ADIABATIC SHEAR BAND LOCALIZATION IN ELASTIC-PLASTIC DAMAGED SOLIDS

The main objective of the paper is the investigation of shear band localization conditions for finite elastic-plastic rate independent deformations of a damaged solid body subjected to an adiabatic process. For the kind of process considered, the thermal effects may play a dominating role. The next objective of the paper is to focus attention on temperature-dependent plastic behaviour of the body considered. Thermomechanical couplings are investigated, and a method is developed that allows application of the standard bifurcation procedure in examination of the shear band localization criteria when influence of thermomechanical couplings and thermal softening effects, together with hardening and micro-damage effects, are taken into consideration. Particular attention is focused on the coupling phenomena generated by the heat resulting from internal dissipation. A set of the coupled evolution equations for the Kirchhoff stress tensor and for temperature is considered. The assumption that the thermodynamic process is adiabatic permits elimination of the rate of temperature and permits us to obtain the general evolution equation for the Kirchhoff stress tensor. The fundamental matrix in this evolution equation describes thermomechanical couplings. For the particular elastic properties of the material and for some simplified cases of the coupling effects the criteria for shear band localization have been obtained in exact analytical form.