Dynamics and destruction of internally pressurized incompressible hyper-elastic spherical shells

Abstract

Dynamical response and destruction of incompressible hyper-elastic spherical shells under a periodic or a constant internal pressure are examined within the framework of finite elasto-dynamics. When a static uniform internal pressure is applied, the spherical shell is subject to an unstable aspherical deformation after the initial stable spherical inflation. When a periodic or a constant internal pressure is applied, an exact differential relation between the deformation of the internal boundary and the pressure is obtained. The displacement response curves, the power spectrum curves, the phase portrait and the Poincaré maps are given by numerical computation. It is shown that the spherical shell will undergo nonlinear periodic oscillation if a constant internal pressure is suddenly applied. It will undergo nonlinear quasi-periodic oscillation if a periodic internal pressure is applied. At the same time, the destruction or the structural catastrophes may be admitted and it is discussed in details.