A finite element data calculation method and system based on a material constitutive model

Abstract

This invention discloses a method and system for calculating finite element data based on a material constitutive model, relating to the field of finite element simulation technology for metal stamping forming. The method includes: calculating the trial stress at the i-th increment step based on the strain increment at the element mesh integration point and the stress at the (i-1)-th increment step; calculating the yield function value based on the Von Mises yield criterion, using the trial stress, the strain at the (i-1)-th increment step, and the equivalent plastic strain rate; if the yield function value does not meet the preset yield condition, marking the trial stress as the actual simulated stress at the i-th increment step and obtaining the corresponding actual simulated strain; if the yield function value meets the preset yield condition, calculating the actual simulated stress at the element mesh integration point and the corresponding actual simulated strain at the i-th increment step based on the plastic flow law. This invention, when applied to finite element software, can accurately and effectively calculate finite element simulation data.

Description

Technical Field

[0001] This invention relates to the field of finite element simulation technology for metal stamping, and in particular to a method and system for calculating finite element data based on the Johnson-Cook material constitutive model. Background Technology

[0002] Dynamic impact phenomena have wide-ranging applications in aerospace and automotive. Constitutive models are extremely useful numerical tools for describing the thermodynamic behavior of materials during dynamic impact processes. The thermodynamic behavior of materials is closely related to strain rate, crystal structure, and temperature. Accurate constitutive models play a crucial role in establishing realistic finite element models of high strain rate events.

[0003] The Johnson-Cook constitutive model and fracture criterion were proposed by Johnson and Cook in the 1980s and have been widely used in the field of impact. Johnson, Cook and other scholars conducted Hopkinson tensile and torsion tests on equivalent materials at different strain rates and temperatures. By comparing numerical simulations with experimental results, they calibrated the parameters of the Johnson-Cook constitutive model for 12 materials. They proposed a fracture criterion that considers the effects of large strain, high temperature and high stress, and verified it by comparing Taylor impact tests with numerical simulations.

[0004] The Johnson-Cook constitutive model is now well-developed, with numerous publications from China and other countries. It decouples material work hardening, strain rate, and temperature effects, resulting in simple equations that facilitate engineering applications. It has been widely used in materials processing, automotive crashworthiness testing, high-speed rail safety testing, and bird strike simulation, providing valuable technical parameters and reference information for materials and structural design.

[0005] Simulating the stamping process of metallic materials using finite element method (FEM) software is an effective way to reduce the time and economic costs of designing, developing, and iteratively optimizing stamped parts. It helps designers optimize the overall performance of stamped parts more accurately. This method is widely used by engineering designers, but it also requires researchers and engineers to develop more constitutive models and their finite element subroutines that can accurately and efficiently describe the dynamic impact mechanics properties of metallic materials. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for calculating finite element data based on a material constitutive model, which can be applied in finite element software to accurately and effectively calculate finite element simulation data.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A method for calculating finite metadata based on a material constitutive model, comprising:

[0009] Obtain the strain increment, stress, strain, and equivalent plastic strain rate at any element mesh integration point in the preset material finite element model at the i-th increment step; i≥2, and the stress evolution function in the preset material finite element model is the Johnson-Cook material constitutive model;

[0010] Based on the strain increment at the unit mesh integration point in the i-th increment step and the stress at the (i-1)-th increment step, calculate the trial stress at the unit mesh integration point in the i-th increment step.

[0011] Based on the Von Mises yield criterion, the yield function value is calculated according to the test stress, the strain at the (i-1)th increment step, and the equivalent plastic strain rate, and it is determined whether the yield function value satisfies the preset yield condition.

[0012] If the yield function value does not meet the preset yield condition, the test stress is marked as the actual simulated stress of the unit mesh integration point at the i-th increment step, and the actual simulated strain corresponding to the actual simulated stress is obtained.

[0013] If the yield function value satisfies the preset yield condition, then based on the plastic flow law, the actual simulated stress and corresponding actual simulated strain of the unit mesh integration point at the i-th increment step are calculated according to the strain increment of the unit mesh integration point at the i-th increment step, the stress, strain and equivalent plastic strain rate at the (i-1)-th increment step.

