Modeling of roll forming process of sheet metal requires efficient treatment of plastic deformations of thin shells and plates. We suggest a new general approach toward constructing the governing equations of bending of an elastic-plastic Kirchhoff plate on the structural mechanics level. The generic function of the isotropic hardening law is formulated in terms of variables, which are meaningful for a material surface, namely resultant bending moments and dissipative work. This function is then identified by comparison of the exact solutions for a uni-axial or isotropic bending experiment within the structural model and with the continuum model of a through-the-thickness element. We validate the approach against both the fully three-dimensional simulations as well as the results of the traditional elastic-plastic plate analysis, the latter one featuring the continuum laws of plasticity treated in the integration points along the thickness direction. We considered benchmark problems from the literature as well as a prototype for the roll forming problem. Besides good agreement regarding the shape of plastic zones and force-deflection characteristics, experiments also demonstrate higher computational efficiency of the new stress resultant model.

中文翻译：

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板料滚压成形过程中板材弯曲的应力合成塑性

钣金滚压成形过程的建模需要有效处理薄壳和薄板的塑性变形。我们提出了一种在结构力学水平上构建弹塑性基尔霍夫板弯曲控制方程的新通用方法。各向同性硬化定律的通用函数是根据对材料表面有意义的变量来表述的，即合成弯矩和耗散功。然后通过比较结构模型内单轴或各向同性弯曲实验的精确解以及与全厚度单元的连续模型的精确解来确定该函数。我们针对全三维模拟以及传统弹塑性板分析的结果验证了该方法，后一个特征是在沿厚度方向的积分点中处理的塑性连续规律。我们考虑了文献中的基准问题以及滚压成型问题的原型。除了关于塑性区的形状和力-挠度特性的良好一致性外，实验还证明了新的应力合成模型具有更高的计算效率。