The cavitation phenomenon in nonlinear elasticity

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 is subjected to a radial dead-load on its boundary. We show that the rotationally symmetric equilibrium solution, in which a spherical cavity forms at the centre of the deformed ball, cannot be a global energy minimiser. This is achieved by proving the existence of a related axisymmetric homogeneous equilibrium with less energy (our arguments are related to the Rivlin instability in incompressible materials). 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 Chapter 4 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.EThOS - Electronic Theses Online ServiceGBUnited Kingdo