A novel implicit cell-based material point method with particle boundaries and its application to contact problems

In this paper, an implicit cell-based material point method (MPM) with particle boundaries is proposed to effectively solve large deformation static problems. The volume integrals of the incremental weak form based on an updated Lagrangian approach are evaluated at integration points defined by equally sub-dividing grid cells, which eliminates the cell-crossing error and reduces the integration error in solving problems with particles not aligned with a background grid. A level set function based on the particle volume is used to define a particle boundary. The number of integration points of the boundary grid cells intersected by the particle boundary is increased to more accurately perform the numerical integration of the incremental weak form over the boundary grid cells. The present method is applied to solve contact problems of two bodies discretized by particles. Contact between particles is detected using the level set values ​​at the integration points of the boundary grid cells. The surface integral of the contact weak form is replaced by a volume integral in the contact penetration domain. Numerical results show that large deformation contact problems can be effectively solved by the implicit cell-based MPM with particle boundaries.