[0014] Output the actual simulated stress and the corresponding actual simulated strain, then update i to i+1. When i+1 is within the preset increment step range, return to the step of obtaining the strain increment, stress, strain and equivalent plastic strain rate at any element mesh integration point in the preset material finite element model at the i-th increment step.

[0015] Optionally, based on the strain increment at the element mesh integration point in the i-th increment step and the stress in the (i-1)-th increment step, the trial stress at the element mesh integration point in the i-th increment step is calculated, specifically including:

[0016] According to the formula

[0017]

[0018] Calculate the trial stress at the integration point of the unit grid in the i-th increment step;

[0019] in, σ represents the trial stress at the integration point of the element mesh in the i-th increment step. n Δε represents the stress at the (i-1)th increment step of the element mesh integration point. n+1 D represents the strain increment at the element mesh integration point in the i-th increment step. e This represents the fourth-order isotropic elastic tensor.

[0020] Optionally, the calculation of the yield function value based on the Von Mises yield criterion, according to the test stress, the strain at the (i-1)th increment step, and the equivalent plastic strain rate, specifically includes:

[0021] According to the formula

[0022]

[0023] Calculate the yield function value;

[0024] in, This represents the yield function value. This represents the trial stress at the integration point of the element mesh in the i-th increment step. A(T), B(T), and C(T) are preset temperature-related model parameters, ε n This represents the strain at the integration point of the element mesh at the (i-1)th increment step. This represents the equivalent plastic strain rate at the element mesh integration point in the (i-1)th increment step.

[0025] To achieve the above objectives, the present invention provides the following technical solution:

[0026] A finite metadata computation system based on a material constitutive model includes:

[0027] The data acquisition module is used to acquire the strain increment, stress, strain, and equivalent plastic strain rate at any unit mesh integration point in the preset material finite element model at the i-th increment step; i≥2, and the stress evolution function in the preset material finite element model is the Johnson-Cook material constitutive model;

[0028] The trial stress calculation module is used to calculate the trial stress of the unit mesh integration point in the i-th increment step based on the strain increment of the unit mesh integration point in the i-th increment step and the stress in the (i-1)-th increment step.

[0029] The yield function value calculation module is used to calculate the yield function value based on the VonMises yield criterion, according to the test stress, the strain at the (i-1)th increment step, and the equivalent plastic strain rate, and to determine whether the yield function value meets the preset yield condition.

[0030] The first yield result processing module is used to mark the test stress as the actual simulated stress of the unit mesh integration point at the i-th increment step when the yield function value does not meet the preset yield condition, and to obtain the actual simulated strain corresponding to the actual simulated stress.

[0031] The second yield result processing module is used to calculate the actual simulated stress and corresponding actual simulated strain of the unit mesh integration point in the i-th increment step based on the plastic flow law when the yield function value meets the preset yield condition.

[0032] The stress-strain output module is used to output the actual simulated stress and the corresponding actual simulated strain, and then update i to i+1. When i+1 is within the preset increment step range, it returns to the data acquisition module.

[0033] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0034] This invention discloses a method and system for calculating finite element data based on a material constitutive model. It utilizes the Johnson-Cook material constitutive model as the stress evolution function in a pre-defined finite element model. Then, based on the strain increment at the element mesh integration point in the i-th increment step and the stress in the (i-1)-th increment step, the trial stress at the i-th increment step is calculated. The yield function value is calculated based on the Von Mises yield criterion, and it is determined whether the yield function value satisfies the pre-defined yield condition. If not, the trial stress is marked as the actual simulated stress, and the corresponding actual simulated strain is obtained. If satisfied, the actual simulated stress at the element mesh integration point in the i-th increment step and the corresponding actual simulated strain are calculated based on the plastic flow law, and finally output. The calculation process stops after all increment steps have been completed. This invention effectively applies a continuous constitutive model describing the complex dynamic impact mechanics of metallic materials to finite element software, enabling accurate and efficient calculation of finite element simulation data. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart illustrating the finite metadata calculation method based on the material constitutive model of the present invention.

