The Cavitation Phenomenon in Nonlinear Elasticity

Abstract

This thesis studies the phenomenon of cavitation in nonlinear elasticity. In Chapter 2 we study the problem of cavitation in a ball of elastic material which issubjected to a radial dead-load on its boundary. We show that the rotationallysymmetric equilibrium solution, in which a spherical cavity forms at the centreof the deformed ball, cannot be a global energy minimiser. This is achieved byproving the existence of a related axisymmetric homogeneous equilibrium withless energy (our arguments are related to the Rivlin instability in incompressiblematerials). In Chapter 3 we develop new necessary conditions for radially symmetric equilibria to be strong local minimisers of the energy. In Chapters 4 and 5 we study cavitation at, or near, the boundary of an elastic body. In Chapter4 we consider cavitation occurring near the boundary of an elastic body occupying a half-space in its reference configuration. We show that the energy of such an equilibrium can be further lowered by moving the point of cavitation further away from the boundary. In Chapter 5, we prove existence of energy minimisers in classes of deformations which allow cavitation to occur at a boundary point.

Date of Award	19 Jul 2013
Original language	English
Awarding Institution	University of Bath
Supervisor	Jeyabal Sivaloganathan (Supervisor)