Over the past two decades several attempts have been made to formulate constitutive models for slow granular flow to remedy the deficiencies of classical plasticity. All the proposed models assume the medium to be incompressible, though it is well known that density change accompanies deformation in granular materials. A particularly important aspect of density change that is distinctive of granular materials is dilatancy, or volume deformation caused by shear deformation. No constitutive model for sustained flow has thus far captured dilatancy. Here we present a non-local constitutive model wherein the deformation rate and density at a point depend on the state of stress in a mesoscopic region around it. Apart from incorporating dilatancy, our model has a physical origin that is distinct from that of the previously proposed non-local models. We test our model on simple shear flow in the absence and presence of gravity, and find its predictions to be in good agreement with particle dynamics simulations.

中文翻译：

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包含剪胀性的慢颗粒流非局部本构模型

在过去的 20 年里，已经进行了几次尝试来制定慢颗粒流的本构模型，以弥补经典可塑性的不足。所有提出的模型都假设介质是不可压缩的，尽管众所周知密度变化伴随着颗粒材料的变形。粒状材料所特有的密度变化的一个特别重要的方面是剪胀或由剪切变形引起的体积变形。迄今为止，还没有持续流动的本构模型能够捕捉到膨胀性。在这里，我们提出了一个非局部本构模型，其中某一点的变形率和密度取决于其周围细观区域中的应力状态。除了包含膨胀性之外，我们的模型还具有不同于先前提出的非局部模型的物理起源。