摘要
本文分别采用Ｊａｕｍａｎｎ应力率、Ｔｒｕｅｓｄｅｌｌ应力率和Ｇｒｅｅｎ－Ｎａｇｈｄｉ应力率导出了非线性各向同性弹性体的率型本构表达形式，通过对Ｍｏｏｎｅｙ－Ｒｉｖｌｉｎ材料的简单剪切大变形分析表明，三种率型的本构关系均与全量本构关系相等价。文中还给出了相应的率型变分原理，并采应Ｒｉｔｚ法，数值求解了受单轴拉伸的矩形橡皮薄膜的大变形问题．
In this paper,we obtain the rate-type constitutive expressions of the nonlinear isotropic elasticity by using the Jaumann,Trucsdell and Green-Naghdi stress rate respectively.Through an alysing the simple shear deformation for Mooney-Rivlin material,three kinds of rate-type constitutive equations are verified to be equivalent to the original equation,Rate-type variational principles are also presented.and the Ritz method is used to obtain the numerical solution of a rec-tangular rubber membrane under uniaxial stretch.
出处
《应用数学和力学》
CSCD
北大核心
1994年第2期121-128,共8页
Applied Mathematics and Mechanics
关键词
非线性
弹性
大变形
应力率
nonlinear elasticity,hypoelasticity,large deformation,stress rate tensor
