Complete Lagrange explicit calculation modeling method for super-elastic material node internal force

Abstract

The invention relates to a complete Lagrangian explicit calculation modeling method for a node internal force of a super-elastic material, and the method comprises the steps: decomposing an energy density function in a second piezo-Kirchhoff stress of the super-elastic material into a volume correlation part and a deflection correlation part according to the characteristics of the super-elastic material; constructing a second piezo-Kirchhoff stress expansion model of the super-elastic material; and re-representing a right Cauchy-Green strain tensor in the second Peixia-Kirchhoff stress expansion model by adopting a calculation formula of the Jacobian matrix, expanding the re-represented right Cauchy-Green strain tensor into a form of combining a quantity and an invariant which change along with time, and reconstructing the second Peixia-Kirchhoff stress expansion model, calculating invariants in advance; and constructing a novel complete Lagrange explicit calculation model of the node internal force of the super-elastic material based on the reconstructed second piezo-Kirchhoff stress expansion model and the deformation gradient, the strain matrix and the initial unit volume of the super-elastic material.

Description

Technical Field

[0001] This application relates to the technical field of numerical simulation analysis, and particularly to a fully Lagrangian explicit calculation and modeling method for the internal force of nodes of hyperelastic materials. Background Art

[0002] Hyperelastic materials are widely used in the automotive industry, electronics field, and mechanical equipment field. The high-precision modeling ability of hyperelastic materials is a key support for product innovation and reliability. Hyperelastic materials have complex characteristics such as large deformation and recoverable hyperelasticity. By calculating the internal force of hyperelastic material nodes, their mechanical responses can be accurately predicted, the trial-and-error cost can be reduced, and the product design efficiency can be improved.

[0003] Currently, most of the calculation models for the internal force of hyperelastic material nodes focus on improving the accuracy and convergence in numerical algorithms, and there are few reports on improving efficiency. The reason is that the calculation model for the internal force of hyperelastic material nodes is usually based on the fully Lagrangian calculation model, and the format of the fully Lagrangian calculation model is relatively fixed, and the calculation process is also basically fixed. In explicit analysis, usually all quantities related to the deformation gradient of hyperelastic materials need to be updated at each time step, and the numerical implementation is relatively complex, which affects the analysis of the mechanical properties of hyperelastic materials and results in a relatively low design efficiency of the final product. Summary of the Invention

[0004] Based on this, it is necessary to provide a fully Lagrangian explicit calculation and modeling method for the internal force of hyperelastic material nodes, including: S1: According to the characteristics of hyperelastic materials, decompose the energy density function in the second Piola-Kirchhoff stress of hyperelastic materials into a volume-related part and a deviatoric-related part, and construct an expansion model of the second Piola-Kirchhoff stress of hyperelastic materials; the hyperelastic material is rubber; S2: Re-express the right Cauchy-Green strain tensor in the expansion model of the second Piola-Kirchhoff stress using the calculation formula of the Jacobian matrix, and expand the re-expressed right Cauchy-Green strain tensor into a form combined with time-varying quantities and invariants, reconstruct the expansion model of the second Piola-Kirchhoff stress, and calculate the invariants therein in advance; S3: Based on the reconstructed expansion model of the second Piola-Kirchhoff stress, the deformation gradient, strain matrix, and initial element volume of hyperelastic materials, construct a new fully Lagrangian explicit calculation model for the internal force of hyperelastic material nodes.

[0005] Preferably, constructing the expansion model of the second Piola-Kirchhoff stress of hyperelastic materials includes: According to the characteristics of hyperelastic materials, decompose the energy density function in the second Piola-Kirchhoff stress of hyperelastic materials into a volume-related part and a deviatoric-related part to obtain a preliminarily expanded second Piola-Kirchhoff stress model; For the second Piola-Kirchhoff stress model with step expansion, the equivalent right Cauchy-Green strain tensor in the deviatoric-related part is replaced by an algebraic expression of the second-order identity tensor and the trace of the second-order identity tensor, resulting in the second Piola-Kirchhoff stress expansion model.

[0006] Preferably, the second Piola-Kirchhoff stress of the hyperelastic material is expressed as: ; where represents the second Piola-Kirchhoff stress of the hyperelastic material at the th moment; represents the energy density function; represents the partial derivative; represents the th moment of the right Cauchy-Green strain tensor.

