Physical and mechanical foundations of the theory of inelastic deformation of solids.

The development of fundamental ideas about the inelastic deformation and fracture of materials is of great practical importance. This is substantiated by the need for a macroscopic theory suitable for solving engineering problems and taking into account real physical processes occurring in a deformed material. Such a theory can be efficiently used in problems of computer-aided design of materials with required mechanical properties. This paper is devoted to the formulation of the principles of the macroscopic theory of inelastic deformation, which couples the mechanical and physical aspects. The theory combines two macroscopic theories: the classical theory of elasticity and the continuum theory of translational defects. The proposed theory uses the Lagrangian formalism in combination with the gauge field method. The latter allows introducing defects of the translational type. The application of the principle of least action to the Lagrangian with gauge fields made it possible to obtain the equations of motion for both elastic displacements and defects. The adequacy of the proposed theory is confirmed by several classical examples. [ABSTRACT FROM AUTHOR]