Numerical aspects of finite elastoplasticity with isotropic ductile damage for metal forming

Abstract

This work is devoted to the study of an efficient numerical algorithm for evaluating damaged-plastic response of a material submitted to large plastic deformations. Fully coupled constitutive equations accounting for both combined isotropic and kinematic hardening as well as the ductile damage are formulated in the framework of Continuum Damage Mechanics (CDM). The associated numerical aspects concerning both the local integration of the coupled constitutive equations and the (global) equilibrium integration schemes are presented and implemented into a general purpose Finite Element code (ABAQUS). For the local integration of the fully coupled constitutive equations an efficient implicit and asymptotic scheme is used. Special care is given to the consistent tangent stiffness matrix derivation as well as to the reduction of the number of constitutive equations. Some numerical results are presented to show the numerical performance of the proposed stress calculation algorithm and the capability of the approach to predict the damage initiation and growth during a given metal forming process.