中文摘要：

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.

英文摘要：

This paper mainly discusses the constitutive laws of incompressible rubber-like materials and the associated finite element analysis method. By a multiplicative decomposition of the deformation gradient 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 problems, a three-field variational principle is developed in which deformation, Jacobian and pressure field are treated independently. The connection between the three-field principle and the Hu-Wasizhu generalized variational principle is established. It is shown that the approach proposed can be degenerated to the B-bar method in the linear case. The derailed FE formulation is given in which deformation is ap proximated by isoparametric conforming element, and Jacobian and pressure by discontinuous approximation. Finally, two numerical examples are presented to show the effectiveness and reliability of the method proposed. The work in this paper provides a corner stone of FEA of this kind of problem. This paper features the combination of the multiplicative decomposition, the three-field principle and YEOH model of rubber-like materials, especially under Lagrangian description, giving an effective way for solving this kind of problems. The Lagrangian description is compatible with usually geometrically nonlinear FEM and the constitutive laws are expressed by the second Kirchhoff stress and the Green strain.