A damage-plasticity model for brittle materials based on an approximation of Rankine type of failure criterion

A damage-plasticity model for tensile failure analyses of brittle materials is developed. The stress states leading to a failure (inelastic strains and damage) are indicated by a rounded approximation of the Rankine criterion. This approximation is expressed in terms of the stress invariants avoiding thus the need of coordinate transformations and eigenvalue solutions required by the classical Rankine criterion. The model is formulated with the effective stress space approach, i.e. the return mapping is first performed in the global effective stress space and then the damage update is performed independently of the plasticity part. The model is consistently linearized, and, finally, some demonstrative simulations of a tensile test on a rock-like material are carried out.