Separation phenomena at the interface of a finitely deformed composite sphere

The problem of the finite deformation of a composite sphere subjected to a spherically symmetric dead load traction is revisited focusing on the formation of a cavity at the interface between a hyperelastic, incompressible matrix shell and a rigid inhomogeneity. Separation phenomena are assumed to be governed by a vanishingly thin interfacial cohesive zone characterized by uniform normal and tangential interface force-separation constitutive relations. Spherically symmetric cavity shapes (spheres) are shown to be solutions of an interfacial integral equation depending on the strain energy density of the matrix, the interface force constitutive relation, the dead loading and the volume concentration of inhomogeneity. Spherically symmetric and non-symmetric bifurcations initiating from spherically symmetric equilibrium states are analyzed within the framework of infinitesimal strain superimposed on a given finite deformation. A simple formula for the dead load required to initiate the non-symmetrical rigid body mode is obtained and a detailed examination of a few special cases is provided. Explicit results are presented for the Mooney-Rivlin strain energy density and for an interface force-separation relation which allows for complete decohesion in normal separation.