Constructive model establishment and transient dynamics analysis method considering plastic domain

Abstract

The invention provides a constitutive model establishment and transient dynamic analysis method considering a plastic domain, and relates to the technical field of constitutive relation and dynamic analysis. The method comprises the following steps: introducing plastic strain parameters corresponding to the yield strength of a material into a J-C constitutive equation at normal temperature, establishing a constitutive model considering a plastic domain, and fitting and solving each parameter in the established constitutive model through test data to obtain a solved constitutive model; the solved constitutive model is subjected to numerical simulation and is compared with test data, so that the reasonability of the solved constitutive model can be verified; the stress deconservative property is verified by establishing an explicit dynamic finite element model and carrying out linear elasticity analysis and elastic-plastic analysis; the method can provide reference for plastic domain constitutive model establishment and transient dynamics deconservative analysis.

Description

Technical Field

[0001] This application relates to the fields of constitutive relations and dynamic analysis technology, and in particular to a method for establishing constitutive models and performing transient dynamic analysis considering plastic domains. Background Technology

[0002] In the field of machinery, mechanical equipment may be subjected to temperature, pressure, self-weight, and high-speed mechanical loads. Under the long-term action of these loads, the materials of the equipment will undergo plastic deformation, leading to the continuous accumulation of plastic strain and accelerating material failure. Currently, research on the mechanical properties of materials under static conditions is relatively mature, but research on the mechanical behavior under dynamic loads is relatively limited. The mechanical properties of materials under dynamic loads differ significantly from those under static conditions, with strain rate being one of the important factors affecting the dynamic mechanical properties of materials. Generally speaking, the yield strength of steel increases with increasing strain rate; this phenomenon is called the strain rate strengthening effect. Typically, the dynamic analysis of mechanical equipment is based on the mechanical properties of materials under quasi-static conditions, often neglecting the improvement in mechanical properties due to plastic deformation under high-speed mechanical loads. To simulate the plastic domain behavior of materials under different strain rates, it is necessary to obtain the constitutive relations of the plastic domain, thereby providing a model foundation for deconservative analysis results under high-speed mechanical loads.

[0003] The constitutive relation of a material reflects the essential differences in the mechanical properties of different materials. Currently, the main constitutive relations for the plastic domain are the Bonder-Partom model, Johnson-Cook model, Zerilli-Armstrong model, MechanicalThreshold Stress model, and Steinberg-Cochran-Guinan model, among which the Johnson-Cook model (JC model) is one of the most commonly used constitutive models for the plastic domain. The JC model's initial constitutive equation uses a series of multiplicative relationships to describe the effects of strain, strain rate, and temperature on the yield stress and failure strain of the material during deformation. This model is characterized by its simple form, relatively clear meaning of model parameters, and ease of fitting through experiments. Furthermore, most computational programs already have the function of setting its model parameters, thus it is widely used in engineering fields.

[0004] Transient dynamic analysis is an important tool for mechanical calculation and analysis. Currently, most transient dynamic analyses of structures are based on the linear elastic constitutive equations of the material, and the results are often quite conservative. However, when considering the constitutive equations of the plastic domain, explicit dynamic analysis methods are needed to fully account for the improvement in the mechanical properties of the material under plastic deformation, thereby providing reasonable deconservatism assessment results. Currently, research on transient dynamic analysis based on the JC initial constitutive equations is relatively limited. Summary of the Invention

[0005] In view of the above problems, this application is made to provide a method, system, and computing device for establishing constitutive models and performing transient dynamic analysis considering the plastic domain, which overcomes or at least partially solves the above problems. The technical solution is as follows: Firstly, a method for establishing a constitutive model and performing transient dynamic analysis considering a plastic domain is provided, the method comprising: The stress-strain test data curves of the material at room temperature under different strain rates are processed into stress-plastic strain test data curves under different strain rates; Based on pre-defined assumptions, the JC constitutive equation at room temperature is rewritten by introducing the plastic strain parameter corresponding to the material's yield strength. D A constitutive model considering the plastic domain is established; where, D Take the minimum value of the plastic strain corresponding to the yield strength at each strain rate; Based on the stress-plastic strain test data curves at different strain rates, the parameters in the established constitutive model are fitted and solved to obtain the solved constitutive model. For the solved constitutive model, the numerical simulation results are compared with the experimental data to verify whether the solved constitutive model meets the preset rationality conditions; If the solved constitutive model is verified to meet the preset rationality conditions, then an explicit dynamic finite element model is established based on the solved constitutive model. The constitutive relation of the material is defined as Hooke's law. Based on the explicit dynamic finite element model, a linear elastic transient dynamic analysis is carried out to obtain the maximum equivalent stress analysis results of the linear elasticity. The material constitutive relations are defined as Hooke's law and JC plastic domain constitutive relations. Based on the explicit dynamic finite element model, elastoplastic transient dynamic analysis is carried out to obtain the elastoplastic maximum equivalent stress analysis results. By comparing the results of the maximum equivalent stress analysis for linear elasticity and the maximum equivalent stress analysis for elastoplasticity, the stress deconservatism is verified.

[0006] In one possible implementation, the stress-strain test data curves of the material at different strain rates at room temperature are processed into stress-plastic strain test data curves at different strain rates using the following equation (1): (1) In equation (1), For plastic strain, In response, For elastic strain, For stress, This is the elastic modulus of the material.

