Effects of Constitutive Parameters and Dynamic Tensile Loads on Radially Periodic Oscillation of Micro-Void Centered at Incompressible Hyperelastic Spheres

摘要

The radially symmetric motion of the pre-existing micro-void centered at an incompressible hyperelastic sphere under the dynamic surface tensile loads relating to time is investigated in this paper. Some interesting conclusions are obtained by qualitatively analyzing the solutions of the motion equation of micro-void in detail; meanwhile, numerical simulations are used for understanding the obtained conclusions. In particular, it is proved that the motion of the micro-void with time would present a nonlinearly periodic oscillation if the values of the constant tensile load, the material and the structure parameters are given and that the oscillation amplitudes of the micro-void are discontinuous in some special cases; under the generalized dynamic surface tensile loads relating to time, the necessary conditions of the nonlinearly periodic oscillation of the micro-void are proposed by using the symmetric principle and the connecting rale of the phase diagrams of the differential equation that governs the motion of the pre-existing micro-void.