不可压缩Rivlin—Saunders材料中空穴现象的定性分析

基于能量原理，研究了由一类均匀各向同性不可压缩的Rivlin-Saunders材料组成的实心球体在给定的表面拉伸死载荷作用下的空穴分岔问题．得到了描述球体内部空穴生成和增长的空穴分岔方程，并给出了此类材料中发生空穴分岔的条件；证明了空穴分岔方程的非平凡解在分岔点附近可以局部向左或向右分岔，这与其他各向同性不可压缩超弹性材料中的空穴生成和增长现象有明显的不同；同时给出了相应的数值算例；最后分析了解的稳定性和实际稳定的平衡状态．

Qualitative Analysis of Cavitation in Incompressible Rivlin-Saunders Materials

Based on the energy principle, a cavitated bifurcation problem is examined for a solid sphere composed of a class of homogeneous isotropic incompressible Rivlin-Saunders materials, where the sphere is subjected to a prescribed tensile dead-load. A cavitated bifurcation equation that describes cavity formation and growth in the interior sphere is obtained. The conditions of cavitated bifurcation in the Rivlin-Saunders materials are presented. It is proved that the nontrivial solution can bifurcate locally to the left or the right near the bifurcation point, which is quite different from other isotropic incompressible hyperelastic materials, and some numerical examples are also carried out. Finally, the stability of the solutions and the actual stable equilibrium state are discussed.