Numerical analysis of accuracy for evolutionary anisotropic plasticity models

In the present paper, elasto-plastic constitutive formulations based on the orthotropic four parametric quadratic Hill (1948) or non-quadratic Karafillis-Boyce (1993) stress function and distortional evolution of the yield function/plastic potential are presented. The anisotropy parameters of the analyzed yield functions/plastic potentials are introduced as functions of the equivalent plastic strain. The formulations are developed and analyzed considering experimental data for the selected steel sheet sample with reported significant variation of the instantaneous Lankford parameter with straining. Predictions of the directional dependences and variations with straining of the yield stress ratios and Lankford parameters obtained by the presented descriptions are considered. The algorithmic formulations of the analyzed constitutive descriptions are derived by application of the implicit return mapping algorithm. In order to estimate accuracy of the developed algorithms, iso-error maps are calculated and analyzed