curve to establish several equations where the experimental values are equal to the theoretical values, and the optimal solutions of these equations are obtained through data fitting, thereby obtaining the random field parameters ξ and δ of the D-Y theoretical relationship. Let:

[0151]

[0152] Z is the inverse function of the standard normal distribution function. Calculate the Z value corresponding to each D value, and solve for the parameters ξ and δ using the non-linear least squares method. The fitting results of the damage evolution equation parameters for each group under quasi-static compression are shown in Table 1, where R 2 is the correlation coefficient.

[0153] Table 1 Fitting results of damage evolution equation parameters

[0154]

[0155] Based on the above-mentioned damage threshold Ω Y expectation and variance calculation method, combined with known parameters, obtain the expressions of the expectation and variance of the damage threshold random variable of HFGPC under 10 -5 s -1 strain rate regarding the fiber eigenvalue for the constitutive model establishment and verification of HFGPC under static and dynamic compression:

[0156]

[0157] Similarly, when the strain rate exceeds 45 s -1 the expressions of the expectation and variance of the damage threshold random variable regarding the fiber eigenvalue and strain rate are as follows:

[0158]

[0159] When the strain rate is 10 s -1 ~45 s -1 the expressions of the expectation and variance of the damage threshold random variable are as follows:

[0160]

[0161] Further, in the embodiments of the present invention, based on the elastoplastic stochastic damage constitutive model established above, a uniaxial compression model of HFGPC is established using the finite element software Abaqus. The specific steps are as follows: (1) Three-dimensional solid models are established according to the actual sizes of the specimens. The geometric size of the axially compressed specimen solid model is 100 mm × 100 mm × 300 mm; the size of the dynamic compression specimen solid model is φ100 mm × 50 mm, and the sizes of the impact bar, incident bar, and transmission bar are φ100 mm × 2400 mm, φ100 mm × 5000 mm, and φ100 mm × 3000 mm respectively. (2) The material properties are defined by a self-written UMAT subroutine, and 8 non-independent variables are set for UMAT to call. Input material parameters, including elastic modulus, Poisson's ratio, peak strength, damage parameter, fiber length, diameter, dosage, etc. (3) Boundary conditions and load steps are set. In the axial compression test, the upper surface is set fixed, and displacement control is applied to the lower surface; in the test, the end surface of the transmission bar is set fixed, the speed of the impact bar is set according to the measured data, and the contact surface is set frictionless. (4) The eight-node hexahedron linear reduced integration element (C3D8R) is used for discretization, which can not only meet the calculation accuracy requirements but also reduce the calculation time. The element size is set to 5 mm × 5 mm × 5 mm. (5) The time step is set, and the time step is set according to the test data to ensure the stability of the numerical simulation. (6) The axial stress-axial strain curve is output.

[0162] Taking a representative group from the previous test results as an example, the constitutive model is numerically verified. The basic material parameters are shown in Table 2.

[0163] Table 2 Basic material parameters

[0164]

[0165] The numerical operation output results of the constitutive model at different strain rates are as Figures 3 - 11 shown. The solid line in the figure is the numerical simulation result, and the dots are the test results. It can be seen from the figure that the simulation curve shows good simulation effects in both the mean value and random fluctuations, verifying the effectiveness of the constitutive model. However, for the curves at the strain rates of 45 s -1 and 60 s -1 there are certain deviations between the peak stress and the trend of the descending section of the model curve and the test curve. This is because at a lower impact strain rate, the impact energy is small, the specimen absorbs the energy but does not break, and there are deviations between the plastic evolution and damage evolution in the model and the actual situation. Therefore, the constitutive model established in this paper is more suitable for predicting the dynamic compression behavior at higher strain rates.

[0166] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other.

[0167] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete, characterized in that: The following steps are involved: S1. In the framework of irreversible thermodynamics and elastoplastic mechanics, the damage energy release rate is selected as the damage variable to derive the elastoplastic damage constitutive model of HFGPC; S2. Analyze the surface element damage mechanism under the concept of random damage, establish the random damage variables of HFGPC, and transform the elastic-plastic damage constitutive model of HFGPC into an elastic-plastic random damage constitutive model; S3. Analyze the influence of fiber on the damage threshold of the surface element based on the fiber failure mechanism, and calculate the expectation and variance of the random function of the HFGPC damage threshold; S4. Combining the influence of strain rate on plastic evolution and damage evolution, the elastic-plastic random damage constitutive model of HFGPC is modified; S5. Static and dynamic uniaxial compression tests were carried out, and the fiber pull-out energy dissipation parameters and damage evolution parameters of the elastic-plastic random damage constitutive model of HFGPC were calibrated based on the test data.