[0007] In one possible implementation, the presuppositions include the following three assumptions: Assumption 1: Since increased strain and strain rate will lead to an increase in material temperature and thus affect mechanical properties, the constitutive model considering the plastic domain to be established will not consider the adiabatic temperature rise effect caused by increased strain and strain rate. Assumption 2: For different strain rates, the material can obtain its yield strength when it reaches the same plastic strain; Assumption 3: Based on the premise of Assumption 2, from the end of the elastic stage to the plastic strain stage, the stress of the material is equal to the yield strength.

[0008] In one possible implementation, the initial constitutive equation of JC describes the stress-plastic strain relationship as shown in equation (2): (2) In equation (2), Stress, also known as equivalent stress; A The yield strength of the material; B For strain enhancement index; C The strain rate sensitivity coefficient; n The hardening index; This is plastic strain, also known as equivalent plastic strain; This is the equivalent plastic strain rate; The normalized equivalent plastic strain rate; For reference strain rate; T The current temperature; For reference temperature; The melting point temperature of the material; m Temperature softening index; Based on the experimental test results, the dynamic properties of the material under normal temperature conditions are studied. That is, the softening effect caused by temperature change is not considered, and only the strain hardening term and strain rate hardening term of the material are simulated. Therefore, the JC constitutive equation at normal temperature is shown in equation (3): (3) Equation (3) is derived from equation (2) without considering the softening effect caused by temperature changes.

[0009] In one possible implementation, based on pre-defined assumptions, the JC constitutive equation at room temperature is rewritten by introducing the plastic strain parameter corresponding to the material's yield strength. D The constitutive model considering the plastic domain is established as shown in equation (4): (4) Equation (4) is based on the presuppositions and rewrites the JC constitutive equation (3) at room temperature by introducing the plastic strain parameter corresponding to the yield strength of the material. D What was obtained A , B , C , n All are parameters.

[0010] In one possible implementation, based on stress-plastic strain test data curves at different strain rates, the parameters in the established constitutive model are fitted and solved, including: Determining parameters under ambient and quasi-static conditions A That is, under normal temperature and quasi-static conditions, simplifying equation (4) yields equation (5): (5) because D The minimum value of the plastic strain corresponding to the yield strength at each strain rate is taken, and a reference strain rate is selected from different strain rates. When plastic strain ,parameter A The yield strength of a material can be directly obtained from the stress-plastic strain test data curve at the material's reference strain rate. It is a simulation of the enhanced segment of the curve; Determining parameters under ambient and quasi-static conditions B and n That is, under normal temperature and quasi-static conditions, through logarithmic transformation, equation (5) yields equation (6): (6) In equation (6), yes A linear function with a slope of n The intercept is Then, the experimental data are plotted according to equation (6) to obtain the linear fitting equation at the reference strain rate, and the parameters are obtained from the slope and intercept of the linear fitting equation. B and n ; Parameters were obtained by fitting under normal temperature conditions. CThat is, under normal temperature conditions, equation (4) is transformed to obtain equation (7): (7) Using equation (7), the experimental data were plotted on graph paper for linear fitting to obtain the values ​​under different strain rates. C Values, taken at different strain rates C The average of the values ​​is used for assignment.

[0011] In one possible implementation, an explicit dynamic finite element model is established based on the solved constitutive model, including: Based on the solved constitutive model, an explicit dynamic finite element model is established by defining the explicit dynamic finite element analysis element type, JC constitutive model parameters, rigid connections, and material properties. The JC constitutive model parameters are the various parameters in the solved constitutive model.

[0012] In one possible implementation, the stress deconservatism is verified by comparing the results of the linear elastic maximum equivalent stress analysis and the elastoplastic maximum equivalent stress analysis, including: By comparing the results of the linear elastic maximum equivalent stress analysis and the elastoplastic maximum equivalent stress analysis, if the difference between the elastoplastic maximum equivalent stress and the linear elastic maximum equivalent stress is greater than the preset difference threshold, then the stress deconservatism is verified.

[0013] Secondly, a constitutive model establishment and transient dynamic analysis system considering the plastic domain is provided, the system comprising: The curve processing unit is used to process stress-strain test data curves of materials at different strain rates at room temperature into stress-plastic strain test data curves at different strain rates. The constitutive model building unit is used to rewrite the JC constitutive equation at room temperature based on preset assumptions, introducing the plastic strain parameter corresponding to the material's yield strength. D A constitutive model considering the plastic domain is established; where, D Take the minimum value of the plastic strain corresponding to the yield strength at each strain rate; The parameter solving unit is used to fit and solve each parameter in the established constitutive model based on the stress-plastic strain test data curves under different strain rates, and obtain the solved constitutive model. The rationality verification unit is used to compare the numerical simulation results with experimental data to verify whether the solved constitutive model meets the preset rationality conditions. The transient dynamics analysis unit is used to establish an explicit dynamic finite element model based on the solved constitutive model if the solved constitutive model is verified to meet the preset rationality conditions. The material constitutive relation is defined as Hooke's law, and linear elastic transient dynamic analysis is performed based on the explicit dynamic finite element model to obtain the linear elastic maximum equivalent stress analysis results. The material constitutive relation is defined as Hooke's law and the JC plastic domain constitutive relation, and elastoplastic transient dynamic analysis is performed based on the explicit dynamic finite element model to obtain the elastoplastic maximum equivalent stress analysis results. The linear elastic maximum equivalent stress analysis results and the elastoplastic maximum equivalent stress analysis results are compared to verify the stress deconservatism.

