Particle-to-surface frictional contact algorithm for material point method using weighted least squares
Particle-to-surface frictional contact algorithm for material point method using weighted least squares
复制标题
DOI：
10.1016/j.compgeo.2021.104069
复制
发表时间：
2021-06
影响因子：
5.3
通讯作者：
Keita Nakamura;S. Matsumura;T. Mizutani
中科院分区：
文献类型：
--
作者：
Keita Nakamura;S. Matsumura;T. Mizutani
提出了一种新的质点-面摩擦接触算法，用于模拟质点与刚体的相互作用。虽然基于网格的多速度场技术是MPM的常用方法，但在开发此类模拟时存在以下几个缺点：（1）该技术需要额外的处理以防止早期接触并满足不可穿透条件。(2)该方法在刚体的接触检测中表现不佳，因为它依赖于其组成材料点的布置。为了克服这些问题，该算法使用基于粒子与表面接触的惩罚方法。然而，由于粒子可能非常接近表面，因此物理量可能会从粒子转移到位于刚体内的网格节点。加权最小二乘近似可以有效地处理这个问题，而不丧失分割的单位属性，而构造的形状函数，因此被纳入MPM框架在这项研究中。通过数值模拟与解析解和有限元结果的比较，验证了该算法的有效性。数值结果表明，该算法对摩擦接触现象产生了合理的结果。
This study presents a new particle-to-surface frictional contact algorithm for the material point method (MPM) to simulate the interaction between material points and rigid bodies. Although a grid-based multivelocity field technique is a common method that works well with MPM, there are several disadvantages in developing such simulations: (1) The technique needs additional treatment to prevent early contact and satisfy the impenetrability condition. (2) The method performs poorly in the contact detection of rigid bodies, as it depends on the arrangement of their constituent material points. To overcome these problems, the proposed algorithm uses the penalty method based on particle-to-surface contact. However, the possibility of physical quantities being transferred from the particles to grid nodes located within the rigid bodies arises since a particle can be very close to the surface. The weighted least squares approximation could effectively handle this problem, without forfeiting the partition-of-unity property while constructing the shape function, and is thus incorporated into the MPM framework in this study. The proposed algorithm is validated by comparing numerical simulations with analytical solutions and FEM results. The numerical results show that the proposed algorithm produces reasonable results for frictional contact phenomena.