2. The method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete according to claim 1, characterized in that: S1 is specifically: S11. The Helmholtz free energy change rate is used as the damage variable D to determine the Helmholtz free energy of HFGPC: F(e e ,k p ,D ± )=F e+ (e e ,D + )+F e -(e e ,D - )+F p -(k p ,D - ) In the formula, ε e is the elastic strain tensor, κ p is the plastic internal variable, D + is the tensile damage variable, D - is the shear damage variable; S12, based on damage variable D = 1-F D / F0 is defined as: Where σ is the stress tensor, F D is the damage elastic free energy, F0 is the initial elastic free energy, is the tensile part of the initial elastic free energy, is the shear part of the initial elastic free energy; S13, based on effective stress tensor The relationship between the elastic free energy and the HFGPC double-scalar elastic-plastic damage constitutive relation is obtained; S14, the Lee-Fenves-Lubiner model is selected as the yield criterion for monotonic compression of HFGPC; S15, by defining the damage potential function G D (Y,Ω Y ), establish the injury criteria for HFGPC: G D (Y, Oh) Y )=g D (Y)-g D (Oh Y )≤0 Where Y is the damage energy release rate at time n, Ω Y represents the damage threshold, Ω0 is the initial damage threshold, g D (·) represents a monotonically increasing scalar function; S16. Establish the damage criterion, obtain the evolution equation of the damage variable according to the orthogonal flow law of classical plastic mechanics, combine the damage criterion with the consistency condition to obtain the damage surface equation, and differentiate and integrate the damage surface equation to obtain the general expression of the damage variable: D=g(Ω Y ) The damage variable D can be obtained by the monotonically increasing function g(·) from the damage threshold Ω Y As long as the damage variable D is determined with respect to the damage threshold Ω Y The specific form of the damage evolution function can be obtained by using the function of 3. The method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete according to claim 1, characterized in that: S2 is specifically: S21. Use the loss rate of Helmholtz free energy to quantify the damage degree of HFGPC and define the damage variable D: Where ΔF represents the Helmholtz free energy loss caused by damage to the surface element, and F i It represents the Helmholtz free energy when the surface element is not damaged. When all the surface elements are destroyed, the damage variable D reaches the limit, Y i =-F i represents the damage energy release rate, is the damage threshold of the ith bin, H(·) is the Heaviside step function; S22. HFGPC is considered to be composed of several facets. Assuming that the external load acts on HFGPC and each facet is loaded uniformly, when the number of facets N→∞, the damage variable D of HFGPC is expressed as: In the formula, x represents the position coordinate along the direction of the panel arrangement; S23. Calculate the expectation and variance of the damage variable D and establish the random damage variable D of HFGPC: Where E(D) is the expected value of the damage variable D, Ω Y represents the damage threshold, f(Ω Y ) represents the probability density function of the damage threshold; S24. Assume that the random damage variable of HFGPC follows a log-normal distribution, and let the random variable γ = ln(Ω Y ) through the expectation ξ and variance δ of the random variable γ 2 Calculate the damage threshold Ω Y Expectations and variance S25. Use the cumulative distribution function Φ of the standard normal distribution to express the expectation E(D) of the random damage variable D: The expectation E(D) of the random damage variable D is the value of the cumulative distribution function of the random variable γ when γ=ln(Y).

