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.

中文翻译：

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由屈服面畸变建模的包辛格效应

摘要 提出了一种通过在加载方向的相反方向展平零件来扭曲屈服面的模型。作为畸变的基础，该模型应用了一对与运动硬化模型中类型相似的二阶背应力张量。屈服面公式提供给定的一阶均匀屈服面在背应力张量的相反方向上的平整和收缩。数学公式基于与 HAH（基于均匀屈服函数的各向异性硬化）模型类似的思想，其中等效应力-应变曲线的校准与模型的 Bauschinger 部分无关。指出了 HAH 模型的严重数学和数值挑战，但在新模型中避免了。此外，屈服面不