[0037] Figure 2 This is a schematic diagram of the structure of the finite metadata calculation system based on the material constitutive model of the present invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] like Figure 1 As shown, this invention provides a finite element data calculation method based on a material constitutive model, comprising:

[0041] Step 100: Obtain the strain increment Δε at any element mesh integration point in the preset material finite element model at the i-th increment step. n+1 The stress σ at the (i-1)th increment step n strain ε n And equivalent plastic strain rate; specifically, the stress, strain, and equivalent plastic strain rate at the element mesh integration point at the end of the (i-1)th increment step. In the text, the characters are bold to represent vectors, characters with the superscript p represent plastic variables, and characters with a hyphen "-" above them represent equivalent variables.

[0042] Additionally, i≥2; for the initial increment step, relevant users can initialize the preset material finite element model as needed to obtain the stress, strain, and equivalent plastic strain rate corresponding to the initial increment step.

[0043] The stress evolution function in the preset material finite element model is the Johnson-Cook material constitutive model. The Johnson-Cook material constitutive model is as follows:

[0044]

[0045] Where σ is the flow stress, ε is the flow stress variation, and A(T), B(T), and C(T) are preset temperature-related model parameters. Let A(T), B(T), and C(T) be the equivalent plastic strain rates. The expressions for A(T), B(T), and C(T) are as follows:

[0046] A(T) = A1T 3 +A2T 2 +A3T+A4

[0047] B(T) = B1T 3 +B2T 2 +B3T+B4

[0048] C(T)=C1T 3 +C2T 2 +C3T+C4

[0049] In the formula, A1, A2, A3, B1, B2, B3, C1, C2, C3 are function coefficients, and A4, B4, C4 are constant values.

[0050] Step 200: Assuming that the strain increment of the unit mesh integration point at the i-th increment step is entirely elastic strain increment and there is no plastic strain increment, then proceed to the trial elastic deformation stage. Based on the strain increment of the unit mesh integration point at the i-th increment step and the stress at the (i-1)-th increment step, calculate the trial stress of the unit mesh integration point at the i-th increment step.

[0051] Step 200 specifically includes: according to the formula

[0052]

[0053] Calculate the trial stress at the integration point of the unit grid in the i-th increment step;

[0054] in, σ represents the trial stress at the integration point of the element mesh in the i-th increment step. n Δε represents the stress at the (i-1)th increment step of the element mesh integration point. n+1 D represents the strain increment at the element mesh integration point in the i-th increment step. e This represents the fourth-order isotropic elastic tensor.

[0055] Step 300: Based on the VonMises yield criterion, calculate the yield function value according to the test stress, the strain at the (i-1)th increment step, and the equivalent plastic strain rate, and determine whether the yield function value satisfies the preset yield condition.

[0056] The formula for calculating the yield function value is:

[0057]

[0058] in, This represents the yield function value. This represents the trial stress at the integration point of the element mesh in the i-th increment step. A(T), B(T), and C(T) are preset temperature-related model parameters, ε n This represents the strain at the integration point of the element mesh at the (i-1)th increment step. This represents the equivalent plastic strain rate at the element mesh integration point in the (i-1)th increment step.

[0059] Step 400: If the yield function value does not meet the preset yield condition, the test stress is marked as the actual simulated stress at the unit mesh integration point in the i-th increment step, and the actual simulated strain corresponding to the actual simulated stress is obtained; that is, if the material does not yield, no plastic strain appears in the current increment step, and the test stress is directly output as the actual simulated stress in the i-th increment step. Specifically, if the yield function value... The material has not yet reached the yield state; the stress is updated according to elastic theory.

[0060] Step 500: If the yield function value satisfies the preset yield condition, then based on the plastic flow law, calculate the actual simulated stress and corresponding actual simulated strain of the element mesh integration point in the i-th increment step according to the strain increment of the element mesh integration point in the i-th increment step, the stress, strain, and equivalent plastic strain rate in the (i-1)-th increment step. That is, if the yield function value... The material enters the yield state, calculated according to plasticity theory.

