| QUALITATIVE ANALYSIS OF SPHERICAL CAVITY NUCLEATION AND GROWTH FOR INCOMPRESSIBLE GENERALIZED VALANIS-LANDEL HYPERELASTIC MATERIALS |
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| 作者姓名： | YuanXuegang ZhuZhengyou ChengChangjun |
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| 作者单位： | Yuan Xuegang1，2 Zhu Zhengyou1 Cheng Changjun1 (1Shanghai Institute of Applied Mathematics and Mechanics，College of science，Shanghai University，Shanghai 200072，China) (2Department of Mathematics and Informational Science，Yantai University，Yantai 264005，China) |
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| 摘 要： | I. INTRODUCTION In practice, cavity formulation in materials is recognized as precursors to failure. Thus void nucleationand growth in solid materials have a great in?uence on failure mechanism. Gent and Lindley1] have observed experimentally the phe…
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| 关 键 词： | 空化分叉 临界负载 稳定性 Valanis-Landel材料 弹塑性 |
| 收稿时间： | 2 January 2003 |
Qualitative Analysis of Spherical Cavity Nucleation and Growth for Incompressible Generalized Valanis-Landel Hyperelastic Materials |
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| YuanXuegang ZhuZhengyou ChengChangjun.QUALITATIVE ANALYSIS OF SPHERICAL CAVITY NUCLEATION AND GROWTH FOR INCOMPRESSIBLE GENERALIZED VALANIS-LANDEL HYPERELASTIC MATERIALS[J].Acta Mechanica Solida Sinica,2004,17(2):158-165. |
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| Authors: | Xuegang Yuan Zhengyou Zhu and Changjun Cheng |
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| Institution: | (1) Shanghai Institute of Applied Mathematics and Mechanics, College of science, Shanghai University, 200072 Shanghai, China;(2) Department of Mathematics and Informational Science, Yantai University, 264005 Yantai, China |
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| Abstract: | 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 vari- ation 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. |
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| Keywords: | incompressible generalized Valanis-Landel material cavitated bifurcation critical dead-load normal form stability and catastrophe |
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