Abstract The coefficients of yield functions have been conventionally determined based on limited number of experiments such as yield stresses and/or R-values along different material orientations. In the present study, a multi objective genetic algorithm (MultiGA) based approach was implemented to obtain coefficients of anisotropic yield functions by simultaneous error minimization for yield stresses and R-values. Three frequently employed yield functions, Hill 1948, Barlat 1989 and Barlat Yld2000-2d, in the sheet metal forming simulations were considered. The performance of the determined coefficients for each yield function was judged by comparing the predicted yield stress and R-values with experimental values. Fundamental questions regarding the effect of experimental data on determining the coefficients were analyzed using the proposed approach. It is generally perceived that increase in experimental data enhances the accuracy of the determination of coefficients. Some counter intuitive results obtained on this regard are discussed. Finally, finite element (FE) simulations were performed to predict earing profile in deep drawn cups and springback profile for split-ring test, which were validated with experimental results. From the comparative study with conventional method and experiment, the yield function coefficients optimized by the MultiGA performed well for predicting the deformation behaviors of various anisotropic sheet metals.

中文翻译：

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各向异性屈服函数系数的稳健多目标优化

摘要 屈服函数的系数通常是基于有限数量的实验确定的，例如沿不同材料方向的屈服应力和/或 R 值。在本研究中，实施了一种基于多目标遗传算法 (MultiGA) 的方法，通过同时最小化屈服应力和 R 值的误差来获得各向异性屈服函数的系数。三个常用的屈服函数，Hill 1948、Barlat 1989 和 Barlat Yld2000-2d，在钣金成形模拟中被考虑在内。通过将预测的屈服应力和 R 值与实验值进行比较来判断每个屈服函数的确定系数的性能。使用所提出的方法分析了关于实验数据对确定系数的影响的基本问题。一般认为，实验数据的增加提高了系数确定的准确性。讨论了在这方面获得的一些反直觉结果。最后，进行有限元 (FE) 模拟以预测深冲杯中的耳廓轮廓和裂环测试的回弹轮廓，并通过实验结果进行验证。通过与传统方法和实验的对比研究，MultiGA优化的屈服函数系数在预测各种各向异性金属板材的变形行为方面表现良好。一般认为，实验数据的增加提高了系数确定的准确性。讨论了在这方面获得的一些反直觉结果。最后，进行有限元 (FE) 模拟以预测深冲杯中的耳廓轮廓和裂环测试的回弹轮廓，并通过实验结果进行验证。通过与传统方法和实验的对比研究，MultiGA优化的屈服函数系数在预测各种各向异性金属板材的变形行为方面表现良好。一般认为，实验数据的增加提高了系数确定的准确性。讨论了在这方面获得的一些反直觉结果。最后，进行有限元 (FE) 模拟以预测深冲杯中的耳廓轮廓和裂环测试的回弹轮廓，并通过实验结果进行验证。通过与传统方法和实验的对比研究，MultiGA优化的屈服函数系数在预测各种各向异性金属板材的变形行为方面表现良好。用实验结果验证。通过与传统方法和实验的对比研究，MultiGA优化的屈服函数系数在预测各种各向异性金属板材的变形行为方面表现良好。用实验结果验证。通过与传统方法和实验的对比研究，MultiGA优化的屈服函数系数在预测各种各向异性金属板材的变形行为方面表现良好。