Non-euclidean continuum model, in which the intrinsic metric and the scalar curvature are additional parameters characterizing the structure of defects in the material, is considered. It is shown that the irrotational displacement field is formed of elastic displacements in the absence of defects and the field which characterizes the difference between the intrinsic geometry of the model of Euclidean geometry. Corresponding components of the internal stresses represent the sum of elastic stresses and self-balanced stress defined by the scalar curvature. It is proved that the invariance of the free energy with respect to gauge transformations is generated by the deformation of the elastic continuum. This property determines the general structure of the internal stress field that does not depend on the choice of interaction. Application of the proposed approach is demonstrated for construction of the exact solution in the case of the vorticity field of the dislocations for the material in the absence of external forces. Conditions for the existence of a non-zero stress field parametrized by the scalar curvature are formulated.
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