Role of nonequilibrium nonlocality and memory effects in structure formation of dynamically deformable media. I. Nonlocal hydrodynamic theory

Abstract

A new theoretical approach to the description of structure formation processes in a solid under dynamic stress, which are initiated by this stress, is developed in the present paper. This approach is based on the similarity between the behavior of a dynamically deformable solid and hydrodynamics of fast processes and differs from classical hydrodynamics by several essential aspects. First, the new approach is based on the nonlocal system description, that is, it retains the integral information on the system as a whole while describing its local properties and also takes into account the long-range influence of the environment. Second, this approach considers the influence of boundary conditions of the problem on the structure formation process in a self-consistent way, by introducing a feedback into the system. The model of the medium suggested here describes the intermediate situation between a perfectly rigid body (the nonlocality parameter increases infinitely) and a viscous liquid (the nonlocality parameter is close to 0). As a result of branching of solutions to the general nonlinear problem of dynamic deformation of a medium for the nonlocal model, the dimensions of structural elements and the types of kinematic deformation mechanisms are simultaneously determined for different scale levels. The results obtained are confirmed by a number of experimentally observed regularities.