Swelling-Induced Cavitation of Elastic Spheres

Abstract

Swelling, generally referring to volumetric change and typically due to mass addition from some diffusive or transport mechanism, is central to a variety of physical phenomena. Here we consider the role of swelling as it relates to the inflation of hollow spheres and to cavity formation at the center of solid spheres. The swelling is modeled in terms of a prescribed scalar field that gives the local free volume. The finite deformation theory of incompressible hyperelasticity is generalized so as to include the effect of this swelling field directly in the stored energy density. The general framework is based on global energy minimization wherein the stored energy density is minimized at the locally prescribed swollen state. On this basis it is found that both inflation and cavitation can be caused solely by swelling. This result is intuitive with respect to inflation where it follows from a simple uniform swelling field. In contrast, to obtain swelling-induced cavitation we consider a non-uniform swelling field and study how this field can cause a cavity to nucleate, grow, shrink and disappear.