Dynamical analysis of cavitation for a transversely isotropic incompressible hyper-elastic medium: Periodic motion of a pre-existing micro-void

作者：Yuan Xue gang^*; Zhu Zheng you; Cheng Chang jun

来源：International Journal of Non-Linear Mechanics, 2007, 42(3): 442-449.

DOI：10.1016/j.ijnonlinmec.2007.01.006

• transversely isotropic incompressible hyper-elastic material
• pre-existing micro-void
• dynamical behavior
• equilibrium point
• non-linear periodic oscillation

In this paper, the dynamical cavitation behavior is analyzed for a sphere composed of a class of transversely isotropic incompressible hyper-elastic materials, where there is a pre-existing micro-void in the interior of the sphere. A second-order non-linear ordinary differential equation that governs the motion of the initial micro-void is obtained by using the boundary conditions. On analyzing the qualitative properties of the solutions of the differential equation, some interesting conclusions are proposed. It is proved that the number of equilibrium points of the differential equation depends on the values of the material parameters, and that the phase diagrams of the equation are closed, smooth and convex trajectories. For any prescribed surface tensile dead-loads, the motion of the initial micro-void undergoes a non-linear periodic oscillation. The dependence of the periodic motion of the initial micro-void on material parameters and the radius of the initial micro-void is examined, and numerical results are also provided. It is worth pointing out that the conclusions in this paper can be used to describe approximately the physical implications of the dynamical formation of a cavity in the sphere.

• 出版日期2007-4
• 单位大连民族大学; 上海大学