超弹性材料中空穴的动态生成

本文在有限变形动力学的框架下研究了一种不可压超弹性材料圆柱体在表面突加均布拉伸载荷作用下空穴的动态生成问题.除一个相应于均匀变形状态的平凡解外,当外加载荷超过其临界值时,柱体内部还有空穴的突然生成,得到了空穴半径和表面载荷之间的一个精确的微分关系,证明了空穴随时间的演化是非线性的周期性振动.给出了空穴振动的相图、最大振幅、临界载荷及近似的周期.

CAVITY FORMATION IN HYPERELASTIC MATERIALS BASED ON THE THEORY OF FINITE DEFORMATION DYNAMICS

The cavity formation in a hyper-elastic cylinder with the incompressible Ogden strain energy function, subjected to a suddenly applied uniform radial tensile boundary dead-load, is studied following the theory of finite deformation dynamics. Beside a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the cylinder when the tensile load is larger than its critical value. An exact differential relation between the cavity radius and the tensile load is obtained. 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 are all presented.