A return mapping algorithm for elastoplastic and ductile damage constitutive equations using the subloading surface method

In this paper is presented a return mapping algorithm for an elastoplastic/damage model that couples the constitutive equations of an unconventional plasticity model with the phenomenological description of ductile damage in the continuum damage mechanics framework. This approach combines the advantages of describing the mechanical property degradation by using the Lemaitre model with the realistic accumulation of plastic deformation in cyclic mobility problems from the subloading surface model. Most of the damage models for ductile failure focus on monotonic loading conditions, whereas the present model aims to extend the investigation to cyclic loading and low‐cycle fatigue problems. A cutting‐plane algorithm is adopted to describe the material behavior that considers both isotropic and kinematic hardening laws. Two simple numerical studies show that the elastoplastic and damage model is implemented correctly, displaying a quadratic rate of convergence for local equilibria and precise solutions, even for large‐prescribed strain increments.