SM_MATLAB_codes.zip from Viscoplastic plates

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams.本研究构建渐近模型，以刻画遵循赫谢尔-布尔利本构定律（Herschel–Bulkley constitutive law）的粘塑性流体薄板或平板的弯曲行为；该本构定律整合了冯·米塞斯屈服条件（von Mises yield condition）与非线性粘性应力。该模型在多种极限工况下，可退化为塑性理论与粘性流体力学领域的诸多已有模型。其核心特征为伊柳申提出的屈服准则，该准则通过三类特定不变量，将弯矩与面内应力张量的效应进行了紧凑结合。本模型被用于探究受载平板的弯曲行为、脉冲驱动圆形平板的挠度特性，以及受载梁的张力控制挠度。