Continuum damage mechanics for the lithosphere

This paper introduces a new mathematical formulation of continuum damage mechanics for deep lithospheric layers subjected to thermomechanical loading. The material's rheology includes isotropic linear elasticity as well as nonlinear viscoplasticity induced by combined creep mechanisms. The formulation is based on the theory of generalized standard materials where the dissipative processes obey the principle of maximum dissipation. The model was implemented numerically using relatively new techniques of thermal and rate dependency considerations. The predictor-corrector algorithm of radial return mapping characterized by high convergence rates was also included. The results show a clear impact of continuum damage on the local material integrity. This weakening effect adds up to the shear heating feedback which accelerates the softening behavior. When considering processes taking place at high temperatures and low rates of loading, neglecting damage leads to overestimated forces in the lithosphere.