[0007] Preferably, the initially expanded second Piola-Kirchhoff stress model is expressed as: ; ; ; ; where represents the initially expanded second Piola-Kirchhoff stress model of the hyperelastic material at the th moment; represents the deviatoric-related part; represents the th moment of the equivalent right Cauchy-Green strain tensor; represents the volume-related part; represents the determinant of the deformation gradient of the hyperelastic material; represents the determinant; represents the th moment of the right Cauchy-Green strain tensor; represents the partial derivative; represents the deformation gradient of the hyperelastic material at the th moment; represents the deviatoric mapping operator; represents performing a double dot product operation with .

[0008] Preferably, the second Piola-Kirchhoff stress expansion model is expressed as: ; where represents the second Piola-Kirchhoff stress expansion model of the hyperelastic material at the th moment; represents the determinant of the deformation gradient of the hyperelastic material; represents the energy density function; represents the trace of the second-order identity tensor; represents the second-order identity tensor; represents the partial derivative; represents the right Cauchy-Green strain tensor at time

[0009] Preferably, the expression of the right Cauchy-Green strain tensor is: ; where represents the right Cauchy-Green strain tensor at time ; represents the deformation gradient of the hyperelastic material at time ; represents the transpose; The right Cauchy-Green strain tensor is re-expressed using the calculation formula of the Jacobian matrix, and the re-expressed right Cauchy-Green strain tensor is denoted as: ; where represents the re-expressed right Cauchy-Green strain tensor at time ; represents the Jacobian matrix of the hyperelastic material at time ; represents the initial Jacobian matrix of the hyperelastic material; represents the transpose.

[0010] Preferably, the re-expressed right Cauchy-Green strain tensor is expanded into a form combined with time-varying quantities and invariants, including: The time-varying Jacobian matrix in the re-expressed right Cauchy-Green strain tensor is rewritten, and the calculation formula is: ; where represents the Jacobian matrix at time ; represents the transpose; ~ respectively represent the elements in the matrix ; The numerical values of the non-diagonal elements symmetric along the diagonal in the rewritten time-varying Jacobian matrix are equal; The re-expressed right Cauchy-Green strain tensor is rewritten into a combination of six groups of time-varying quantities and invariants, and the calculation formula is: ; ; ; ; ; ; ; Among them, represents the modified right Cauchy-Green strain tensor; represents the initial Jacobian matrix; , , , , , respectively represent the first invariant, the second invariant, the third invariant, the fourth invariant, the fifth invariant, and the sixth invariant.

[0011] Preferably, constructing a new total Lagrangian explicit calculation model for the internal force of hyperelastic material nodes includes: Multiplying the reconstructed second Piola-Kirchhoff stress expansion model by the deformation gradient, strain matrix, and initial element volume of the hyperelastic material to obtain a preliminary calculation model for the internal force of hyperelastic material nodes; According to the expansion formulas of the deformation gradient, strain matrix, and initial element volume, and the reconstructed second Piola-Kirchhoff stress expansion model, adjusting the preliminary calculation model for the internal force of hyperelastic material nodes to construct a new total Lagrangian explicit calculation model for the internal force of hyperelastic material nodes.

[0012] Preferably, the preliminary calculation model for the internal force of hyperelastic material nodes is expressed as: ; ; ; Among them, represents the internal force of the node of the hyperelastic material at the th moment; represents the deformation gradient of the hyperelastic material at the th moment; represents the second Piola-Kirchhoff stress expansion model of the hyperelastic material at the th moment; represents the strain matrix; represents the initial element volume of the hyperelastic material; represents the Jacobian matrix of the hyperelastic material at the th moment; represents the initial Jacobian matrix of the hyperelastic material; represents the transpose; represents the energy density function; represents the partial derivative; It represents the partial derivative matrix of the shape function with respect to the natural coordinates in the natural coordinate system of the element.

[0013] Preferably, the new fully Lagrangian explicit calculation model of the internal force of the hyperelastic material nodes is expressed as: ; ; Wherein, represents the internal force of the nodes of the hyperelastic material at the th moment; represents the determinant of the deformation gradient of the hyperelastic material; represents the initial element volume of the hyperelastic material; represents the Jacobian matrix of the hyperelastic material at the th moment; represents the initial Jacobian matrix of the hyperelastic material; represents the transpose; represents the energy density function; represents the partial derivative; represents the trace of the second-order unit tensor; represents the second-order unit tensor; It represents the partial derivative matrix of the shape function with respect to the natural coordinates in the natural coordinate system of the element; represents a quantity that does not change with time.

