Non-classical solutions of a continuum model for rock descriptions

Abstract

The strain-gradient and non-Euclidean continuum theories are employed for construction of non-classical solutions of continuum models. The linear approximation of both models' results in identical structures in terms of their kinematic and stress characteristics. The solutions obtained in this study exhibit a critical behaviour with respect to the external loading parameter. The conclusions are obtained based on an investigation of the solution for the scalar curvature in the non-Euclidean continuum theory. The proposed analysis enables us to use different theoretical approaches for description of rock critical behaviour under different loading conditions.