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.

这项研究为材料点方法（MPM）提出了一种新的粒子-表面摩擦接触算法，以模拟材料点与刚体之间的相互作用。尽管基于网格的多速度场技术是一种适用于MPM的常用方法，但在开发此类模拟时仍存在一些缺点：（1）该技术需要进行额外的处理以防止早期接触并满足不可渗透性条件。（2）该方法在刚体的接触检测中表现不佳，这取决于其组成材料点的布置。为了克服这些问题，该算法使用了基于粒子与表面接触的惩罚方法。然而，由于粒子可能非常靠近表面，因此物理量可能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解决此问题，而不会在构造形状函数时丧失单元划分属性，因此在本研究中将其合并到MPM框架中。通过将数值模拟与解析解和有限元结果进行比较，对所提出的算法进行了验证。数值结果表明，该算法对摩擦接触现象产生了合理的结果。并因此纳入本研究的MPM框架。通过将数值模拟与解析解和有限元结果进行比较，对所提出的算法进行了验证。数值结果表明，该算法对摩擦接触现象产生了合理的结果。并因此纳入本研究的MPM框架。通过将数值模拟与解析解和有限元结果进行比较，对所提出的算法进行了验证。数值结果表明，该算法对摩擦接触现象产生了合理的结果。