A Staggered Coupling Scheme of the Material Point Method and the Finite Element Method using Gauss Seidel Communication Pattern

Abstract

The goal of the present work is the simulation mass movement hazards, involving fast and large soil deformation, interacting with flexible protection structures. For the simulation of those large deformation phenomena, involving complex history dependent material laws, the Material Point Method (MPM) is a powerful method, as the particles move trough a fixed background mesh. This allows to overcome the classical limitation of the Finite Element Method (FEM) related to mesh distortion in large strain problems. Therefore, a staggered or partitioned coupling scheme is proposed, combining the advantages of FEM and MPM by solving both models separately using their respective established environment, whereas the communication between the two fields is achieved by mapping boundary conditions on the shared interface. In this work a Gauss-Seidel communication pattern is considered, leading to the necessity of imposing Dirichlet Boundary Conditions on one interface (in this study: FEM) and Neumann Boundary Conditions on the corresponding counterpart (in this study: MPM). For validation purposes, a structural example with analytical solution is chosen.

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