[0014] Thirdly, a computing device is provided, comprising a processor and a memory, wherein the memory stores a computer program, and the processor is configured to run the computer program to perform the constitutive model establishment and transient dynamic analysis method considering the plastic domain as described in any of the preceding claims.

[0015] By utilizing the above technical solutions, the present application provides a method, system, and computing device for establishing a constitutive model considering the plastic domain and performing transient dynamic analysis. This method introduces the plastic strain parameter corresponding to the material's yield strength into the JC constitutive equation at room temperature to establish a constitutive model considering the plastic domain. The parameters in the established constitutive model are then solved by fitting experimental data to obtain the solved constitutive model. The rationality of the solved constitutive model can be verified by performing numerical simulations and comparing them with experimental data. The stress deconservatism is verified by establishing an explicit dynamic finite element model and performing linear elastic and elastoplastic analyses. This method can provide a reference for establishing a plastic domain constitutive model and performing transient dynamic deconservatism analysis. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below.

[0017] Figure 1 A flowchart is shown showing the constitutive model establishment and transient dynamic analysis method considering the plastic domain provided in the embodiments of this application; Figure 2 A flowchart is shown below illustrating a constitutive model establishment and transient dynamic analysis method considering the plastic domain provided in another embodiment of this application; Figure 3 The stress-plastic strain test data curves provided in the embodiments of this application are shown. Figure 4 The solution provided in the embodiments of this application is illustrated. B and n The fitting results at that time; Figures 5a to 5d The solution provided in the embodiments of this application is illustrated. C Fitting results at different strain rates; Figures 6a to 6e The numerical simulation results and experimental data under different strain rates provided in the embodiments of this application are shown in the figure. Figure 7 This is a schematic diagram of the structural model in this embodiment; Figure 8 This is the explicit dynamic finite element model in this embodiment; Figure 9 This is the result of the linear elastic maximum equivalent stress analysis in this embodiment; Figure 10 This is the result of the elastoplastic maximum equivalent stress analysis in this embodiment; Figure 11 The diagram shows the structure of the constitutive model establishment and transient dynamic analysis system considering the plastic domain provided in the embodiments of this application. Detailed Implementation

[0018] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0019] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such use can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the term "comprising" and its variations should be interpreted as open-ended terms meaning "including but not limited to."

[0020] To address the aforementioned technical problems, embodiments of this application provide a method for establishing a constitutive model and performing transient dynamic analysis considering the plastic domain, such as... Figure 1 As shown, the constitutive model establishment and transient dynamic analysis method considering the plastic domain may include the following steps S101 to S108: Step S101: Process the stress-strain test data curves of the material at room temperature under different strain rates into stress-plastic strain test data curves under different strain rates. Step S102: Based on the preset assumptions, rewrite the JC constitutive equation at room temperature by introducing the plastic strain parameter corresponding to the yield strength of the material. DA constitutive model considering the plastic domain is established; where, D Take the minimum value of the plastic strain corresponding to the yield strength at each strain rate; Step S103: Based on the stress-plastic strain test data curves at different strain rates, fit and solve each parameter in the established constitutive model to obtain the solved constitutive model. Step S104: For the solved constitutive model, the numerical simulation results are compared with the experimental data to verify whether the solved constitutive model meets the preset rationality conditions. Here, the preset rationality conditions can be set according to actual needs, such as the difference between the numerical simulation results and the experimental data being less than the first preset value, or the square of the difference being less than the second preset value, etc. This embodiment does not limit this. Step S105: If the solved constitutive model is verified to meet the preset rationality conditions, then an explicit dynamic finite element model is established based on the solved constitutive model. Step S106: Define the material constitutive relation as Hooke's law, and conduct linear elastic transient dynamic analysis based on the explicit dynamic finite element model to obtain the linear elastic maximum equivalent stress analysis results; Step S107: Define the material constitutive relation as Hooke's law and JC plastic domain constitutive relation, and carry out elastoplastic transient dynamic analysis based on explicit dynamic finite element model to obtain the elastoplastic maximum equivalent stress analysis results; Step S108: Compare the results of the linear elastic maximum equivalent stress analysis and the elastoplastic maximum equivalent stress analysis to verify the stress deconservatism.

[0021] This embodiment introduces the plastic strain parameter corresponding to the yield strength of the material into the JC constitutive equation at room temperature to establish a constitutive model considering the plastic domain. The parameters in the established constitutive model are then solved by fitting experimental data, yielding the solved constitutive model. The rationality of the solved constitutive model can be verified by performing numerical simulations and comparing them with experimental data. The stress deconservatism is verified by establishing an explicit dynamic finite element model and performing linear elastic and elastoplastic analyses. This method can provide a reference for establishing plastic domain constitutive models and performing transient dynamic deconservatism analysis.

[0022] This application provides a possible implementation method, which uses the following formula (1) to process the stress-strain test data curves of the material at different strain rates at room temperature into stress-plastic strain test data curves at different strain rates: (1) In equation (1), Plastic strain, dimensionless; For adaptability, dimensionless; It is elastic strain, dimensionless; Stress is expressed in Pascals (Pa). This represents the elastic modulus of the material, expressed in Pa.

