Evaluation of constitutive models for voided solids

In this work four constitutive models for voided solids are reviewed and evaluated; namely, Gurson's, Green's, Liao's et al. and Shima-Oyane's models. Two modified forms of Gurson's model and a non-quadratic form of Green's model are developed for normal anisotropy prevailing in the analysis of sheet metal forming. A simplified version — more amenable to analytical derivations — of Gurson's yield function and its modified forms are proposed for plane stress conditions. The associated flow rules are presented and the laws governing void growth with accumulated strain are derived using the above models. Their predictions are compared with experiments. As an application, the flow curves of voided materials of known initial porosities are predicted and compared with experiments.