An efficient pseudo-inverse approach for damage modeling in the sheet forming process

A simplified method called the “inverse approach” (IA) has been developed for sheet forming modeling. The assumptions of proportional loading and simplified tool actions lead to an “one step” algorithm. This IA is less accurate but much faster than classical incremental approaches, so it is largely used in the preliminary design of sheet forming tools. Numerous benchmark tests have proved that the IA gives a fairly good strain estimation but a poor stress estimation. The pseudo-inverse approach (PIA) was developed recently by the authors’ group, taking into account the loading history: some realistic intermediate configurations are determined without contact treatment to consider the loading history due to bending; and a new algorithm of plastic integration is proposed to consider bending–unbending effects. These new aspects in the PIA lead to a large improvement of the stress evaluation, which makes possible damage modeling in the sheet forming process. In this study, a simplified model of ductile damage based on continuum damage mechanics is implanted into the PIA. For this first exploration, the authors limit themselves to a material with isotropic hardening and damage. A 3D damage model in deformation is adopted: the assumptions of proportional loading and damage saturation after the damage threshold lead to an integrated damage evaluation method. A more accurate damage rate model is also developed which allows a strong coupling between plasticity and damage. These models are implemented in two ways: the inverse calculation is either coupled or uncoupled with the damage effect. The numerical results obtained show the feasibility of damage consideration in the PIA and the influence of damage effects on the sheet formability.