Non-spherical axisymmetric deformations of hyperelastic shells

Abstract

Spherical elastic shells commonly appear both in nature and man-made devices. Often, their functionality is governed by an incoming- or outgoing flux of fluid. The transient traction that the fluid exerts in the process causes the shell to depart from sphericity. Here, we develop a framework for determining non-spherical axisymmetric deformations, by combining tools from nonlinear continuum mechanics, structural mechanics, and asymptotic analysis. We apply our framework to analyze an exemplary problem of a Mooney–Rivlin shell that is filled by viscous fluid. Collectively, our framework and the insights gained from its application, promote the understanding of the mechanics of such fluid-filled deformable membranes and shells.