Qualitative Analysis of Spherical Cavity Nucleation and Growth for Incompressible Generalized Valanis-Landel Hyperelastic Materials

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• 作者：Xuegang Yuan ^{A1 A2} ; Zhengyou Zhu ^A1 ; Changjun Cheng ^A1
• 关键词：incompressible generalized Valanis-Landel material ; cavitated bifurcation ; critical dead-load ; normal form ; stability and catastrophe
• 刊名：Acta Mechanica Solida Sinica
• 出版年：2004
• 出版时间：June 2004
• 年：2004
• 卷：17
• 期：2
• 页码：158-165
• 全文大小：233 KB
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Mechanics, Fluids and Thermodynamics
  Engineering Fluid Dynamics
  Numerical and Computational Methods in Engineering
  Chinese Library of Science
  
• 出版者：The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of
• ISSN：1614-3116

文摘

A cavitated bifurcation problem is examined for a sphere composed of a class of generalized Valanis-Landel materials subjected to a uniform radial tensile dead-load. A cavitated bifurcation equation is obtained. An explicit formula for the critical value associated with the variation of the imperfection parameters is presented. The distinguishing between the left-bifurcation and right-bifurcation of the nontrivial solution of the cavitated bifurcation equation at the critical point is made. It is proved that there exists a secondary turning bifurcation point on the nontrivial solution branch, which bifurcates locally to the left. It is shown that the dimensionless cavitated bifurcation equation is equivalent to normal forms with single-sided constraint conditions at the critical point by using the singularity theory. The stability and catastrophe of the solutions of the cavitated bifurcation equation are discussed.