Model of Elastoplastic Deformation of Materials, Based on the Gauge Theory of Defects with Allowance for Energy Dissipation

Mathematical models of plasticity and creep for the case of small deformations are proposed on the basis of the gauge theory of defects with allowance for energy dissipation. It is assumed that plasticity is related to the motion of dislocations, which occurs without changes in volume. In the creep model, the motion of dislocations can proceed with changes in volume, and the extra volume is entrained (brought) by point defects. With the help of Godunov's generalized thermodynamic approach, it is shown that the proposed plasticity model is hyperbolic according to Friedrichs.