On the role of material dissipation for the crack-driving force

The thermodynamic setting for the formulation of the “crack-driving force” for a singular crack in conjunction with rate-independent material response is discussed. One key ingredient is the introduction of a fixed (absolute) configuration, relative to which both physical and (virtual) configurational and spatial changes can be described. Only quasistatic and isothermal conditions are considered in this paper. A variational framework is established for the rate of global energy dissipation (integrated over the whole material domain) due to the combined action of a (discrete) crack extension and continuum inelasticity, whereby the material time derivative of internal variables and the rate of crack extension are coupled. The classical assumption (previously adopted in the literature) is that there is no coupling, i.e. the internal variables are considered as fixed (material) fields just like an inhomogeneous material property. The other (extreme) assumption is that the internal variables fields are convected with the configurational motion due to the virtual crack extension. Both cases are investigated in this paper for a simple 2D example of an edge crack in a plate in a setting of small strains and hardening plasticity. In particular, we consider convergence issues from mesh refinement.