Theoretical and numerical plastic strain localization analysis at plane strain of isotropic dilating non-associated media at plane strain conditions

The article is devoted to the limit plastic state and localization of plastic deformations along shear bands in dilating media with a non-associative flow rule. The equations of the characteristics of systems of equations for stresses and velocities in a plane strain state for an arbitrary function of the yield surface dependenе on the first two invariants in the rigid-plastic framework are obtained. Equations for stresses along the characteristics for the limit state and the condition of their hyperbolicity are obtained. A numerical model of the solution of the elastic-plastic problem by Galerkin equations on high-order spectral elements is presented. Numerical experiments have been carried out for the linear function of the yield surface in order to establish the boundaries of the range of possible slopes of the shear bands and to test the theoretical results.