组合超弹性材料中的空穴生成与增长  

Formation and Growth of Cavity in Composed Hyper-elastic Materials

作　　者：任九生[1] 程昌钧[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所力学系,上海200072

出　　处：《力学季刊》2004年第2期175-182,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金资助项目(No.10272069);上海市重点学科建设资助项目

摘　　要：本文研究了一种组合不可压超弹性材料圆柱体中空穴的生成与增长问题,得到了这种材料受表面均布拉伸死荷载和轴向拉压共同作用下空穴生成问题的解析解,得到了不同组合情况下圆柱体中空穴生成时的临界载荷及分叉曲线,发现组合材料可以发生右分叉,也可以发生左分叉;给出了空穴生成后的应力分布,并讨论了所存在的应力间断和应力集中问题;通过能量比较分析了解的稳定性,讨论了发生右分叉或左分叉的条件,并分析了材料中预存微孔的增长情况。The problem of cavity formation and growth in a solid circular cylinder composed of two incompressible hyper-elastic materials under a uniform radial tensile boundary dead-load and an axial stretch was examined. The analytic solution for the bifurcation problem was obtained. The critical load and the bifurcation curves were given and the left bifurcation as well as the right bifurcation may be found here. The catastrophe and concentration of stresses as well as the stress contributions subsequent to the cavitation were discussed. The stability of solutions was discussed through the energy comparison and the condition for the right or left bifurcation was discussed. The growth of a pre-existing void was also observed.

关 键 词：组合不可压超弹性材料 空穴的生成与增长 应力间断和应力集中 能量比较 

分 类 号：O343[理学—固体力学]