[0061] The calculation process of the actual simulated stress and corresponding actual simulated strain at the unit mesh integration point in the i-th increment step specifically includes:

[0062] 1) Using the regression mapping algorithm, the equivalent plastic strain increment after yielding is calculated based on the strain increment at the unit mesh integration point in the i-th increment step, the strain in the (i-1)-th increment step, and the equivalent plastic strain rate.

[0063] The formula for calculating the equivalent plastic strain increment after yielding is:

[0064]

[0065] in, D represents the equivalent plastic strain increment after yielding. e Let H represent the fourth-order isotropic elastic tensor, H represent the plastic hardening modulus, and Δε represent the fourth-order isotropic elastic tensor. n+1 This represents the strain increment at the element mesh integration point in the i-th increment step;

[0066] F represents the yield function, σ * Represents the test stress tensor; The equivalent plastic strain increment at the element mesh integration point in the (i-1)th increment step is determined based on the equivalent plastic strain rate in the (i-1)th increment step.

[0067] 2) Based on the equivalent plastic strain increment, the stress and strain at the element mesh integration point in the (i-1)th increment step, calculate the actual simulated stress and strain at the element mesh integration point in the i-th increment step. Specifically:

[0068] 21) Calculate the actual stress increment Δσ at the i-th increment step of the element mesh integration point based on the equivalent plastic strain increment. n+1 and actual strain increment Δε n+1 .

[0069] 22) Add the actual stress increment to the stress at the element mesh integration point in the (i-1)th increment step to calculate the actual simulated stress at the element mesh integration point in the i-th increment step. The specific formula is: σ n+1 =σ n +Δσ n+1 .

[0070] 23) Add the actual strain increment to the strain at the element mesh integration point in the (i-1)th increment step to calculate the actual simulated strain at the element mesh integration point in the i-th increment step. The specific formula is: ε n+1 =ε n +Δε n+1 .

[0071] Step 600: Save and output the actual simulated stress and the corresponding actual simulated strain, then update i to i+1. When i+1 is within the preset increment step range, return to step 100.

[0072] In summary, this invention develops a finite element subroutine algorithm for a Johnson-Cook constitutive model with non-associated flow characteristics by constructing a yield function using the Von Mises yield criterion and using the Johnson-Cook model as the hardening function during the material yielding process, while considering the influence of strain rate and temperature on the material. The algorithm is solved using a regression mapping algorithm, resulting in a concise and easily implemented finite element method. This invention is applicable to solving newly developed comprehensive solutions considering the dynamic impact characteristics of metallic materials; for example, in the stamping of metal parts, a finite element model of the blank to be stamped is first constructed, and the incremental step is set. Then, based on the constitutive model finite element data calculation method provided by this invention, the stress and strain data of the blank under stamping load are simulated, calculated, and output.

[0073] Example 2

[0074] like Figure 2 As shown, in order to implement the technical solution in Embodiment 1, this embodiment provides a finite metadata calculation system based on a material constitutive model, including:

[0075] The data acquisition module 101 is used to acquire the strain increment, stress, strain and equivalent plastic strain rate at any unit mesh integration point in the preset material finite element model at the i-th increment step; i≥2, and the stress evolution function in the preset material finite element model is the Johnson-Cook material constitutive model.

[0076] The test stress calculation module 201 is used to calculate the test stress of the unit mesh integration point at the i-th increment step based on the strain increment at the unit mesh integration point at the i-th increment step and the stress at the (i-1)-th increment step.

[0077] The yield function value calculation module 301 is used to calculate the yield function value based on the VonMises yield criterion, according to the test stress, the strain at the (i-1)th increment step, and the equivalent plastic strain rate, and to determine whether the yield function value satisfies the preset yield condition.

[0078] The first yield result processing module 401 is used to mark the test stress as the actual simulated stress of the unit mesh integration point at the i-th increment step when the yield function value does not meet the preset yield condition, and to obtain the actual simulated strain corresponding to the actual simulated stress.

