Elastoplastic Model of Rocks with a Linear Structural Parameter

Abstract

A closed mathematical model is formulated, which takes into account elastoplastic strains and the medium capability of accumulating the energy of internal self-balanced stresses. Satisfaction of the diffeomorphism postulate (assumption of displacement field smoothness) is not required; as a result, the strains depend on the stresses and second derivatives of the stresses with respect to the coordinates. The model involves a linear structural parameter. Relations that take into account local bending of the elementary volumes of the medium are derived.