[0014] Beneficial effects: According to the characteristics of the hyperelastic material, this method decomposes the energy density function in the second Piola-Kirchhoff stress of the hyperelastic material into a volume-related part and a deviatoric-related part, and constructs an expansion model of the second Piola-Kirchhoff stress of the hyperelastic material; the right Cauchy-Green strain tensor in the second Piola-Kirchhoff stress expansion model is re-expressed by the calculation formula of the Jacobian matrix, and the re-expressed right Cauchy-Green strain tensor is expanded into a form composed of time-varying quantities and invariants, reconstructing the second Piola-Kirchhoff stress expansion model and calculating the invariants therein in advance; based on the reconstructed second Piola-Kirchhoff stress expansion model, the deformation gradient, strain matrix and initial element volume of the hyperelastic material, a new fully Lagrangian explicit calculation model of the internal force of the hyperelastic material nodes is constructed; this method is based on the original fully Lagrangian explicit calculation model, without changing the model framework of the explicit calculation, only re-deriving the parameter calculation model of the hyperelastic material. In the explicit time step analysis process, this calculation model only needs to calculate the internal force based on the pre-calculated invariants at each time step. The internal force of the nodes obtained based on this calculation model is convenient for subsequent analysis of the mechanical properties of the hyperelastic material, reduces the trial-and-error cost of the product, and improves the design efficiency of the product. Description of the Drawings

[0015] To more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0016] Figure 1 This is a flowchart of the fully Lagrangian explicit calculation and modeling method for the internal force of the hyperelastic material node in the embodiment of the present application. Specific embodiments

[0017] To make the above objects, features, and advantages of the present application more obvious and understandable, the following will describe the specific embodiments of the present application in detail with reference to the accompanying drawings. Many specific details are set forth in the following description to fully understand the present application. However, the present application can be implemented in many other ways different from those described herein. Those skilled in the art can make similar improvements without departing from the connotation of the present application. Therefore, the present application is not limited by the specific embodiments disclosed below.

[0018] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present application, "a plurality" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0019] As Figure 1 shown, this embodiment provides a fully Lagrangian explicit calculation and modeling method for the internal force of the hyperelastic material node, including: S1: According to the characteristics of the hyperelastic material, decompose the energy density function in the second Piola-Kirchhoff stress of the hyperelastic material into a volume-related part and a deviatoric-related part, and construct an expansion model of the second Piola-Kirchhoff stress of the hyperelastic material; in this embodiment, the hyperelastic material is rubber.

[0020] Specifically, constructing the expansion model of the second Piola-Kirchhoff stress of the hyperelastic material includes: According to the characteristics of the hyperelastic material, decompose the energy density function in the second Piola-Kirchhoff stress of the hyperelastic material into a volume-related part and a deviatoric-related part, and obtain a preliminarily expanded second Piola-Kirchhoff stress model; For the preliminarily expanded second Piola-Kirchhoff stress model, replace the equivalent right Cauchy-Green strain tensor in the deviatoric-related part with an algebraic expression of the second-order unit tensor and the trace of the second-order unit tensor to obtain the expansion model of the second Piola-Kirchhoff stress.

[0021] Furthermore, the second Piola-Kirchhoff stress of the hyperelastic material is expressed as: ; where represents the second Piola-Kirchhoff stress of the hyperelastic material at the th moment; represents the energy density function; represents the partial derivative; represents the th moment of the right Cauchy-Green strain tensor.

[0022] Even further, the initially expanded second Piola-Kirchhoff stress model is expressed as: ; ; ; ; where represents the initially expanded second Piola-Kirchhoff stress model of the hyperelastic material at the th moment; represents the deviatoric-related part; represents the th moment of the equivalent right Cauchy-Green strain tensor; represents the volume-related part; represents the determinant of the deformation gradient of the hyperelastic material; represents the determinant; represents the th moment of the right Cauchy-Green strain tensor; represents the partial derivative; represents the deformation gradient of the hyperelastic material at the th moment; represents the deviatoric mapping operator; represents performing a double dot product operation with .