[0079] The second yield result processing module 501 is used to calculate the actual simulated stress and corresponding actual simulated strain of the unit mesh integration point in the i-th increment step based on the plastic flow law when the yield function value meets the preset yield condition. This is done by considering the strain increment of the unit mesh integration point in the i-th increment step, the stress, strain, and equivalent plastic strain rate in the (i-1)-th increment step.

[0080] The stress-strain output module 601 is used to output the actual simulated stress and the corresponding actual simulated strain, and then update i to i+1. When i+1 is within the preset increment step range, it returns to the data acquisition module.

[0081] Compared with the prior art, the present invention also has the following advantages:

[0082] This invention considers strain hardening, strain rate hardening, and temperature softening effects, and uses a regression mapping algorithm to solve for the equivalent plastic strain increment after yielding. It also considers the influence of the equivalent strain rate and establishes a simple rate-related algorithm.

[0083] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0084] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A finite element data calculation method based on a material constitutive model, characterized by, The method comprises: acquiring any element grid integral point in the preset material finite element model, strain increment at the i-th increment step, stress, strain and equivalent plastic strain rate at the i-1-th increment step; i 2, the stress evolution function in the preset material finite element model is Johnson-Cook material constitutive model; calculating a trial stress of the element grid integration point at the i-th increment step according to a strain increment of the element grid integration point at the i-th increment step and a stress at the (i-1)-th increment step; calculating a yield function value according to the trial stress, a strain at the (i-1)-th increment step and an equivalent plastic strain rate based on a Von Mises yield criterion, and determining whether the yield function value meets a preset yield condition; if the yield function value does not meet the preset yield condition, marking the trial stress as an actual simulation stress of the element grid integration point at the i-th increment step, and obtaining an actual simulation strain corresponding to the actual simulation stress; if the yield function value meets the preset yield condition, calculating the actual simulation stress and the actual simulation strain of the element grid integration point at the i-th increment step according to the strain increment of the element grid integration point at the i-th increment step, the stress at the (i-1)-th increment step, the strain and the equivalent plastic strain rate based on a plastic flow rule; wherein the calculation process of the actual simulation stress and the actual simulation strain of the element grid integration point at the i-th increment step comprises: calculating a post-yield equivalent plastic strain increment according to the strain increment of the element grid integration point at the i-th increment step, the strain at the (i-1)-th increment step and the equivalent plastic strain rate by using a regression mapping algorithm; the calculation formula of the post-yield equivalent plastic strain increment is: ； wherein, represents the increment of the equivalent plastic strain after yielding, represents the fourth order isotropic elastic tensor, H represents the plastic hardening modulus, represents the strain increment of the integration point of the element mesh at the i-th increment step; , , F represents a yield function, represents a trial stress tensor; represents the equivalent plastic strain increment of the element integration point at the i-1th increment step, which is determined according to the equivalent plastic strain rate at the i-1th increment step; , A T B T C T are preset model parameters related to temperature, represents the equivalent plastic strain of the element integration point at the i-1th increment step, represents the equivalent plastic strain rate of the element integration point at the i-1th increment step;​​​​​ calculating the actual simulation stress and the actual simulation strain of the element grid integration point at the i-th increment step according to the post-yield equivalent plastic strain increment, the stress at the (i-1)-th increment step and the strain; specifically as follows: calculating an actual stress increment of the element mesh integration point at the i-th increment step according to the equivalent plastic strain increment and an actual strain increment ; The actual stress increment and the stress of the element grid integration point at the i-1 increment step are added to calculate the actual simulation stress of the element grid integration point at the i increment step; the specific formula is: ; The actual strain increment and the strain of the element grid integration point at the i-1 increment step are added to calculate the actual simulation strain of the element grid integration point at the i increment step; the specific formula is: ; outputting the actual simulation stress and the actual simulation strain, and then updating i to i+1; when i+1 is in a preset increment step range, returning to the step of obtaining the strain increment of any element grid integration point in the preset material finite element model at the i-th increment step, the stress at the (i-1)-th increment step, the strain and the equivalent plastic strain rate.