[0023] This application provides a possible implementation method, and the JC initial constitutive equation describes the stress-plastic strain relationship as shown in equation (2): (2) In equation (2), Stress, also known as equivalent stress, is measured in Pa. A The yield strength of the material is expressed in Pa. B The strain intensification index is expressed in Pa. C The strain rate sensitivity coefficient is dimensionless. n The hardening index is dimensionless. Plastic strain, also known as equivalent plastic strain, is dimensionless. Equivalent plastic strain rate, in seconds (s) -1 ); The normalized equivalent plastic strain rate is dimensionless. Reference strain rate, in seconds (s) -1 ); T The current temperature; For reference temperature, room temperature, also known as normal temperature, is generally used. A Measured at this temperature; The melting point temperature of the material; m The temperature softening index is dimensionless and generally... ; Based on the experimental test results, the dynamic properties of the material under normal temperature conditions are studied. That is, the softening effect caused by temperature change is not considered, and only the strain hardening term and strain rate hardening term of the material are simulated. Therefore, the JC constitutive equation at normal temperature is shown in equation (3): (3) Equation (3) is derived from equation (2) without considering the softening effect caused by temperature changes.

[0024] As an ideal rigid-plastic model, the JC constitutive equation (3) at room temperature shows that: under plastic strain At this strain rate, the yield strength of the material can be obtained. It is assumed that the point where the stress-strain test data curve transitions from the elastic stage to the plastic stage is the yield point, thus ignoring the flow yield stage. This assumption is more ideal than material test results. Actual material test results often involve elastic, yield, hardening, and necking stages. The stress-strain test data curve fluctuates around the yield stage. In engineering, the yield strength is generally taken as the material's yield strength, and the plastic strain corresponding to this yield point is generally not zero. Based on the above reasons, the following three assumptions are made: Assumption 1: Since increased strain and strain rate will lead to an increase in material temperature and thus affect mechanical properties, the constitutive model considering the plastic domain to be established will not consider the adiabatic temperature rise effect caused by increased strain and strain rate.

[0025] Assumption 2: For different strain rates, the material can obtain its yield strength when it reaches the same plastic strain; the same plastic strain here is often relatively small.

[0026] Assumption 3: Based on the premise of Assumption 2, from the end of the elastic stage to the plastic strain stage, the stress of the material is equal to the yield strength.

[0027] This application provides a possible implementation method. Step S102 above is based on preset assumptions, rewriting the JC constitutive equation at room temperature, and introducing the plastic strain parameter corresponding to the yield strength of the material. D The constitutive model considering the plastic domain is established as shown in equation (4): (4) Equation (4) is based on the presuppositions and rewrites the JC constitutive equation (3) at room temperature by introducing the plastic strain parameter corresponding to the yield strength of the material. D What was obtained D Take the minimum value of the plastic strain corresponding to the yield strength at each strain rate. A , B , C , n These are all parameters. Generally speaking, this plastic strain is often very small and can be ignored when using software programs for calculation.

[0028] This application embodiment provides a possible implementation method. In step S103 above, the parameters in the established constitutive model are fitted and solved based on the stress-plastic strain test data curves under different strain rates, as detailed below: Determining parameters under ambient and quasi-static conditionsA That is, under normal temperature and quasi-static conditions, simplifying equation (4) yields equation (5): (5) because D The minimum value of the plastic strain corresponding to the yield strength at each strain rate is taken, and a reference strain rate is selected from different strain rates. When plastic strain ,parameter A The yield strength of a material can be directly obtained from the stress-plastic strain test data curve at the material's reference strain rate. It is a simulation of the enhanced segment of the curve; Determining parameters under ambient and quasi-static conditions B and n That is, under normal temperature and quasi-static conditions, through logarithmic transformation, equation (5) yields equation (6): (6) In equation (6), yes A linear function with a slope of n The intercept is Then, the experimental data are plotted according to equation (6) to obtain the linear fitting equation at the reference strain rate, and the parameters are obtained from the slope and intercept of the linear fitting equation. B and n ; Parameters were obtained by fitting under normal temperature conditions. C That is, under normal temperature conditions, equation (4) is transformed to obtain equation (7): (7) Using equation (7), the experimental data were plotted on graph paper for linear fitting to obtain the values ​​under different strain rates. C Values, taken at different strain rates C The average of the values ​​is used for assignment.

[0029] In this way, we can obtain the constitutive model after solving.

[0030] This application provides a possible implementation method. Step S105 above establishes an explicit dynamic finite element model based on the solved constitutive model. Specifically, it can be based on the solved constitutive model and establish an explicit dynamic finite element model by defining the explicit dynamic finite element analysis element type, JC constitutive model parameters, rigid connection, and material properties. The JC constitutive model parameters are the various parameters in the solved constitutive model.

[0031] This application provides a possible implementation method in which step S108 compares the maximum equivalent stress analysis results of linear elasticity and the maximum equivalent stress analysis results of elastoplasticity to verify the stress deconservatism. Specifically, it can compare the maximum equivalent stress analysis results of linear elasticity and the maximum equivalent stress analysis results of elastoplasticity. If the difference between the maximum equivalent stress of elastoplasticity and the maximum equivalent stress of linear elasticity is greater than a preset difference threshold, then it is determined that the stress deconservatism has been verified.

[0032] This application provides a possible implementation method, which utilizes the APDL (ANSYS core scripting language, which drives the software to complete all operations such as geometric modeling, mesh generation, material definition, load application, and solution settings in the form of commands) command flow to establish an explicit dynamic finite element analysis model readable by LS-DYNA (an explicit dynamic analysis tool), using ANSYS (a general-purpose finite element analysis software that integrates structural, fluid, electromagnetic, thermal, acoustic, and multiphysics coupling analysis). The element correspondence between common implicit and explicit dynamic analysis models is shown in Table 1. The JC constitutive model parameters are defined using the TB and TBDATA commands in APDL; load groups are defined, and transient loads are loaded using the EDLOAD command; the K-file (LS-DYNA input file, containing all information such as model, loads, and solution control) is defined and read / written using the EDOPT (set output options) and EDWRITE (write the current model to the K-file) commands.

