The Influence of Distributed Dislocations on Large Deformations of an Elastic Sphere

From the point of view of nonlinear elasticity theory the equilibrium problem for elastic sphere was considered taking into account distributed edge dislocations. We used the system of equations that consists of the incompatibility equations with a given dislocation density tensor, equilibrium equations, and constitutive equations of the material. For the isotropic material and spherically symmetric distribution of the edge dislocations, the problem was reduced to the second-order ordinary differential equation. In the framework of harmonic (semi-linear) material, the exact solution of this equation was found for any function which defines the edge dislocation density. In particular, we studied the case of dislocations concentrated on a spherical surface within a body. It was established that this surface was the discontinuity surface of strains and stresses. In addition to eigenstress problem, we solved a problem of the loading of a hollow sphere with external or internal hydrostatic pressure. Influence of dislocations on resistance of the sphere to the compression or blowing was investigated.