A thermodynamically consistent large deformation elastic–viscoplastic model with directional tensile failure

The main objective of this paper is to develop a continuum model for directional tensile failure that can simulate weakening and void formation due to tensile failure. Directionality in the model allows simulation of weakening to tension applied in one direction, without weakening to subsequent tension applied in perpendicular directions. The model is developed within the context of a properly invariant non-linear thermomechanical theory. Specifically, it is shown how the model can be combined with general constitutive equations for porous compaction and dilation, as well as viscoplasticity. The thermoelastic response is hyperelastic, with the stress being determined by derivatives of the Helmholtz free energy, and the material is considered to be elastically isotropic. In particular, it is assumed that the rate of inelasticity due to tensile failure is coaxial with the tensor measure of elastic deformation (and hence stress). This causes the rate of dissipation to take a particularly simple form which can be shown to satisfy the second law of thermodynamics. A numerical procedure for integrating these evolution equations is proposed and a number of examples are considered to explore the response of the model to different loading histories.