[0033] Table 1 Unit Correspondence

[0034] For rigid connections, you need to open the K file in the LS DYNA post-processing interface, recreate the rigid connection through the path Model and Part→Create entity→Entity Creation→Constrained→Nodal Rigid Body, and save the file.

[0035] Since only ambient temperature conditions are considered, the standard JC model keyword MAT_JOHNSON_COOK can be changed to MAT_SIMPLIFIED_JOHNSON_COOK in the K file. The simplified JC model is defined, the relevant parameters of the JC model are input, and the epso option is defined as the reference strain rate value under quasi-static conditions.

[0036] Material properties are defined using the MAT_ELASTIC keyword (linear elastic analysis parameters: elastic modulus, density, and Poisson's ratio); spring stiffness is defined using the MAT_SPRING_ELASTIC keyword.

[0037] The constitutive equation is considered to be Hooke's law, and linear elastic analysis is performed to obtain the linear elastic analysis results; the constitutive equation is considered to be Hooke's law and JC plastic domain constitutive, and elastoplastic analysis is performed to obtain the elastoplastic analysis results; the elastoplastic analysis results are compared with the linear elastic analysis results to verify its deconservatism.

[0038] The above introduces Figure 1 The embodiments shown have various implementation methods for each step. The constitutive model establishment and transient dynamic analysis method considering the plastic domain of the present application will be further explained below through specific embodiments.

[0039] Figure 2 A flowchart of a constitutive model establishment and transient dynamic analysis method considering the plastic domain, as provided in another embodiment of this application, is shown. Figure 2 As shown, it can specifically include S10 to S100: S10, based on the stress-strain test curves (i.e., stress-strain test data curves) at different strain rates at room temperature, is processed to obtain the stress-plastic strain test curves (stress-plastic strain test data curves) at different strain rates. See [link / reference] Figure 3 The different strain rates are 0.001, 0.01, 0.1, 1, and 10.

[0040] After step S10, the method of this embodiment proceeds to step S20, where the JC constitutive equation at room temperature is rewritten based on preset assumptions, and the plastic strain parameter corresponding to the yield strength of the material is introduced. D In order to satisfy the mathematical solution conditions, the parameters D Take the minimum value of the plastic strain corresponding to the yield strength at each strain rate.

[0041] After step S20, the method of this embodiment proceeds to step S30, taking a strain rate of 0.001 as the reference strain rate. Clearly, in... Figure 3 The yield strength corresponding to the curve at a strain rate of 0.001 is... A .

[0042] After step S30, the method of this embodiment proceeds to step S40, where a logarithmic transformation is performed and a graph is plotted according to equation (6). See [link to relevant documentation]. Figure 4 The linear fitting equation at a strain rate of 0.001 can be obtained as follows: y =0.5051 x +6.43. Therefore, we can calculate it in reverse. B =620.1739, n =0.5051.

[0043] After step S40, the method of this embodiment proceeds to step S50, where the experimental data is plotted on graph paper according to equation (7) for linear fitting. See [link to relevant documentation]. Figures 5a to 5d .exist Figures 5a to 5d Different strain rates can be obtained (0.01 s⁻¹, respectively). -1 0.1s -1 1s -1 10s -1 (under) C Values, take the average C =0.009663.

[0044] After step S50, the method of this embodiment proceeds to step S60. After steps S10 to S50, the complete JC constitutive equation (i.e., the solved constitutive model) is obtained, as shown in equation (8). The correctness of the JC constitutive equation is verified by comparing numerical simulations with experimental data. See [link to relevant documentation]. Figures 6a to 6e For different strain rates (0.001s), -1 0.01s -1 0.1s -1 1s -1 10s -1 The following is a comparison chart of numerical simulation and experimental data.

[0045] (8) After step S60, the method of this embodiment proceeds to step S70, considering the mass-spring-solid-shell-solid-spring structural model, see [link to relevant documentation]. Figure 7 The upper and lower rectangles were simulated using solid elements, the four vertical plates in the middle were simulated using shell elements, and the lower connection was simulated using spring elements. A concentrated mass was applied to the top of the upper spring, and a full constraint condition was applied to the bottom of the lower spring. An explicit dynamic finite element model was established by defining the explicit dynamic finite element analysis element type, JC constitutive model parameters, rigid connections, and material properties. (See [link to relevant documentation]). Figure 8 .

[0046] After step S70, the method of this embodiment proceeds to step S80, where the material constitutive relation is defined as Hooke's law, a displacement time-history load is applied to the bottom of the lower spring for transient solution, and the maximum equivalent stress analysis result of the linear elasticity is obtained. See [link to relevant documentation]. Figure 9 ,exist Figure 9In the diagram, Contours of Effective Stress (vm) represents the isoline map of equivalent stress; max IP.value represents the maximum integral point value; min=0,at elem#16593 indicates that the minimum value is 0, appearing in cell number 16593; max=1.17454e+09,at elem#13147 indicates that the maximum value is 1.17454e+09, appearing in cell number 13147.

