ILS-MPM: an implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles
ILS-MPM: an implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles
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DOI：
10.1016/j.cma.2020.113168
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
Chuanqi Liu;WaiChing Sun
中科院分区：
文献类型：
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作者：
Chuanqi Liu;WaiChing Sun
用保角网格对摩擦多体接触问题进行有限元模拟是一项具有挑战性和计算要求的工作。为了渲染几何特征，非结构化网格通常是通过试错法生成的。这种处理也不可避免地增加了自由度，并使从/主对的构造变得繁琐。在这项工作中，我们介绍了一种隐式物质点方法，通过使用水平集函数来表示结构网格上的边界，从而绕过了实体的网格划分。这种隐函数表示提供了一种优雅的方法，可以通过最近点投影将无偏中间参考曲面与真实边界联系起来，如Leichner等人所示。(2019年)。然后，我们通过惩罚方法加强接触约束，其中库仑摩擦定律被实施，使得返回映射算法可以用于提供粘滞状态和滑移状态的本构更新。为了适当地演化接触的几何形状，对Hamilton-Jacobi方程进行了增量求解，使得水平集和材质点都根据变形场进行了更新。为了提高物质点方法数值积分的精度和正则性，采用移动最小二乘法将物质点的数值投影回高斯-勒让德求积的标准位置。几个基准被用来验证所提出的模型。通过与离散元模拟的比较，分析了应力场在预测颗粒集合体宏观响应中的重要性。
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.