[0023] Even further, the second Piola-Kirchhoff stress expansion model is expressed as: ; where represents the second Piola-Kirchhoff stress expansion model of the hyperelastic material at the th moment; represents the determinant of the deformation gradient of the hyperelastic material; represents the energy density function; represents the trace of the second-order identity tensor; represents the second-order unit tensor; represents the partial derivative; represents the right Cauchy-Green strain tensor at time

[0024] S2: Re-express the right Cauchy-Green strain tensor in the second Piola-Kirchhoff stress expansion model using the calculation formula of the Jacobian matrix, and expand the re-expressed right Cauchy-Green strain tensor into a form composed of time-varying quantities and invariants, reconstruct the second Piola-Kirchhoff stress expansion model, and calculate the invariants therein in advance.

[0025] Specifically, the expression of the right Cauchy-Green strain tensor is: ; where represents the right Cauchy-Green strain tensor at time represents the deformation gradient of the hyperelastic material at time ; represents the transpose; Re-express the right Cauchy-Green strain tensor using the calculation formula of the Jacobian matrix, and the re-expressed right Cauchy-Green strain tensor is denoted as: ; where represents the re-expressed right Cauchy-Green strain tensor at time represents the Jacobian matrix of the hyperelastic material at time ; represents the initial Jacobian matrix of the hyperelastic material; represents the transpose.

[0026] Furthermore, expanding the re-expressed right Cauchy-Green strain tensor into a form composed of time-varying quantities and invariants includes: Rewrite the time-varying Jacobian matrix in the re-expressed right Cauchy-Green strain tensor, and the calculation formula is: ; where represents the Jacobian matrix at time represents the transpose; ~ respectively represent the elements in the matrix ; The numerical values of the non-diagonal elements symmetric along the diagonal in the rewritten time-varying Jacobian matrix are equal; Rewrite the re - represented right Cauchy - Green strain tensor as a combination of six groups of time - varying quantities and invariants, and the calculation formula is: ; ; ; ; ; ; ; Among them, represents the rewritten right Cauchy - Green strain tensor; represents the initial Jacobian matrix; , , , , , represent the first invariant, the second invariant, the third invariant, the fourth invariant, the fifth invariant, and the sixth invariant respectively. Calculate each invariant in advance.

[0027] S3: Based on the reconstructed second Piola - Kirchhoff stress expansion model, the deformation gradient, strain matrix, and initial element volume of the hyperelastic material, construct a new fully Lagrangian explicit calculation model for the internal force of the hyperelastic material nodes.

[0028] Specifically, constructing a new fully Lagrangian explicit calculation model for the internal force of the hyperelastic material nodes includes: Multiply the reconstructed second Piola - Kirchhoff stress expansion model by the deformation gradient, strain matrix, and initial element volume of the hyperelastic material to obtain a preliminary calculation model for the internal force of the hyperelastic material nodes; According to the expansion formulas of the deformation gradient, strain matrix, and initial element volume and the reconstructed second Piola - Kirchhoff stress expansion model, adjust the preliminary calculation model for the internal force of the hyperelastic material nodes to construct a new fully Lagrangian explicit calculation model for the internal force of the hyperelastic material nodes.

[0029] Furthermore, the preliminary calculation model for the internal force of the hyperelastic material nodes is expressed as: ; ; ; Among them, represents the internal force of the hyperelastic material nodes at the th moment; represents the deformation gradient of the hyperelastic material at the th moment; represents the deformation gradient of the hyperelastic material at the Second Piola-Kirchhoff stress expansion model at a moment; Denote the strain matrix; Denote the initial element volume of the hyperelastic material; Denote the Jacobian matrix of the hyperelastic material at the Denote the initial Jacobian matrix of the hyperelastic material; Denote the transpose; Denote the energy density function; Denote the partial derivative; Denote the matrix of partial derivatives of the shape functions with respect to the natural coordinates in the natural coordinate system of the element.

[0030] Expand the preliminary nodal internal force calculation model of the hyperelastic material, which is expressed as: ; To more clearly express the direct Jacobi update calculation method, replace the quantities that do not change with time in the above formula with the parameter , and these quantities that do not change with time can be directly calculated at the initial configuration, so as to obtain a new fully Lagrangian explicit calculation model for the nodal internal forces of the hyperelastic material, which is expressed as: ; ; Among them, Denote the nodal internal force of the hyperelastic material at the moment; Denote the determinant of the deformation gradient of the hyperelastic material; Denote the initial element volume of the hyperelastic material; Denote the Jacobian matrix of the hyperelastic material at the Denote the initial Jacobian matrix of the hyperelastic material; Denote the transpose; Denote the energy density function; Denote the partial derivative; Denote the trace of the second-order unit tensor; Denote the second-order unit tensor; Denote the matrix of partial derivatives of the shape functions with respect to the natural coordinates in the natural coordinate system of the element; Denote the quantity that does not change with time.

