In many geomechanics applications, material boundaries are subjected to large displacements and deformation. Under these circumstances, the application of boundary conditions using particle methods, such as the material point method (MPM), becomes a challenging task since material boundaries do not coincide with the background mesh. This paper presents a formulation of penalty augmentation to impose nonhomogeneous, nonconforming Dirichlet boundary conditions in implicit MPM. The penalty augmentation is implemented utilizing boundary particles, which can move either according to or independently from the material deformation. Furthermore, releasing contact boundary condition, as well as the capability to accommodate slip boundaries, is introduced in the current work. The accuracy of the proposed method is assessed in both 2D and 3D cases, by convergence analysis reaching the analytical solution and by comparing the results of nonconforming and classical grid-conforming simulations.

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.

Mass-movement hazards involving fast and large soil deformation often include huge rocks or other significant obstacles increasing tremendously the risks for humans and infrastructures. Therefore, numerical investigations of such disasters are in high economic demand for prediction as well as for the design of countermeasures. Unfortunately, classical numerical approaches are not suitable for such challenging multiphysics problems. For this reason, in this work we explore the combination of the Material Point Method, able to simulate elasto-plastic continuum materials and the Discrete Element Method to accurately calculate the contact forces, in a coupled formulation. We propose a partitioned MPM-DEM coupling scheme, thus the solvers involved are treated as black-box solvers, whereas the communication of the involved sub-systems is shifted to the shared interface. This approach allows to freely choose the best suited solver for each model and to combine the advantages of both physics in a generalized manner. The examples validate the novel coupling scheme and show its applicability for the simulation of large strain flow events interacting with obstacles.