[0047] After step S80, the method of this embodiment proceeds to step S90, where the material constitutive relation is defined as Hooke's law and JC plastic domain constitutive relation. A displacement time-history load is applied to the bottom end of the lower spring for transient solution, and the elastoplastic maximum equivalent stress analysis result is obtained. See [link to relevant documentation]. Figure 10 ,exist Figure 10 In the diagram, Contours of Effective Stress (vm) represents the isoline map of equivalent stress; max IP.value represents the maximum integral point value; min=0,at elem#16593 indicates that the minimum value is 0, appearing in cell number 16593; max=5.89659e+08,at elem#13828 indicates that the maximum value is 5.89659e+08, appearing in cell number 13828.

[0048] After step S90, the method of this embodiment proceeds to step S100, comparing... Figure 9 and Figure 10 The results of the maximum equivalent stress in the linear elastic and elastoplastic analyses show that the maximum equivalent stress in the elastoplastic analysis is significantly smaller than that in the linear elastic analysis, thus verifying the stress deconservatism.

[0049] The technical solutions provided in this application embodiment have at least the following technical effects or advantages: 1) For the JC constitutive equation at room temperature, given that the plastic strain corresponding to the yield point of the stress-strain curve is generally not zero in engineering, a plastic strain parameter corresponding to the material's yield strength is introduced. D By rewriting the equations based on experimental data, the mechanical properties of materials can be simulated relatively accurately.

[0050] 2) Regarding the sensitivity coefficient of strain rate C When solving the problem, the fitting results under different strain rates are taken into account. By averaging the results, the mechanical properties of the material under different strain rates can be simulated well.

[0051] 3) The reference strain rate in the initial constitutive equation of JC is assumed to be 1s. -1 Modify it to the quasi-static value of 0.001s. -1The expression is more intuitive.

[0052] 4) By comparing the results of explicit dynamic elastoplastic analysis and linear elastic analysis, the deconservatism of the elastoplastic analysis method can be verified.

[0053] It should be noted that the sequence numbers of the steps in the above embodiments do not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. In practical applications, all the above possible implementation methods can be arbitrarily combined in a combined manner to form possible embodiments of this application, which will not be described in detail here.

[0054] Based on the constitutive model establishment and transient dynamic analysis methods considering the plastic domain provided in the above embodiments, and based on the same inventive concept, this application also provides a constitutive model establishment and transient dynamic analysis system considering the plastic domain.

[0055] Figure 11 This is a structural diagram of the constitutive model establishment and transient dynamic analysis system considering the plastic domain provided in the embodiments of this application. Figure 11 As shown, the constitutive model establishment and transient dynamic analysis system considering the plastic domain may specifically include a curve processing unit 1110, a constitutive model establishment unit 1120, a parameter solving unit 1130, a rationality verification unit 1140, and a transient dynamic analysis unit 1150.

[0056] The curve processing unit 1110 is used to process the stress-strain test data curves of materials at different strain rates at room temperature into stress-plastic strain test data curves at different strain rates. Constitutive model building element 1120 is used to rewrite the JC constitutive equation at room temperature based on preset assumptions, and to introduce the plastic strain parameter corresponding to the yield strength of the material. D A constitutive model considering the plastic domain is established; where, D Take the minimum value of the plastic strain corresponding to the yield strength at each strain rate; The parameter solving unit 1130 is used to fit and solve each parameter in the established constitutive model based on the stress-plastic strain test data curves under different strain rates, and obtain the solved constitutive model. The rationality verification unit 1140 is used to compare the numerical simulation results with the experimental data to verify whether the solved constitutive model meets the preset rationality conditions. The transient dynamics analysis unit 1150 is used to establish an explicit dynamics finite element model based on the solved constitutive model if the solved constitutive model is verified to meet the preset rationality conditions; the material constitutive relation is defined as Hooke's law, and linear elastic transient dynamics analysis is carried out based on the explicit dynamics finite element model to obtain the linear elastic maximum equivalent stress analysis result; the material constitutive relation is defined as Hooke's law and JC plastic domain constitutive, and elastoplastic transient dynamics analysis is carried out based on the explicit dynamics finite element model to obtain the elastoplastic maximum equivalent stress analysis result; the linear elastic maximum equivalent stress analysis result and the elastoplastic maximum equivalent stress analysis result are compared to verify the stress deconservatism.

[0057] This application provides a possible implementation method in which the curve processing unit 1110 processes the stress-strain test data curves of the material at different strain rates at room temperature into stress-plastic strain test data curves at different strain rates using the following formula (1): (1) In equation (1), For plastic strain, In response, For elastic strain, For stress, This is the elastic modulus of the material.

[0058] This application provides a possible implementation method, with the following three assumptions: Assumption 1: Since increased strain and strain rate will lead to an increase in material temperature and thus affect mechanical properties, the constitutive model considering the plastic domain to be established will not consider the adiabatic temperature rise effect caused by increased strain and strain rate. Assumption 2: For different strain rates, the material can obtain its yield strength when it reaches the same plastic strain; Assumption 3: Based on the premise of Assumption 2, from the end of the elastic stage to the plastic strain stage, the stress of the material is equal to the yield strength.

[0059] This application provides a possible implementation method, and the JC initial constitutive equation describes the stress-plastic strain relationship as shown in equation (2): (2) In equation (2), Stress, also known as equivalent stress; A The yield strength of the material; B For strain enhancement index; C The strain rate sensitivity coefficient; n The hardening index; This is plastic strain, also known as equivalent plastic strain; This is the equivalent plastic strain rate; The normalized equivalent plastic strain rate; For reference strain rate; T The current temperature; For reference temperature; The melting point temperature of the material; m Temperature softening index; Based on the experimental test results, the dynamic properties of the material under normal temperature conditions are studied. That is, the softening effect caused by temperature change is not considered, and only the strain hardening term and strain rate hardening term of the material are simulated. Therefore, the JC constitutive equation at normal temperature is shown in equation (3): (3) Equation (3) is derived from equation (2) without considering the softening effect caused by temperature changes.