[0031] The fully Lagrangian explicit calculation and modeling method for the nodal internal forces of the hyperelastic material provided in this embodiment has the following beneficial effects: This method is based on the total Lagrangian (TL) explicit calculation format for hyperelastic materials. It re-derives the calculation model for the constitutive calculation of hyperelastic materials. By directly calculating the Jacobian matrix at each time step, only updating the Jacobian matrix, other invariants can be pre-calculated in the initial configuration, without the need to update all quantities related to the deformation gradient as in the traditional total Lagrangian format. This reduces the computational cost and further improves the computational efficiency of large deformation calculations for hyperelastic materials. The nodal internal forces obtained based on this calculation model are convenient for subsequent mechanical property analysis of hyperelastic materials, reduce the trial-and-error cost of products, and improve the design efficiency of products.

[0032] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0033] The above-described embodiments merely represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A fully Lagrangian explicit calculation and modeling method for internal forces of hyperelastic material nodes, characterized in that Including: S1: According to the characteristics of the hyperelastic material, decompose the energy density function in the second Piola-Kirchhoff stress of the hyperelastic material into a volume-related part and a deviatoric-related part, and construct a second Piola-Kirchhoff stress expansion model for the hyperelastic material; the hyperelastic material is rubber. S2: Represents the right Cauchy-Green strain tensor in the second Piola-Kirchhoff stress expansion model using the calculation formula of the Jacobian matrix, and expands the re-represented right Cauchy-Green strain tensor into a form combined with time-varying quantities and invariants, reconstruct the second Piola-Kirchhoff stress expansion model, and calculate the invariants therein in advance. S3: Based on the reconstructed second Piola-Kirchhoff stress expansion model, the deformation gradient, strain matrix, and initial element volume of the hyperelastic material, construct a new fully Lagrangian explicit calculation model for the internal force of the hyperelastic material nodes.

2. The total Lagrangian explicit calculation and modeling method for internal forces of the hyperelastic material nodes according to claim 1, characterized in that, Constructing the second Piola-Kirchhoff stress expansion model of the hyperelastic material includes: According to the characteristics of the hyperelastic material, decompose the energy density function in the second Piola-Kirchhoff stress of the hyperelastic material into a volume-related part and a deviatoric-related part, and obtain a preliminarily expanded second Piola-Kirchhoff stress model. For the preliminarily expanded second Piola-Kirchhoff stress model, replace the equivalent right Cauchy-Green strain tensor in the deviatoric-related part with an algebraic expression of the second-order unit tensor and the trace of the second-order unit tensor to obtain the second Piola-Kirchhoff stress expansion model.

3. The total Lagrangian explicit calculation and modeling method for internal forces of the hyperelastic material node according to claim 2, characterized in that The second Piola-Kirchhoff stress of the hyperelastic material is expressed as: ； in, Represents hyperelastic material the second Piola-Kirchhoff stress at moment ; represents the energy density function; represents partial derivative; Indicates the The right Cauchy-Green strain tensor at time .

4. The total Lagrangian explicit calculation and modeling method for internal forces of the hyperelastic material node according to claim 3, characterized in that The preliminarily expanded second Piola-Kirchhoff stress model is expressed as: ； ； ； ； Among them, represents the second Piola - Kirchhoff stress model of the hyperelastic material at the initial expansion moment; represents the deviatoric - related part; represents the equivalent right Cauchy - Green strain tensor at the moment; represents the determinant of the deformation gradient of the hyperelastic material; represents the determinant; represents the right Cauchy - Green strain tensor at the moment; represents the deformation gradient of the hyperelastic material at the moment; represents the deviatoric mapping operator; represents a double - dot product operation with .

