Calculation of Stress Concentration in a Generalized Elastoplastic Medium

A mathematical model from the class of generalized media possessing an internal microstructure is proposed. The model considers the nonuniform deformation of an infinitesimal elementary volume, where plastic shears at the volume boundaries are taken into account. Unlike the classical description of a continuum, additional kinematic degrees of freedom are introduced; in the planar case, these are described by two independent smooth displacement fields. This leads to the fact that a length-dimensional parameter that characterizes the structure of the medium is introduced into the constitutive equations. This model is applied to numerically solve the problem of stress redistribution in the near-boundary region of a system of mine workings within a rock mass, arising from the application of a specific mining technology. It is revealed that accounting for the microstructure of the medium—a feature absent in classical elastoplastic models—results in a significant transfer of the load from the working boundaries deeper into the deformed medium.