For modern engineering applications, the prediction of residual stresses is a starting-point for the subsequent optimisation of the design with regard to the process induced stresses on the macro and the grain scale. In this paper, a new approach for the numerically efficient prediction of phase-specific residual stresses (residual stresses of second kind) in two-phase materials is presented. The proposed model allows for a two-scale simulation of complex forming processes, solely based on the phase-specific constitutive equations. This enables the calculation of the average stresses and strains in each phase during the entire process and the prediction of the macroscopic material response. The numerical results are compared to experimental diffraction-based data of a bending bar and a deep drawn cup and are aligned better compared to existing models.

对于现代工程应用，残余应力的预测是随后针对宏观和晶粒尺度上的过程诱导应力进行设计优化的起点。本文提出了一种新的方法，用于数值有效地预测两相材料中的相比残余应力（第二种残余应力）。提出的模型仅基于特定于相位的本构方程就可以对复杂的成形过程进行两尺度模拟。这样就可以计算整个过程中每个阶段的平均应力和应变，并可以预测宏观材料的响应。