Bauschinger effect modelled by yield surface distortions

Abstract

A model for distorting the yield surface by flattening the part in the reverse of the loading direction, is suggested. As the basis for the distortion, the model applies a pair of second-order back-stress tensors of similar type as in kinematic hardening models. The yield-surface formulation provides a flattening and shrinkage of a given first-order homogeneous yield surface in the reverse directions of the back-stress tensors. The mathematical formulation is based on similar ideas as the HAH (homogeneous yield function-based anisotropic hardening) model, for which the calibration of the equivalent stress-strain curve is independent of the Bauschinger part of the model. Severe mathematical and numerical challenges of the HAH model are pointed out, but are avoided in the new model. Furthermore, the yield surface doesn't have to contain the origin, and the r-value is conserved in stress reversals.