Numerical simulation of ductile fracture with the Rousselier constitutive law

Abstract

This contribution aims at developing robust and reliable tools dedicated to predictive numerical simulation of ductile fracture. Description of damage mechanisms relies here on the Rousselier constitutive law. To achieve robustness and objectivity, several points need then to be addressed: reduction of the set of internal variables so as to recast the model into the framework of generalised standard materials; proper expression of the normal plastic flow rule at the vertex of the yield surface; finite strain formulation based on a multiplicative split of the deformation gradient; fully implicit integration of the constitutive equations leading to a single scalar equation that admits a unique root; use of mixed finite elements to avoid volumetric locking; strain gradient-based nonlocal model to control strain localisation and remedy spurious mesh dependency. The capabilities of the resulting numerical formulation are demonstrated through simulating the cup–cone fracture of a notched tensile specimen.