The mechanical response of granular materials, exemplified by frictional grain interactions, is characterized by a critical state in which deformation occurs without change of material volume or stresses when subjected to large shear deformation. In this work, a granular micromechanics approach (GMA) based continuum model is used to investigate the emergence of such a critical state. The continuum description is constructed through mechanical concepts based upon elastic and dissipation energies defined for a generic grain‐pair interaction. A hemivariational principle provides the basis for considering the evolution of damage and plasticity phenomena comprising grain‐pair contact loss and irreversible deformation. As a consequence, the Karush–Kuhn–Tucker (KKT)‐type conditions are derived, which give the evolution equations for the irreversible phenomena. Notably, in this derivation there is no invocation of flow rules and other similar assumptions of classical phenomenological continuum damage and plasticity. Further, Piola's ansatz is elaborated to kinematically connect granular micromechanics of grain‐pair to the continuum description. While the concept of critical state analysis has been handled with either phenomenological approaches or discrete numerical frameworks, in the present paper this concept is examined within a micromechanics‐based continuum description. The constitutive model is established and the coupled damage and plastic irreversible quantities are assessed. The critical state is shown to emerge as grain‐pair related damage and plastic evolution in a competitive/collaborative manner during the imposed loading path.

中文翻译：

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使用基于变分的损伤弹塑性微机械连续体模型出现颗粒材料的临界状态


颗粒材料的机械响应（以摩擦颗粒相互作用为例）的特征是临界状态，在该状态下，当受到大的剪切变形时，材料体积或应力不会发生变化。在这项工作中，使用基于颗粒微力学方法（GMA）的连续体模型来研究这种临界状态的出现。连续统描述是通过基于为一般颗粒对相互作用定义的弹性能和耗散能的力学概念构建的。半变分原理为考虑损伤和塑性现象（包括晶粒对接触损失和不可逆变形）的演变提供了基础。因此，推导了卡鲁什-库恩-塔克（KKT）型条件，给出了不可逆现象的演化方程。值得注意的是，在这个推导中没有调用流动规则和经典现象学连续体损伤和可塑性的其他类似假设。此外，皮奥拉的 ansatz 被精心设计，以在运动学上将颗粒对的颗粒微观力学与连续统描述联系起来。虽然临界状态分析的概念已经通过现象学方法或离散数值框架来处理，但在本文中，这个概念是在基于微观力学的连续体描述中进行研究的。建立本构模型并评估耦合损伤和塑性不可逆量。临界状态显示为在施加的载荷路径期间以竞争/协作的方式出现与晶粒对相关的损伤和塑性演化。