Structure of kinematic and force fields in the Riemannian continuum model

In this paper, we consider a non-Euclidean continuum model for which the structure of defects in the material is characterized by an internal metric and scalar curvature. It is shown that the irrotational displacement field for points of this medium is composed of elastic displacements (in the absence of defects) and the field which characterizes the deviation of the internal geometry of the model from Euclidean geometry. The corresponding components of the internal stresses are the sum of elastic stresses and the self-equilibrated stresses determined by the scalar curvature. The exact solution for the vortex field of dislocations is constructed, and conditions of the existence of a nonzero stress field parametrized by a scalar curvature in the absence of external forces are formulated.