不可压各向同性超弹性物质的响应函数  

The Stress Response Functions of Isotropic Incompressible Hyperelastic Materials

作　　者：陈良森[1] 扶名福[1] 兰志文[1] 

机构地区：[1]南昌大学工程力学所,江西南昌330029

出　　处：《南昌大学学报（工科版）》2002年第4期7-11,共5页Journal of Nanchang University(Engineering & Technology)

摘　　要：本文假设不可压各向性超弹性物质的单位体积贮能函数σ∧是Cauchy-Green伸长张量的三个特征值λ1,λ2和λ3的函数=1.根据超弹性物质的定义,证明只有引入某种条件如正规化条件,才能得到不可压各向同性超弹性物质的响应函数.由于正规化条件更为合理,因此,文献中的有关响应函数的表达式就是不正确的.本文还以一个例子说明本文提出的分析方法导出的响应函数的表达式与Chen,Xiao与Fu[1]中的推导方法导出的结果一样,这也进一步说明[1]中所得到的结果是合理的.在本文中还讨论了橡胶的贮能函数,发现不可能通过实验来验证正规化条件的合理性.This paper assumes that the stored energy function σ∧ per unit volume of an isotropic incompressible hyperelastic material is a function of the three eigenvalues λ1,λ2 and λ3 of Cauchy-Green stretch tensor with λ1λ2λ3=1.According to the definition of hyperelasticity,it is proved that only by introducing some condition such as the normalization condition can we derive the stress response function of isotropic incompressible hyperelastic materials.Since the normalization condition is reasonable;therefore,the formulus of related stress response function is not correct.It is shown with an example that the stress response function derived by the approach used in the present paper is the same as that given in Chen.Xiao and Fu.This reflects the fact that the analysis in is correct.The form of stored energy function is also discussed.It is found that it is impossible to examine the reasonability of the normalization condition by experiments.

关 键 词：响应函数 不可压各向同性超弹性物质 本构关系 橡胶 理性力学 贮能函数 

分 类 号：O331[理学—一般力学与力学基础]