Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation such derived. Results related to analysis fields and their geometric properties are presented. Using these results, formulation the problem nonlinear theory dislocations given. For an isotropic elastic material with arbitrary distribution dislocations, this reduced boundary value for system ordinary differential equations. In case incompressible screw in radial direction, exact analytical solution found equilibrium hollow sphere loaded from outside inside by hydrostatic pressures. This suitable any models body, i.e., universal specified class materials. Based on obtained solution, numerical calculations effect stress state at large deformations carried out.