Construction method and simulation method of hyperelastic constitutive model under global strain

Abstract

The invention belongs to the field of nonlinear material mechanics, and particularly relates to a construction method and a simulation method of a hyperelastic constitutive model under global strain, and the method comprises the steps: screening a hyperelastic constitutive model which has description potential for mechanical response characteristics under global strain as a basic model; extracting a strain energy function item in the basic model; and combining the strain energy function items to obtain the hyperelastic constitutive model under the global strain. According to the superelastic constitutive model under the global strain obtained by the construction method of the superelastic constitutive model under the global strain, a user-defined subprogram is written, the user-defined subprogram is called in finite element software, and material parameters are input for simulation. Compared with an existing hyperelastic constitutive model, the method has the advantages that the mechanical response characteristic description capability of an elastomer material under global strain is improved, and a theoretical basis and a technical route are provided for subsequent researchers to construct a new hyperelastic constitutive model based on an elastomer microscopic network structure.

Description

Technical Field

[0001] The invention belongs to the field of nonlinear material mechanics, and specifically relates to a hyperelastic constitutive model construction method and a simulation method under global strain. Background Art

[0002] In recent years, the use of various new elastomeric materials has increased, and there is an urgent need for a more accurate hyperelastic constitutive model that can be applied in commercial finite element software to quantitatively describe the mechanical behavior of elastomeric materials under complex working conditions.

[0003] The research on hyperelastic constitutive models has a history of nearly 100 years, and a large number of hyperelastic constitutive models describing elastic materials have been proposed. Hyperelastic constitutive models can be divided into phenomenological models and micro-network models: Li and Zhang et al. summarized 85 important hyperelastic constitutive models in the past 100 years and quantitatively analyzed the ability of each hyperelastic constitutive model to describe the mechanical response of elastic materials.

[0004] The current research idea is to use different hyperelastic constitutive models to describe small strain conditions and large strain conditions respectively, and for different mechanical response characteristics under the same strain conditions, hyperelastic constitutive models need to be developed specifically, resulting in a large number of models and low model selection efficiency. Summary of the invention

[0005] The purpose of the present invention is to solve the above-mentioned problems existing in the prior art and to provide a method for constructing a hyperelastic constitutive model under global strain.

[0006] The present invention is achieved through the following technical solution: A method for constructing a hyperelastic constitutive model under global strain, comprising the following steps:

[0007] Screening a hyperelastic constitutive model that has the potential to describe the mechanical response characteristics under global strain as the basic model;

[0008] Extracting the strain energy function term in the basic model;

[0009] The strain energy function terms are combined to obtain a hyperelastic constitutive model under global strain.

[0010] Furthermore, the basic models include Li-Zhang, Gregory, Davis-De-Thomas, gen-Yeoh, Alexander, and modified Yeoh hyperelastic constitutive models.

[0011] Furthermore, the strain energy function term includes:

[0012]

[0013] Among them, C1 ,γ,A,α,M,D,μ,C 2 , B, N, β all represent material parameters; I 1 I represents the first invariant of the left Cauchy-Green deformation tensor; 2 represents the second invariant of the left Cauchy–Green deformation tensor.

[0014] Furthermore, In the formula, λ i Represents the principal stretching ratio of the material in the i direction.

[0015] Furthermore, at least two different strain energy function terms are selected for combination to form 26 new hyperelastic constitutive models under global strain.

[0016] Furthermore, based on the stress-strain curve data of the experimentally tested elastic material, the stress-strain curve is fitted by iterating the material parameters of the hyperelastic constitutive model under global strain, and the highest determination coefficient R 2 Determine optimal material parameters.

[0017] The present invention also provides a simulation method for an elastomeric material under global strain, wherein a user-defined subroutine is written based on the hyperelastic constitutive model under global strain obtained by the method for constructing a hyperelastic constitutive model under global strain described in the present invention, and the user-defined subroutine is called in finite element software and material parameters are input for simulation.

[0018] Furthermore, the steps of writing a user-defined subroutine include:

[0019] Calculate the partial derivative of the strain energy function term of the hyperelastic constitutive model under global strain with respect to the first invariant of the left Cauchy-Green deformation tensor or the second invariant of the left Cauchy-Green deformation tensor;

[0020] The partial derivatives are embedded into a secondary development interface framework provided in the finite element software.

[0021] Furthermore, the finite element software is Abaqus, and the user-defined subroutine is UHYPER.

