A damage coupled orthotropic finite plasticity model for sheet metal forming: CDM approach

A framework for orthotropic finite plasticity coupled with a Lemaitre type isotropic ductile damage is presented in a thermodynamically sound setting for sheet metal forming. The finite plasticity utilizes Green-Naghdi type additive decomposition in the logarithmic Lagrangean strain space, which allows adaptation of the return mapping schemes of damage coupled infinitesimal plasticity. Hydrostatic stress state and principal stress state dependent unilateral damage evolutionary conditions are efficiently formulated without need for repetitive tensor transformations, taking advantage of the eigenvalue equivalence in between the stress measure conjugate to the logarithmic Lagrangean strain and the Kirchhoff stress. For the sake of completeness a Perzyna type viscous regularization is also elaborated. A three-step, staggered local integration algorithm, composed of elastic prediction, plastic correction and damage deterioration, is performed for return mapping at integration points. To this end, the framework is implemented as a VUMAT subroutine for ABAQUS/Explicit and used in a set of simulations. Besides proving the applicability range of the methodology, the outcomes show that Lemaitre model, once enhanced with unilateral damage evolutionary conditions, gives physically meaningful results in cup drawing simulations.