Numerical simulation of damage using an elastic-viscoplastic model with directional tensile failure

Abstract
A new continuum model for directional tensile failure has been developed that can simulate weakening and void formation due to directional tensile failure. The model is developed within the context of a properly invariant nonlinear thermomechanical theory. A second order damage tensor is introduced which allows simulation of weakening to tension applied in one direction, without weakening to subsequent tension applied in perpendicular directions. This damage tensor can be advected using standard methods in computer codes. Porosity is used as an isotropic measure ouf volumetrie void strain and its evolution is influence by tensile failure. The rate of dissipation due to directional tensile failure takes a particularly simple form, which can be analyzed easily. Specifically, the model can be combined with general constitutive equations for porous compaction and dilation, as well as viscoplasticity. A robust non-iterative numerical scheme for integrating these evolution equations is proposed. This constitutive model has been implemented into an Eulerian shock wave code with adaptive mesh refinement. A number of simulations of complicated shock loading of different materials have been performed including problems of fracture of rock. These simulations show that directionality of damage can play a significant role in material failure.