橡胶类材料大变形本构关系及其有限元方法

ON THE LARGE DEFORMATION RUBBER LIKE MATERIALS: CONSTITUTIVE LAWS AND FINITE ELEMENT METHOD

讨论大变形拟不可压缩橡胶类材料的本构关系及有限元分析方法.采用乘法分解,将变形梯度表示成等容和体积变形两部分,在此基础上,推导了克希荷夫应力和格林应变表示的Yeoh 形式应变能橡胶类材料的本构关系及数值处理方法.为处理不可压缩问题,采用三场变分原理,其中静水压力,体积膨胀,以及位移均作为独立变量进行处理.并指出该变分原理同胡鹫津广义变分原理的联系.变形采用相容等参插值,压力及体积膨胀采用低阶插值,推导了详细的有限元列式.最后给出了两个数值算例,结果表明了该方法的有效与可靠.为这类材料的精确的有限元分析打下了良好的基础.

On the constitutive laws of incompressible rubber like materials and the corresponding finite element analysis method. By the multiplicative decomposition of the deformation gradient into volume preserving and dilatational parts, the Yeoh mode type constitutive laws of rubber like materials and its 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 principle is established. The detail FE formulation is developed in which deformation is approximated by isoparametric conforming element, and the Jacobian and pressure by discontinuous interpolation. In the end, two numerical examples are given to show the effectiveness and reliability of the proposed method. The work in this paper established a foundtion of the treatment of the incompressible problem of rubber like materials under large deformation.