[0022] Compared with the prior art, the beneficial effects of the present invention include:

[0023] 1. Based on the basic theory of hyperelastic constitutive model, the present invention summarizes the universal strain energy function term of the hyperelastic constitutive model that accurately describes the mechanical response characteristics of elastomeric materials under global strain, and constructs 26 hyperelastic constitutive models that accurately describe the mechanical response characteristics of elastomeric materials under global strain by cross-combining the strain energy function terms based on the hyperelastic constitutive theory of elastomeric materials. Compared with the existing hyperelastic constitutive model, it not only improves the ability to describe the mechanical response characteristics of elastomeric materials under global strain, but also provides a theoretical basis and technical route for subsequent researchers to construct a new hyperelastic constitutive model based on the microscopic network structure of the elastomer.

[0024] 2. The present invention realizes the application of 26 hyperelastic constitutive models constructed by the present invention that accurately describe the mechanical response characteristics of elastomeric materials under global strain in the commercial finite element analysis software Abaqus by writing a user-defined subroutine UHYPER, which greatly improves the simulation accuracy of the mechanical response of elastomeric materials under global strain and provides technical support for improving the accuracy of high-precision nonlinear finite element simulation of nonlinear materials and their products. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Flowchart of the method for constructing a hyperelastic constitutive model under global strain;

[0026] Figure 2(a) shows the experimental data of uniaxial tensile stress-strain curve of VHB 4910 elastomer material;

[0027] Figure 2(b) is the experimental data of uniaxial tensile stress-strain curve of TPU elastomer material;

[0028] Figure 2(c) shows the experimental data of uniaxial tensile stress-strain curves of three groups of EPDM-filled elastomer materials;

[0029] FIG3(a) is a diagram showing the fitting results of the Li-Wan-Zhang 1 model for the experimental data of the uniaxial tensile stress-strain curve of the VHB 4910 elastomer material;

[0030] FIG3( b ) is a diagram showing the fitting results of the experimental data of the uniaxial tensile stress-strain curve of the TPU elastomer material using the Li-Wan-Zhang 1 model;

[0031] FIG3(c) is a diagram showing the fitting results of the experimental data of the uniaxial tensile stress-strain curve of the filled EPDM elastomer material using the Li-Wan-Zhang 1 model;

[0032] FIG4(a) is a diagram showing the fitting results of the Li-Wan-Zhang 2 model for the experimental data of the uniaxial tensile stress-strain curve of the VHB 4910 elastomer material;

[0033] FIG4( b ) is a diagram showing the fitting results of the experimental data of the uniaxial tensile stress-strain curve of the TPU elastomer material using the Li-Wan-Zhang 2 model;

[0034] FIG4(c) is a diagram showing the fitting results of the Li-Wan-Zhang 2 model for the experimental data of the uniaxial tensile stress-strain curves of three groups of EPDM-filled elastomer materials;

[0035] FIG5(a) is a diagram showing the fitting results of the Li-Wan-Zhang 3 model for the experimental data of the uniaxial tensile stress-strain curve of the VHB 4910 elastomer material;

[0036] FIG5( b ) is a diagram showing the fitting results of the Li-Wan-Zhang 3 model for the experimental data of the uniaxial tensile stress-strain curve of the TPU elastomer material;

[0037] Fig. 5(c) is a diagram showing the fitting results of the experimental data of the uniaxial tensile stress-strain curves of three groups of EPDM-filled elastomer materials using the Li-Wan-Zhang 3 model;

[0038] FIG6(a) is a diagram showing the fitting results of the Li-Wan-Zhang 4 model for the experimental data of the uniaxial tensile stress-strain curve of the VHB 4910 elastomer material;

[0039] FIG6( b ) is a diagram showing the fitting results of the Li-Wan-Zhang 4 model for the experimental data of the uniaxial tensile stress-strain curve of the TPU elastomer material;

[0040] Fig. 6(c) is a diagram showing the fitting results of the experimental data of the uniaxial tensile stress-strain curves of three groups of EPDM-filled elastomer materials using the Li-Wan-Zhang 4 model;

[0041] FIG7( a ) is a diagram showing the fitting results of the Li-Wan-Zhang 5 model for the experimental data of the uniaxial tensile stress-strain curve of the VHB 4910 elastomer material;

[0042] FIG7( b ) is a diagram showing the fitting results of the experimental data of the uniaxial tensile stress-strain curve of the TPU elastomer material using the Li-Wan-Zhang 5 model;

[0043] FIG7(c) is a diagram showing the fitting results of the Li-Wan-Zhang 5 model for the experimental data of uniaxial tensile stress-strain curves of three groups of EPDM-filled elastomer materials;

