Dynamical Formation of Cavity in a Composed Hyper-Elastic Sphere
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摘要: 根据有限变形动力学理论，研究了一个不可压超弹性材料组合球体在突加表面均布拉伸载荷作用下空穴的动态生成问题．当外加载荷超过其临界值时，除一个平凡解外，还有一个包含着球体内部生成的空穴的分叉解；证明空穴随时间的演化是周期性的非线性振动；同时给出了空穴生成时的临界载荷值、空穴振动的相图、振幅及近似的周期．
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关键词:
- 组合不可压超弹性材料 /
- 有限变形动力学 /
- 空穴的动态生成 /
- 非线性周期振动
Abstract: The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected a suddenly applied uniform radial tensile boundary dead-load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed. -
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