[0060] This application embodiment provides a possible implementation, wherein the constitutive model establishment unit 1120 is further configured to: Based on pre-defined assumptions, the JC constitutive equation at room temperature is rewritten by introducing the plastic strain parameter corresponding to the material's yield strength. D The constitutive model considering the plastic domain is established as shown in equation (4): (4) Equation (4) is based on the presuppositions and rewrites the JC constitutive equation (3) at room temperature by introducing the plastic strain parameter corresponding to the yield strength of the material. D What was obtained A , B , C , n All are parameters.

[0061] This application embodiment provides a possible implementation, wherein the parameter solving unit 1130 is further configured to: Determining parameters under ambient and quasi-static conditions A That is, under normal temperature and quasi-static conditions, simplifying equation (4) yields equation (5): (5) because D The minimum value of the plastic strain corresponding to the yield strength at each strain rate is taken, and a reference strain rate is selected from different strain rates. When plastic strain ,parameter A The yield strength of a material can be directly obtained from the stress-plastic strain test data curve at the material's reference strain rate. It is a simulation of the enhanced segment of the curve; Determining parameters under ambient and quasi-static conditions Band n That is, under normal temperature and quasi-static conditions, through logarithmic transformation, equation (5) yields equation (6): (6) In equation (6), yes A linear function with a slope of n The intercept is Then, the experimental data are plotted according to equation (6) to obtain the linear fitting equation at the reference strain rate, and the parameters are obtained from the slope and intercept of the linear fitting equation. B and n ; Parameters were obtained by fitting under normal temperature conditions. C That is, under normal temperature conditions, equation (4) is transformed to obtain equation (7): (7) Using equation (7), the experimental data were plotted on graph paper for linear fitting to obtain the values ​​under different strain rates. C Values, taken at different strain rates C The average of the values ​​is used for assignment.

[0062] This application embodiment provides a possible implementation, wherein the transient dynamics analysis unit 1150 is further configured to: Based on the solved constitutive model, an explicit dynamic finite element model is established by defining the explicit dynamic finite element analysis element type, JC constitutive model parameters, rigid connections, and material properties. The JC constitutive model parameters are the various parameters in the solved constitutive model.

[0063] This application embodiment provides a possible implementation, wherein the transient dynamics analysis unit 1150 is further configured to: By comparing the results of the linear elastic maximum equivalent stress analysis and the elastoplastic maximum equivalent stress analysis, if the difference between the elastoplastic maximum equivalent stress and the linear elastic maximum equivalent stress is greater than the preset difference threshold, then the stress deconservatism is verified.

[0064] Based on the same inventive concept, this application also provides a computing device, including a processor and a memory, wherein the memory stores a computer program, and the processor is configured to run the computer program to execute the constitutive model establishment and transient dynamic analysis method considering the plastic domain of any of the above embodiments.

[0065] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that within the spirit and principles of this application, modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the corresponding technical solutions to leave the protection scope of this application.

Claims

1. A method for establishing a constitutive model considering a plastic zone and transient dynamic analysis, characterized in that, The method comprises: processing the stress-strain test data curves of the material at normal temperature under different strain rates into stress-plastic strain test data curves under different strain rates; Based on the preset assumption, the J-C constitutive equation at normal temperature is rewritten, and a plastic strain parameter corresponding to the yield strength of the material is introduced D , and a constitutive model considering the plastic domain is established; wherein, D The minimum value of the plastic strain corresponding to the yield strength at each strain rate is taken solving and obtaining each parameter in the established constitutive model according to the stress-plastic strain test data curves under different strain rates; verifying whether the solved constitutive model meets the preset rationality condition by comparing the numerical simulation result with the test data for the solved constitutive model; if the solved constitutive model meets the preset rationality condition, establishing an explicit dynamics finite element model based on the solved constitutive model; defining the material constitutive relation as the Hooke's law, carrying out linear elastic transient dynamics analysis based on the explicit dynamics finite element model, and obtaining linear elastic maximum equivalent stress analysis result; defining the material constitutive relation as the Hooke's law and J-C plastic zone constitutive, carrying out elastic-plastic transient dynamics analysis based on the explicit dynamics finite element model, and obtaining elastic-plastic maximum equivalent stress analysis result; comparing the linear elastic maximum equivalent stress analysis result with the elastic-plastic maximum equivalent stress analysis result to verify stress de-conservatism.

2. The method of claim 1, wherein, The stress-plastic strain test data curves of the material at normal temperature under different strain rates are processed into stress-plastic strain test data curves under different strain rates through the following formula (1): （1） In formula (1), is the plastic strain, is the strain, is the elastic strain, is the stress, is the elastic modulus of the material.

3. The method according to claim 1 or 2, characterized in that, The preset assumptions include the following three assumptions: Assumption one, since the increase of strain and strain rate will lead to the increase of material temperature and thus affect the mechanical properties, that is, the established constitutive model considering plastic zone does not consider the adiabatic temperature rise effect caused by the increase of strain and strain rate; Assumption two, for different strain rates, the material can obtain its yield strength when reaching the same plastic strain; Assumption three, based on the premise of assumption two, the stress of the material is equal to the yield strength from the end of the elastic stage to the plastic strain stage.