[0044] Figure 8 Mises stress distribution of the three-dimensional dumbbell spline uniaxial tension finite element simulation analysis of the Li-Wan-Zhang 1 model;

[0045] Fig. 9 Mises stress distribution of 3D dumbbell spline uniaxial tension finite element simulation analysis of Li-Wan-Zhang 2 model;

[0046] Fig.10 Mises stress distribution of 3D dumbbell spline uniaxial tension finite element simulation analysis of Li-Wan-Zhang 3 model;

[0047] Fig.11 Mises stress distribution of 3D dumbbell spline uniaxial tension finite element simulation analysis of Li-Wan-Zhang 4 model;

[0048] Fig.12 Mises stress distribution of the three-dimensional dumbbell spline uniaxial tension finite element simulation analysis of the Li-Wan-Zhang 5 model. DETAILED DESCRIPTION

[0049] The existing technology adopts different hyperelastic constitutive models to describe small strain conditions and large strain conditions respectively, and it is necessary to develop hyperelastic constitutive models specifically for different mechanical response characteristics under the same strain conditions, resulting in a large number of models and low model selection efficiency.

[0050] The present invention breaks through the dilemma of the number of models by developing a hyperelastic constitutive model with global strain description capability. The global strain description capability refers to the ability to describe both the mechanical response characteristics under small strain and the mechanical response characteristics under large strain at the same time, and the mechanical response characteristics include stress steep rise characteristics and non-stress steep rise characteristics.

[0051] In order to obtain a hyperelastic constitutive model with global strain description capability, refer to Figure 1 As shown, the present invention provides a method for constructing a hyperelastic constitutive model under global strain, comprising the following steps:

[0052] Screening a hyperelastic constitutive model that has the potential to describe the mechanical response characteristics under global strain as the basic model;

[0053] Extracting the strain energy function term in the basic model;

[0054] The strain energy function terms are combined to obtain a hyperelastic constitutive model under global strain.

[0055] Preferably, the screened basic models include Li-Zhang, Gregory, Davis-De-Thomas, gen-Yeoh, Alexander, and modified Yeoh hyperelastic constitutive models, as shown in Table 1 below.

[0056] Table 1

[0057]

[0058]

[0059] According to the theoretical basis of the hyperelastic constitutive model, the common strain energy function terms in the basic model are extracted as follows: The strain energy function terms include:

[0060]

[0061] Among them, C 1 ,γ,A,α,M,D,μ,C 2 , B, N, β all represent material parameters; I 1 I represents the first invariant of the left Cauchy-Green deformation tensor; 2 represents the second invariant of the left Cauchy–Green deformation tensor.

[0062] The functional expression of uniaxial tensile engineering stress-stretching ratio is as follows:

[0063]

[0064] Where P UT represents uniaxial tensile stress; W represents strain energy function; λ i Indicates the main stretching ratio of the material in the i direction; i = 1, 2, 3, respectively representing the three main stretching directions; λ = λ 1 ;I 1 represents the first invariant of the left Cauchy-Green deformation tensor, I 2 represents the second invariant of the left Cauchy–Green deformation tensor,

[0065] At least two different strain energy function terms are selected for combination to form a new hyperelastic constitutive model under 26 global strains, as shown in Table 2 below.

[0066] Table 2

[0067]

[0068]

[0069] Based on the stress-strain curve data of the experimentally tested elastic material, the material parameters of the hyperelastic constitutive model under global strain are iterated, and the highest determination coefficient R is used to calculate the material parameters of the hyperelastic constitutive model under global strain. 2 Determine optimal material parameters.

[0070] The present invention also provides a simulation method for an elastomeric material under global strain, wherein a user-defined subroutine is written based on the hyperelastic constitutive model under global strain obtained by the method for constructing a hyperelastic constitutive model under global strain of the present invention, and the user-defined subroutine is called in finite element software and material parameters are input for simulation.

[0071] Utilizing the secondary development interface provided by the commercial finite element software Abaqus for the hyperelastic constitutive model, a user-defined subroutine UHYPER for the 26 hyperelastic constitutive models constructed above was written. The hyperelastic constitutive model, which can accurately describe the mechanical response characteristics of the elastic material under global strain, was integrated into the finite element software for finite element analysis.

[0072] A finite element model of a three-dimensional dumbbell spline for tensile tests (uniaxial tensile, planar tensile, equibiaxial tensile tests, etc.) is established in the finite element software. The user-defined subroutine UHYPER constructed above is called in the finite element software Abaqus, the optimal material parameters of the model are input, the analysis work is submitted, the finite element simulation analysis results are obtained, and the mechanical characteristic curves in the finite element model are extracted.

