Search

CN-121980859-A - Construction method of rubber material super-elastic constitutive model

CN121980859ACN 121980859 ACN121980859 ACN 121980859ACN-121980859-A

Abstract

The invention belongs to the field of nonlinear material mechanics, and relates to a construction method of a rubber material superelasticity constitutive model, which comprises the following steps of deriving a strain energy function with non-integer power strain invariants; the method comprises the steps of obtaining stress strain test data by adopting a quasi-static tensile superelastic constitutive test, fitting to obtain material parameters of a non-integer power strain invariant strain energy function according to the function and the test data, writing the strain energy function into finite element software, fitting material parameters of a Neo-Hookean model according to the obtained test data, establishing a single-unit three-dimensional model, carrying out finite element simulation by utilizing the obtained material parameters to obtain a finite element stress strain simulation result, and comparing the simulation result with the test data. According to the invention, parameter fitting is performed by adopting the relation between modulus and strain, so that the strain energy function with non-integer power of the strain invariant is obtained by deduction, and the flexibility and accuracy of data fitting are improved.

Inventors

  • LI XIANGXIN
  • MA GANG
  • GONG TINGTING
  • MENG ZHAOHONG

Assignees

  • 山东金宇轮胎有限公司

Dates

Publication Date
20260505
Application Date
20260116

Claims (8)

  1. 1. The construction method of the super-elastic constitutive model of the rubber material is characterized by comprising the following steps of: (1) Deriving a strain energy function with non-integer power strain invariants; (2) Adopting a quasi-static stretching superelastic constitutive test to obtain stress strain test data; (3) Fitting to obtain material parameters of a non-integer power strain invariant strain energy function according to the steps (1) and (2); (4) Writing the strain energy function in the step (1) into finite element software, and fitting material parameters of a Neo-Hookean model according to the step (2); (5) Establishing a single-unit three-dimensional model, performing finite element simulation by using the material parameters obtained in the steps (3) and (4) to obtain a finite element stress strain simulation result, and comparing the simulation result with the test data of the step (2).
  2. 2. The method of claim 1, wherein the strain energy function of the first strain invariant having a non-integer power obtained in step (1) is: ; Wherein a and b are material parameters, I 1 is a first strain invariant, and the relation between the first strain invariant I 1 and strain epsilon is as follows: 。
  3. 3. The method according to claim 2, wherein the modulus G and strain e satisfy the following relation: ; The formula of the strain energy function is as follows: ; And introducing the relation between the first strain invariant I 1 and the strain epsilon into a formula of a strain energy function to obtain the strain energy function with the first strain invariant of the non-integer power.
  4. 4. The method of claim 1, wherein step (2) employs a quasi-static uniaxial tensile test with a uniaxial tensile strain of 50% to 100%.
  5. 5. The method of claim 4, wherein the strain energy function is:
  6. 6. Wherein a 1 、a 2 、b 1 、b 2 is a material parameter and I 1 is a first strain invariant.
  7. 7. The method according to claim 1, wherein in the step (4), the strain energy function obtained in the step (1) is written into Abaqus, and the material calibration function of Abaqus/Standard is used to fit the test data in the step (2) to obtain the material parameters of the Neo-Hookean model.
  8. 8. The method of claim 1, wherein a single-unit three-dimensional model is established, boundary setting is performed according to uniaxial tensile deformation characteristics, finite element simulation calculation is performed by using the strain energy function parameters obtained in the step (3) and the Abaqus self-contained Neo-Hookean strain energy function parameters in the step (4), and simulation results are compared with the test data in the step (2).

Description

Construction method of rubber material super-elastic constitutive model Technical Field The invention belongs to the field of nonlinear material mechanics, and particularly relates to a construction method of a rubber material superelasticity constitutive model. Background The rubber material has good nonlinear characteristics and is widely applied to the fields of tires, railways, aviation and the like. The rubber material is a super-elastic material, can bear larger deformation, and shows elastic deformation under the action of an applied load, and can recover after unloading. The mechanical properties of rubber materials, such as superelasticity and large deformations, are typically described using a superelastic constitutive model. At present, super-elastic constitutive models of rubber materials are studied and mainly divided into two types, namely a unique image model and a statistical mechanical model, and the constitutive relation of the materials describes stress as a function of deformation history of an object. The constitutive model is a mathematical mechanical description of the constitutive behavior of an idealized material. To fully describe the mechanical behavior of rubber, the strain energy function of rubber at generally pure uniform deformation is determined. For rubber articles, performance simulations, including structural optimization design and reliability analysis of complex elastomeric components, are typically performed using finite element simulation analysis (FEA). Among the elastic constitutive models, models suitable for finite element analysis include Neo-Hookean models, etc., however, if the strain energy function of the rubber material cannot be accurately expressed, reliable simulation results cannot be obtained. In the relation of the strain energy function of the strain invariants in finite element simulation software (such as Abaqus), the exponent of the strain invariants is usually an integer, so that the strain energy function has certain limitation in fitting test data, and the accuracy of the superelastic constitutive model in the process of fitting the test data cannot be ensured. The method for constructing the superelastic constitutive model of the strain energy function with the strain invariant of the non-integer power is provided for rubber materials, so that flexibility and accuracy of the strain energy function in fitting test data are improved, and better fitting effect is achieved by using fewer parameters through introduction of the strain invariant of the non-integer power. Disclosure of Invention The invention provides a method for constructing a super-elastic constitutive model of a rubber material, which aims to solve the problem that in the prior art, the power exponent in a strain energy function of a strain invariant is an integer, so that the problem of certain limitation in fitting test data is solved. The strain energy function of the method can be expressed as a non-integer power form of a strain invariant, so that the fitting flexibility is improved, and better fitting data can be obtained by using a simple constitutive model and fewer material parameters. The technical scheme of the invention is as follows: The invention provides a construction method of a super-elastic constitutive model of a rubber material, which comprises the following steps: (1) Deriving a strain energy function with non-integer power strain invariants; (2) Adopting a quasi-static stretching superelastic constitutive test to obtain stress strain test data; (3) Fitting to obtain material parameters of a non-integer power strain invariant strain energy function according to the steps (1) and (2); (4) Writing the strain energy function in the step (1) into finite element software, and fitting material parameters of a Neo-Hookean model according to the step (2); (5) Establishing a single-unit three-dimensional model, performing finite element simulation by using the material parameters obtained in the steps (3) and (4) to obtain a finite element stress strain simulation result, and comparing the simulation result with the test data of the step (2). Further, the strain energy function with the first strain invariant of the non-integer power obtained in the step (1) is: ; Wherein a and b are material parameters, I 1 is a first strain invariant, and the relation between the first strain invariant I 1 and strain epsilon is as follows: 。 Further, the modulus G and strain epsilon satisfy the following relationship: ; The strain energy function formula is: ; And introducing the relation between the first strain invariant I 1 and the strain epsilon into a formula of a strain energy function to obtain the strain energy function with the first strain invariant of the non-integer power. Further, the step (2) adopts a quasi-static uniaxial tensile test, and the uniaxial tensile strain is 50% to 100%. Further, when the uniaxial tensile strain is 100%, the strain energy function is: Where