2. The finite element data calculation method based on a material constitutive model according to claim 1, characterized by, calculating the trial stress of the element grid integration point at the i-th increment step according to the strain increment of the element grid integration point at the i-th increment step and the stress at the (i-1)-th increment step, specifically comprising: calculating the trial stress of the element grid integration point at the i-th increment step according to the formula calculating the trial stress of the element grid integration point at the i-th increment step according to the formula where, denotes the trial stress at the integration point of the element at the i-th increment step, denotes the stress at the integration point of the element at the i-1-th increment step, denotes the strain increment at the integration point of the element at the i-th increment step, denotes the fourth order isotropic elastic tensor.

3. The finite element data calculation method based on a material constitutive model according to claim 1, characterized by, calculating the yield function value according to the formula The system comprises: a trial stress calculation module configured to calculate a trial stress of the element grid integration point at the i-th increment step according to a strain increment of the element grid integration point at the i-th increment step and a stress at the (i-1)-th increment step; wherein, represents the yield function value, represents the trial stress of the unit grid integration point at the i-th increment step.

4. A finite element data calculation system based on a material constitutive model, characterized by, a yield function value calculation module configured to calculate a yield function value according to the trial stress, a strain at the (i-1)-th increment step and an equivalent plastic strain rate based on a Von Mises yield criterion, and determine whether the yield function value meets a preset yield condition; a data acquisition module, configured to acquire a strain increment at any unit grid integral point in a preset material finite element model, a stress, a strain and an equivalent plastic strain rate at an i-th increment step, and a stress at an i-1-th increment step; i 2, the stress evolution function in the preset material finite element model is a Johnson-Cook material constitutive model; ​ ​ The first yield result processing module is configured to, when the yield function value does not satisfy the preset yield condition, mark the trial stress as actual simulation stress of the unit grid integration point at the i th increment step, and obtain actual simulation strain corresponding to the actual simulation stress; The second yield result processing module is configured to, when the yield function value satisfies the preset yield condition, based on a plastic flow rule, calculate actual simulation stress and corresponding actual simulation strain of the unit grid integration point at the i th increment step according to strain increment of the unit grid integration point at the i th increment step, stress, strain and equivalent plastic strain rate at the i-1 th increment step. The calculation process of the actual simulation stress and the corresponding actual simulation strain of the unit grid integration point at the i th increment step specifically includes: The regression mapping algorithm is adopted to calculate post-yield equivalent plastic strain increment according to the strain increment of the unit grid integration point at the i th increment step, strain at the i-1 th increment step and equivalent plastic strain rate; the calculation formula of the post-yield equivalent plastic strain increment is as follows: ； wherein, represents the increment of the equivalent plastic strain after yielding, represents the fourth order isotropic elastic tensor, H represents the plastic hardening modulus, represents the strain increment of the integration point of the element mesh at the i-th increment step; , , F represents a yield function, represents a trial stress tensor; represents the equivalent plastic strain increment of the element grid integration point at the i-1 increment step, which is determined according to the equivalent plastic strain rate at the i-1 increment step; , A T , B T , C T are preset model parameters related to temperature, represents the equivalent plastic strain of the element grid integration point at the i-1 increment step, represents the equivalent plastic strain rate of the element grid integration point at the i-1 increment step;​​​ The actual simulation stress and the actual simulation strain of the unit grid integration point at the i th increment step are calculated according to the post-yield equivalent plastic strain increment, stress and strain of the unit grid integration point at the i-1 th increment step; specifically as follows: calculating an actual stress increment at the integration point of the element mesh at the i-th increment step from the equivalent plastic strain increment and the actual strain increment ; The actual stress increment and the stress of the element grid integration point at the i-1 increment step are added to calculate the actual simulation stress of the element grid integration point at the i increment step; the specific formula is: ; The actual strain increment and the strain of the element grid integration point at the i-1 increment step are added to calculate the actual simulation strain of the element grid integration point at the i increment step; the specific formula is: ; The stress-strain output module is configured to output the actual simulation stress and the corresponding actual simulation strain, and then update i to i+1; when i+1 is in the preset increment step range, return to the data acquisition module.

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