Particle-to-surface frictional contact algorithm for material point method using weighted least squares

Abstract 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.