[0073] Example 1

[0074] It should be noted that the small strain intervals corresponding to different elastomeric materials are different, and the large strain intervals corresponding to different elastomeric materials are also different. Small strain interval: the strain interval before the modulus of the stress-strain curve drops sharply. Large strain interval: the strain area after the modulus of the stress-strain curve drops sharply. Among them, modulus refers to the slope of the stress-strain curve.

[0075] Referring to Figure 2, the uniaxial tensile stress-strain curve experimental data of three groups of elastomer materials, VHB 4910, TPU and filled EPDM, can be obtained from Figure 2 (a), (b), and (c) respectively:

[0076] The small strain range of VHB 4910 elastic material is 0-1.0, and the large strain range is 1.0-12.1. VHB 4910 elastic material has a mechanical response characteristic of steep stress rise under both small strain (0-1.0) and large strain (1.0-12.1);

[0077] The small strain range of TPU elastomer material is 0-0.5, and the large strain range is 0.5-2.5. TPU elastomer material has a stress steep rise characteristic under small strain (0-0.5), but no stress steep rise characteristic under large strain (0.5-2.5).

[0078] The small strain range of the filled EPDM elastomer material is 0-0.5, and the large strain range is 0.5-2.7. The filled EPDM elastomer material has a stress steep rise characteristic under a small strain (0-0.5), but has no stress steep rise characteristic under a large strain (0.5-2.7).

[0079] In this embodiment, the Li-Wan-Zhang 1 model in Table 2 is used to fit the experimental data of the uniaxial tensile stress-strain curves of VHB 4910, TPU, and filled EPDM elastomer materials. The fitting results are shown in Figures 3(a), (b), and (c), respectively. The fitting accuracy, i.e., the determination coefficient R 2 All reached above 0.988.

[0080] Example 2

[0081] In this embodiment, the Li-Wan-Zhang 2 model in Table 2 is used to fit the experimental data of the uniaxial tensile stress-strain curves of VHB 4910, TPU, and filled EPDM elastomer materials. The fitting results are shown in Figures 4(a), (b), and (c), respectively. The fitting accuracy, i.e., the determination coefficient R 2 All reached above 0.990.

[0082] Example 3

[0083] In this embodiment, the Li-Wan-Zhang 3 model in Table 2 is used to fit the experimental data of the uniaxial tensile stress-strain curves of VHB 4910, TPU, and filled EPDM elastomer materials. The fitting results are shown in Figures 5(a), (b), and (c), respectively. The fitting accuracy, i.e., the determination coefficient R 2 All reached above 0.989.

[0084] Example 4

[0085] In this embodiment, the Li-Wan-Zhang 4 model in Table 2 is used to fit the experimental data of the uniaxial tensile stress-strain curves of VHB 4910, TPU, and filled EPDM elastomer materials. The fitting results are shown in Figures 6(a), (b), and (c), respectively. The fitting accuracy, i.e., the determination coefficient R 2 All reached above 0.988.

[0086] Example 5

[0087] In this embodiment, the Li-Wan-Zhang 5 model in Table 2 is used to fit the experimental data of the uniaxial tensile stress-strain curves of VHB 4910, TPU, and filled EPDM elastomer materials. The fitting results are shown in Figures 7(a), (b), and (c), respectively. The fitting accuracy, i.e., the determination coefficient R 2All reached above 0.998.

[0088] Example 6

[0089] This embodiment takes the uniaxial tensile simulation of a three-dimensional dumbbell-shaped specimen as an example, and uses five hyperelastic constitutive models (Li-Wan-Zhang 1, Li-Wan-Zhang 2, Li-Wan-Zhang 3, Li-Wan-Zhang 4, and Li-Wan-Zhang 5) constructed by the present invention to accurately describe the mechanical response characteristics of the elastomeric material under global strain, and fills in EPDM experimental data to perform uniaxial tensile simulation analysis on the three-dimensional dumbbell elastomer specimen.

