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Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (9): 1009-1016.

• 论文 • 上一篇    下一篇

CAVITY FORMATION AT THE CENTER OF A SPHERE COMPOSED OF TWO COMPRESSIBLE HYPER-ELASTIC MATERIALS

任九生1, 程昌钧2, 朱正佑3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    2. Department of Mechanics, Shanghai University, Shanghai 200436, P. R. China;
    3. Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China
  • 收稿日期:2002-04-15 修回日期:2003-03-25 出版日期:2003-09-18 发布日期:2003-09-18
  • 基金资助:

    the National Natural Science Foundation of China (19871059);the Natural Science Foundation of Education Department of Sichuan Province ([2000] 25)

CAVITY FORMATION AT THE CENTER OF A SPHERE COMPOSED OF TWO COMPRESSIBLE HYPER-ELASTIC MATERIALS

REN Jiu-sheng1, CHENG Chang-jun2, ZHU Zheng-you3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China;
    2. Department of Mechanics, Shanghai University, Shanghai 200436, P. R. China;
    3. Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China
  • Received:2002-04-15 Revised:2003-03-25 Online:2003-09-18 Published:2003-09-18
  • Supported by:

    the National Natural Science Foundation of China (19871059);the Natural Science Foundation of Education Department of Sichuan Province ([2000] 25)

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摘要： The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials under a uniform boundary radial stretch was examined. The solutions, including the trivial solution and the cavitated solutions, were obtained. The bifurcation curves and the stress contributions subsequent to cavitation were discussed. The phenomena of the right and the left bifurcations as well as the catastrophe and concentration of stresses are observed. The stability of solutions is discussed through the energy comparison.

Abstract: The cavitated bifurcation problem in a solid sphere composed of two compressible hyper-elastic materials under a uniform boundary radial stretch was examined. The solutions, including the trivial solution and the cavitated solutions, were obtained. The bifurcation curves and the stress contributions subsequent to cavitation were discussed. The phenomena of the right and the left bifurcations as well as the catastrophe and concentration of stresses are observed. The stability of solutions is discussed through the energy comparison.

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