Mesoelastic deformation with strain singularities

We study material deformations of polycrystals, rocks and other elastic materials that display different types of imperfections with a typical size of 1 mu m. Stress-strain relationships of these materials depend on the processing history and exhibit common behavior, including nonlinearity, hysteresis, etc. We focus our study on the continuous distribution of singularities in the strain field, which we describe in terms of surface densities and fluxes. We define the mass mesodensity tensor and deduce the constitutive relationships between the strain singularity current and the linear mesomomentum. Based on the modification of Peach-Koehler formula we consider the constitutive relation between the line mesostress tensor and the strain singularities density. These constitutive relationships allow us to model stresses in mesoelastic materials.