Algorithmic Formulations of Evolutionary Anisotropic Plasticity Models Based on Non-Associated Flow Rule

In the present paper, orthotropic elasto-plastic constitutive formulations for sheet metal forming based on non-associated flow rule that assume distortion of yield function/plastic potential with ongoing deformation process are analyzed. The yield function/plastic potential are considered as two different functions with functional form as orthotropic quadratic Hill or non-quadratic Karafillis-Boyce stress function. Based on the principle of plastic work equivalence, anisotropy parameters of the utilized yield function/plastic potential are set as functions of the equivalent plastic strain. In the constitutive formulation, for this internal variable, evolution equation consistent with the same principle of plastic work equivalence is introduced. For DC06 sheet sample with reported significant variation of the incremental r-values with straining, predictions of the evolution of the yield stress and r-value directional dependences with straining obtained by the analyzed models are presented. The algorithmic formulations of the analyzed constitutive models are derived by application of the implicit return mapping algorithm. For the derived stress integration procedures the accuracy is investigated by calculating iso-error maps. The maps are compared according to the flow rule and involved orthotropic stress functions. It has been revealed that although there is a difference in maps configuration there is no prominent difference in error magnitudes.