Spatially non-local model of inelastic deformations: applications for rock failure problem

A spatially non-local model for inelastic deformation of solids is proposed and studied. The non-locality of deformation is taken into account by the additional parameter of state beyond the classical parameters such as stress and strain tensors. This additional parameter is the curvature tensor expressed in terms of the metric strain tensor, and it is called the failure parameter. In the case of small deformation, it is equivalent to the Saint-Venant incompatibility tensor. Thermodynamic properties of the model are studied, and governing differential equations for spatially non-local model are formulated, which are composed by the elasticity equations and parabolic equation for the failure parameter. The model can be applied to the study of the rock failure problem, and as an example, the one-dimensional problem for the deformation of half-plane loaded by the normal surface stress is studied. Stationary and non-stationary formulations of the problem are considered, and qualitative agreement with available experimental data is observed.