[0090] The hyperelastic constitutive model (Li-Wan-Zhang 1, Li-Wan-Zhang 2, Li-Wan-Zhang 3, Li-Wan-Zhang 4, Li-Wan-Zhang 5) constructed by the present invention is written as a user-defined subroutine UHYPER. The hyperelastic constitutive model that can accurately describe the mechanical response characteristics of the elastic material under global strain is integrated into the finite element software for finite element analysis, including the following sub-steps:

[0091] Step 1: Based on the basic theory of the hyperelastic constitutive model, derive the partial derivative of the strain energy function of the constitutive model with respect to the first invariant of the left Cauchy-Green deformation tensor or the second invariant of the left Cauchy-Green deformation tensor;

[0092] Step 2: Based on the secondary development interface framework provided in the commercial finite element software, the strain energy function of the constitutive model and the partial derivative of the strain energy function with respect to the first invariant of the left Cauchy-Green deformation tensor or the second invariant of the left Cauchy-Green deformation tensor are implemented through Fortran language and embedded into the corresponding interface framework to complete the numerical implementation of the hyperelastic constitutive model that accurately describes the mechanical response characteristics of the elastic material under global strain.

[0093] The boundary condition of the three-dimensional dumbbell spline is that one end is fixed and the other end is stretched 100% along the x-direction. Next, the material properties of the three-dimensional dumbbell spline are changed, and only the user-defined subroutine UHYPER is used to replace the hyperelastic model of the material. The geometric characteristics, boundary conditions, and loading conditions of the other finite element models remain unchanged. Finally, the simulation analysis results corresponding to the five hyperelastic constitutive models (Li-Wan-Zhang 1, Li-Wan-Zhang 2, Li-Wan-Zhang 3, Li-Wan-Zhang 4, and Li-Wan-Zhang 5) are compared. The Mises stress distribution is shown in the figure. Figures 8 to 12As shown in the figure, the simulation results of different models are basically consistent, and the maximum Mises stress error is less than 2%. The results show that the constructed hyperelastic constitutive model has a good description ability for the mechanical response characteristics of elastic materials under global strain.

[0094] The above technical scheme is only a specific implementation method of the present invention. For those skilled in the art, it is easy to make various types of improvements or modifications based on the principles disclosed in the present invention, and it is not limited to the technical scheme described in the above specific embodiments of the present invention. Therefore, the above description is only preferred and does not have a restrictive meaning.

Claims

1. A method for constructing a hyperelastic constitutive model under global strain, characterized in that: The following steps are involved: Screening a hyperelastic constitutive model that has the potential to describe the mechanical response characteristics under global strain as the basic model; Extracting the strain energy function term in the basic model; The strain energy function terms are combined to obtain a hyperelastic constitutive model under global strain.

2. The method for constructing a hyperelastic constitutive model under global strain according to claim 1, characterized in that: The basic models include Li-Zhang, Gregory, Davis-De-Thomas, gen-Yeoh, Alexander, and modified Yeoh hyperelastic constitutive models.

3. The method for constructing a hyperelastic constitutive model under global strain according to claim 2, characterized in that: The strain energy function term includes: Among them, C1, γ, A, α, M, D, μ, C2, B, N, and β all represent material parameters; I1 represents the first invariant of the left Cauchy-Green deformation tensor; I2 represents the second invariant of the left Cauchy-Green deformation tensor.

4. The method for constructing a hyperelastic constitutive model under global strain according to claim 3, characterized in that: In the formula, λ i Represents the principal stretching ratio of the material in the i direction.

5. The method for constructing a hyperelastic constitutive model under global strain according to claim 3, characterized in that: At least two different strain energy function terms are selected for combination to form a new hyperelastic constitutive model under 26 global strains.

6. The method for constructing a hyperelastic constitutive model under global strain according to claim 3, characterized in that: Based on the stress-strain curve data of the experimentally tested elastic material, the stress-strain curve is fitted by iterating the material parameters of the hyperelastic constitutive model under global strain, and the highest determination coefficient R 2 Determine optimal material parameters.

7. A simulation method for elastic materials under global strain, characterized in that: A user-defined subroutine is written according to the hyperelastic constitutive model under global strain obtained by the method for building a hyperelastic constitutive model under global strain as claimed in any one of claims 1 to 6, and the user-defined subroutine is called in finite element software and material parameters are input for simulation.

8. The method for simulating an elastic material under global strain according to claim 7, characterized in that: The steps to write a user-defined subroutine include: Calculate the partial derivative of the strain energy function term of the hyperelastic constitutive model under global strain with respect to the first invariant of the left Cauchy-Green deformation tensor or the second invariant of the left Cauchy-Green deformation tensor; The partial derivatives are embedded into a secondary development interface framework provided in the finite element software.

9. The method for simulating an elastic material under global strain according to claim 8, characterized in that: The finite element software is Abaqus, and the user-defined subroutine is UHYPER.

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