可压超弹性材料组合球体中心的空穴生成

基金项目: 国家自然科学基金资助项目(10272069);上海市重点学科建设资助项目

Cavity Formation at the Center of a Sphere Composed of Two Compressible Hyper-Elastic Materials

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

摘要: 研究了一种可压超弹性材料组合球体中的空穴生成问题,得到了组合球体在径向拉伸作用下空穴生成时分叉问题的解,包括均匀变形的平凡解和有内部空穴生成的分叉解。给出了空穴生成时的分叉曲线和球体中的应力分布,观察到了右分叉和左分叉现象及应力间断和应力集中现象。通过能量的比较分析了解的稳定性。
- 可压超弹性材料 /
- 空穴分叉 /
- 应力间断和应力集中 /
- 能量分析
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.
- compressible hyper-elastic material /
- cavitated bifurcation /
- catastrophe and concentration of stress /
- energy comparison

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