4. The method according to claim 1 or 2, characterized in that, The J-C initial constitutive equation describes the relationship between stress and plastic strain, as shown in formula (2): （2） In formula (2), σ is the stress, also called the equivalent stress; A σy is the yield strength of the material; B n is the strain hardening exponent; C is a strain rate sensitivity coefficient; n is a hardening index; is a plastic strain, also referred to as an equivalent plastic strain; is an equivalent plastic strain rate; is a normalized equivalent plastic strain rate; is a reference strain rate; T is a current temperature; is a reference temperature; is a melting temperature of the material; m is a temperature softening index; According to the test results, the dynamic performance of the material under normal temperature is studied, that is, the temperature rise softening effect caused by temperature change is not considered, only the strain hardening term and the strain rate hardening term of the material are simulated, and thus the J-C constitutive equation under normal temperature is as shown in formula (3): （3） Formula (3) is obtained by formula (2) without considering the temperature rise softening effect caused by temperature change.

5. The method of claim 4, wherein, Based on the preset assumption, the J-C constitutive equation at normal temperature is rewritten, and a plastic strain parameter corresponding to the yield strength of the material is introduced D The constitutive model considering the plastic domain is established as shown in equation (4): （4） The formula (4) is based on a preset assumption, revises the J-C constitutive equation (3) at normal temperature, and introduces a plastic strain parameter corresponding to the yield strength of the material D obtained, A , B , C , n are all parameters.

6. The method of claim 5, wherein, According to the stress-plastic strain test data curves under different strain rates, each parameter in the established constitutive model is solved and obtained, including: Determination of parameters at room temperature and quasi-static conditions A i.e. simplifying equation (4) at room temperature and quasi-static conditions gives equation (5): （5） Since D The minimum value of plastic strain corresponding to the yield strength at each strain rate is taken as the reference plastic strain When the plastic strain The parameter A As the yield strength of the material, it can be directly read from the stress-plastic strain test data curve of the material at the reference strain rate, Is simulated on the curve strengthening section; Determination of parameters at normal temperature and quasi-static conditions B and n i.e. by logarithmic transformation from equation (5) at normal temperature and quasi-static conditions, equation (6) is obtained: （6） In equation (6), yes A linear function with a slope of n The intercept is Then, the experimental data are plotted according to equation (6) to obtain the linear fitting equation at the reference strain rate, and the parameters are obtained from the slope and intercept of the linear fitting equation. B and n ; The parameters are fitted at room temperature C i.e. at room temperature, equation (7) is obtained from equation (4) by transformation （7） The test data is plotted on the coordinate paper using equation (7) to perform linear fitting, and the values of different strain rates are obtained C The average value of the values of different strain rates is taken to perform assignment. C The average value of the values of different strain rates is taken to perform assignment.

7. The method of claim 6, wherein, Based on the solved constitutive model, the explicit dynamics finite element model is established by defining the explicit dynamics finite element analysis unit type, J-C constitutive model parameters, rigid connection and material properties, wherein the J-C constitutive model parameters are each parameter in the solved constitutive model. Comparing the linear elastic maximum equivalent stress analysis result with the elastic-plastic maximum equivalent stress analysis result to verify stress de-conservatism, including:

8. The method of claim 7, wherein, ​ The linear-elastic maximum equivalent stress analysis result and the elastic-plastic maximum equivalent stress analysis result are compared, and if the difference between the elastic-plastic maximum equivalent stress and the linear-elastic maximum equivalent stress is greater than a preset difference threshold, it is determined that stress de-conservatism is verified.

9. A system for constitutive model development and transient dynamic analysis considering plastic domain, characterized by, The system comprises: a curve processing unit configured to process stress-strain test data curves at different strain rates of a material at normal temperature into stress-plastic strain test data curves at different strain rates; The constitutive model establishing unit is configured to rewrite the J-C constitutive equation at normal temperature based on a preset assumption, introduce a plastic strain parameter corresponding to the yield strength of the material, and establish a constitutive model considering a plastic domain D , wherein D The minimum value of the plastic strain corresponding to the yield strength at each strain rate is taken. a parameter solving unit configured to solve each parameter in the established constitutive model according to the stress-plastic strain test data curves at different strain rates, and obtain a solved constitutive model; a rationality verification unit configured to compare numerical simulation results with test data for the solved constitutive model, and verify whether the solved constitutive model meets a preset rationality condition; a transient dynamics analysis unit configured to, if the solved constitutive model meets the preset rationality condition, establish an explicit dynamics finite element model based on the solved constitutive model, define a material constitutive relation as a Hooke's law, carry out linear-elastic transient dynamics analysis based on the explicit dynamics finite element model, obtain linear-elastic maximum equivalent stress analysis results, define the material constitutive relation as a Hooke's law and a J-C plastic zone constitutive, carry out elastic-plastic transient dynamics analysis based on the explicit dynamics finite element model, obtain elastic-plastic maximum equivalent stress analysis results, and compare the linear-elastic maximum equivalent stress analysis results and the elastic-plastic maximum equivalent stress analysis results to verify stress de-conservatism.

10. A computing device, comprising: A processor and a memory are included, wherein the memory stores a computer program, and the processor is configured to run the computer program to execute the constitutive model establishment and transient dynamics analysis method considering a plastic zone according to any one of claims 1 to 8.

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