论文部分内容阅读
This paper mainly discusses the constitutive Iaws of incompressible rubber-like materialsand the aaaociated finite element analysis method.By a multiplicative decomposition of the deformationgradient into distortional and dilatational parts,the YEOH mode type constitutive laws of rubber-likematerials and their numerical implementation are presented.In order to deal with incompressible prob-lends,a three-field variational principle is developed in which deformation,Jacobian and pressure fieldare treated independently.The connection between the three-field principle and the Hu-Wasizhu gener-alized variational principle is established.It is shown that the approach proposed can be degenerated tothe B-bar method in the linear case.The detailed FE formulation is given in which deformation is ap-proximated by isoparametric conforming element,and Jacobian and pressure by discontinuous approxi-mation.Finally,two numerical examples are presented to show the effectiveness and reliability of themethod proposed.The work in this paper provides a corner stone of FEA of this kind of problem.This paper features the combination of the muhiplicative decomposition,the three-field principleand YEOH model of rubber like materials,especially under Lagrangian description,giving an effec-tive way for solving this kind of problems.The Lagrangian description is compatible with usually geo-metrically nonlinear FEM and the constitutive laws are expressed by the second Kirchhoff stress and theGreen strain.
This paper mainly discusses the constitutive Iaws of incompressible rubber-like materials and the aaaociated finite element analysis method. By a multiplicative decomposition of the deformationgradient into distortional and dilatational parts, the YEOH mode type constitutive laws of rubber-like materials and their numerical implementation are presented. In order to deal with incompressible prob-lends, a three-field variational principle is developed in which deformation, Jacobian and pressure fieldare treated independently. The connection between the three-field principle and the Hu-Wasizhu gener-alized variational principle is established. It is shown that the proposed solution can be degenerated tothe B-bar method in the linear case. The detailed FE formulation is given in which deformation is ap-proximated by isoparametric conforming element, and Jacobian and pressure by discontinuous approxi- mation. two numerical examples are presented to show the effectiveness and reliability of theme thod proposed. The work in this paper provides a corner stone of FEA of this kind of problem. This paper features the combination of the muhiplicative decomposition, the three-field principle and YEOH model of rubber like materials, especially under Lagrangian description, giving an effec -tive way for solving this kind of problem. Lagrangian description is compatible with usually geo-metrically nonlinear FEM and the constitutive laws are expressed by the second Kirchhoff stress and the Green strain.