4. The method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete according to claim 1, characterized in that: S3 is specifically: S31. Calculation of damage threshold considering fiber reinforcement In the formula, Ω Y is the damage threshold, Λ is the fiber characteristic parameter, W represents the energy consumption during fiber pulling out or breaking, L is the length of the fiber, d is the diameter of the fiber, V f is the volume content of fiber; S32, respectively analyze the pull-out energy consumption of end hook steel fiber, straight steel fiber copper-plated microwire and PVA fiber; S33, ξ of the damage threshold random function when end hook steel fiber and PVA fiber are doped based on pull-out energy consumption calculation HP and variance ξ of the random function of damage threshold when doping straight steel fiber with copper-plated microwire and PVA fiber MP and variance 5. The method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete according to claim 4, characterized in that: ξ of the random function of damage threshold when S33 mid-end hook-shaped steel fiber and PVA fiber are mixed HP and variance ξ of the random function of damage threshold when doping straight steel fiber with copper-plated microwire and PVA fiber MP and variance Specifically: Where ξC is the expectation of the random function of the damage threshold of undoped fibers, is the variance of the random function of the damage threshold in the case of undoped fibers, V H 、V M are the volume content of the end hook steel fiber and the straight steel fiber copper-plated microwire, Λ p is the characteristic parameter of PVA fiber, W θH , W θM , W p The pull-out energy consumption of end hook steel fiber, straight steel fiber copper-plated microwire, and PVA fiber, E(W θH )、E(W θM )、E(W p ) are W θH , W θM , W p Expectations, Var(W θH )、Var(W θM )、Var(W p ) are W θH , W θM , W p The variance of H , τ M They represent the energy dissipation parameters of the end hook steel fiber and the straight steel fiber copper-plated microwire, respectively. H , l M Respectively represent the length of the end hook type steel fiber and the straight type steel fiber copper-plated microwire, d H ,d M They respectively represent the diameters of the end hook type steel fiber and the straight type steel fiber copper-plated microwires.

6. The method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete according to claim 1, characterized in that: S4 is specifically: S41, is t n The elastic strain tensor at time Elastic scalar E0, plastic strain Plastic internal variables Damage variable D n , damage threshold Ω Y，n , strain increment Δε n+1 Assignment; S42. Predict t through elastic calculation n+1 Predicted value of effective stress tensor at time Predicted elastic strain tensor Plastic strain prediction Prediction value of plastic internal variables S43, Trial Yield Condition if It shows that in the increment step [t n , t n+1 ] No new plastic flow occurs within , enter S45; if Then enter S44; S44, using the result predicted by the elastic trial calculation as the initial variable, calculating the plastic correction through an iterative algorithm; S45. Calculate t n+1 The damage energy release rate Y at the time n+1 , corrected damage threshold Ω Y，n+1 and the damage variable D n+1 .

7. The method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete according to claim 6, characterized in that: S44 is specifically: S441, set initial value S442, solving the state variable increment Δx by Newton-Raphson iterative algorithm; S443, judging whether ||Δx|| is less than the convergence value Thd; S444. If ||Δx||≥Thd, then according to the updated state variable Re-iterate; S445. If ||Δx||<Thd, update the state variable 8. The method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete according to claim 6, characterized in that: S45 is specifically: S451, calculate t n+1 The damage energy release rate Y at the time n+1 ; S452, when Y n+1 >Ω Y，n When n , t n+1 ] if new damage occurs, go to S453; otherwise, go to S454; S453, corrected damage threshold Ω Y，n+1 and the damage variable D n+1 ; S454, Update σ n+1 , Damage threshold Ω Y，n+1 and the damage variable D n+1 .

9. The method for constructing a static and dynamic compressive constitutive model of hybrid fiber reinforced geopolymer concrete according to claim 1, characterized in that: S5 is specifically as follows: static and dynamic uniaxial compression tests are carried out, and the relationship between the damage variable D and the damage energy release rate Y is obtained by test fitting. Combined with the cumulative distribution function of the random variable γ, the damage value of the static and dynamic uniaxial compression tests is made equal to the theoretical damage value, and the random variable γ is obtained. Y )’s normal distribution parameter expectation ξ and variance δ 2 , and then determine the damage threshold Ω Y Expectations and variance Calibration of energy dissipation parameter τ of end hook steel fiber and straight steel fiber copper-plated microwire H , τ M , the expected energy consumption of PVA fiber extraction E(W p ) and variance Var(W p ), fitting the relationship between the damage variable D and the damage energy release rate Y at different strain rates, and obtaining the damage threshold Ω at different strain rates Y Expectations and variance Expressions for fiber characteristic values.

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