5. The total Lagrangian explicit calculation and modeling method for internal forces of the hyperelastic material node according to claim 4, characterized in that, The second Piola-Kirchhoff stress expansion model is expressed as: ； Among them, represents the second Piola-Kirchhoff stress expansion model of the hyperelastic material at the th moment; represents the determinant of the deformation gradient of the hyperelastic material; represents the energy density function; represents the trace of the second-order identity tensor; represents the second-order identity tensor; represents the partial derivative; represents the right Cauchy-Green strain tensor at the th moment.

6. The total Lagrangian explicit calculation and modeling method for internal forces of hyperelastic material nodes according to claim 5, characterized in that The expression of the right Cauchy-Green strain tensor is: ； Among them, represents the right Cauchy-Green strain tensor at the moment; represents the deformation gradient of the hyperelastic material at the moment; represents the transpose; Represents the right Cauchy-Green strain tensor using the calculation formula of the Jacobian matrix, and the re-represented right Cauchy-Green strain tensor is denoted as: ； in, Indicates the The right Cauchy-Green strain tensor reformulated at the moment; Represents hyperelastic material Jacobian matrix at time instant; represents the initial Jacobian matrix of the hyperelastic material; Indicates transpose.

7. The total Lagrangian explicit calculation and modeling method for internal forces of hyperelastic material nodes according to claim 6, characterized in that, Expanding the re-represented right Cauchy-Green strain tensor into a form combined with time-varying quantities and invariants includes: Rewrite the time-varying Jacobian matrix in the re-represented right Cauchy-Green strain tensor, and the calculation formula is: ； in, Indicates the Jacobian matrix at time instant; represents transpose; ~ Represents matrices respectively The elements in The numerical values of the non-diagonal elements symmetric along the diagonal in the rewritten time-varying Jacobian matrix are equal. Rewrite the re-represented right Cauchy-Green strain tensor into a combination of six groups of time-varying quantities and invariants, and the calculation formula is: ； ； ； ； ； ； ； Among them, represents the rewritten right Cauchy-Green strain tensor; represents the initial Jacobian matrix; , , , , , represent the first invariant, the second invariant, the third invariant, the fourth invariant, the fifth invariant, and the sixth invariant, respectively.

8. The total Lagrangian explicit calculation and modeling method for internal forces of hyperelastic material nodes according to claim 7, characterized in that Constructing a new fully Lagrangian explicit calculation model for the internal force of the hyperelastic material nodes includes: Multiply the reconstructed second Piola-Kirchhoff stress expansion model by the deformation gradient, strain matrix, and initial element volume of the hyperelastic material to obtain a preliminary calculation model for the internal force of the hyperelastic material nodes. According to the expansion formulas of the deformation gradient, strain matrix, and initial element volume and the reconstructed second Piola-Kirchhoff stress expansion model, adjust the preliminary calculation model for the internal force of the hyperelastic material nodes to construct a new fully Lagrangian explicit calculation model for the internal force of the hyperelastic material nodes.

9. The total Lagrangian explicit calculation and modeling method for internal forces of the hyperelastic material node according to claim 8, characterized in that, The preliminary calculation model for the internal force of the hyperelastic material nodes is expressed as: ； ； ； Among them, represents the internal force of the node of the hyperelastic material at the moment; represents the deformation gradient of the hyperelastic material at the moment; represents the second Piola-Kirchhoff stress expansion model of the hyperelastic material at the moment; represents the strain matrix; represents the initial element volume of the hyperelastic material; represents the Jacobian matrix of the hyperelastic material at the moment; represents the initial Jacobian matrix of the hyperelastic material; represents the transpose; represents the energy density function; represents the partial derivative; represents the partial derivative matrix of the shape function with respect to the natural coordinates in the natural coordinate system of the element.

10. The total Lagrangian explicit calculation and modeling method for internal forces of the hyperelastic material nodes according to claim 9, characterized in that, The new fully Lagrangian explicit calculation model for the internal force of the hyperelastic material nodes is expressed as: ； ； Among them, represents the internal force of the node of the hyperelastic material at the moment; represents the determinant of the deformation gradient of the hyperelastic material; represents the initial element volume of the hyperelastic material; represents the Jacobian matrix of the hyperelastic material at the moment; represents the transpose; represents the energy density function; represents the partial derivative; represents the trace of the second-order unit tensor; represents the second-order unit tensor; represents the partial derivative matrix of the shape function with respect to the natural coordinates in the natural coordinate system of the element; represents a quantity that does not change with time.

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