Mathematical theory and numerical computation of cavitation in nonlinear elasticity

Abstract

Many soft nonlinear elastic materials, such as polymers, organic tissues, etc., can produce special singular deformation called cavitation under certain conditions. The study of cavitation is an important part of the effort to understand, characterize, analyze and apply the materials. In this paper, we will try to show the readers a rough picture of the computation and simulation of the cavitation phenomenon in nonlinear elasticity by a brief review on some of the representative mathematical models and theories, numerical methods and corresponding analytical and numerical results.