Nonlinear Deformations of an Elastic Sphere with Couple Stresses and Distributed Dislocations

Abstract

The problem of nonlinear moment theory of elasticity about the equilibrium of a hollow sphere with distributed dislocations is considered. For an arbitrary isotropic micropolar elastic material and a spherically symmetric distribution of screw and edge dislocations, the problem is reduced to a system of nonlinear ordinary differential equations. In the case of a physically linear micropolar body model, exact solutions are found for the eigenstresses in the sphere due to the spherically symmetric distribution of edge dislocations.