Abstract Finite element simulations of frictional multi-body contact problems via conformal meshes can be challenging and computationally demanding. To render geometrical features, unstructured meshes are often generated via a trial-and-error procedure. This treatment also unavoidably increases the degrees of freedom and makes the construction of slave/master pairs cumbersome. In this work, we introduce an implicit material point method designed to bypass meshing of bodies by employing level set functions to represent boundaries at structured grids. This implicit function representation provides an elegant mean to link an unbiased intermediate reference surface with the true boundaries by closest point projection as shown in Leichner et al. (2019). We then enforce the contact constraints by a penalty method where the Coulomb friction law is implemented such that a return mapping algorithm can be used to provide constitutive updates for both the stick and slip states. To evolve the geometry of the contacts properly, the Hamilton–Jacobi equation is solved incrementally such that the level set and material points are both updated according to the deformation field. To improve the accuracy and regularity of the numerical integration of the material point method, a moving least square method is used to project numerical values of the material points back to the standard locations for Gaussian-Legendre quadrature. Several benchmarks are used to verify the proposed model. Comparisons with discrete element simulations are made to analyze the importance of stress fields on predicting the macroscopic responses of granular assemblies.

中文翻译：

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ILS-MPM：一种用于可变形颗粒摩擦颗粒接触力学的基于隐式水平集的材料点方法

摘要 通过共形网格对摩擦多体接触问题进行有限元模拟具有挑战性且计算量大。为了渲染几何特征，通常通过试错程序生成非结构化网格。这种处理也不可避免地增加了自由度，并使从/主对的构建变得繁琐。在这项工作中，我们引入了一种隐式材料点方法，旨在通过使用水平集函数来表示结构化网格的边界来绕过物体的网格划分。这种隐式函数表示提供了一种优雅的方法，通过最近点投影将无偏中间参考表面与真实边界联系起来，如 Leichner 等人所示。(2019)。然后我们通过惩罚方法强制接触约束，其中实施库仑摩擦定律，以便返回映射算法可用于为粘滞和滑动状态提供本构更新。为了适当地演化接触的几何形状，Hamilton-Jacobi 方程被增量求解，使得水平集和材料点都根据变形场进行更新。为提高质点法数值积分的准确性和规律性，采用移动最小二乘法将质点数值投影回高斯-勒让德求积的标准位置。几个基准用于验证所提出的模型。