BFEMP: Interpenetration-Free MPM-FEM Coupling with Barrier Contact

TL;DR

This paper presents BFEMP, a novel, robust coupling method for MPM and FEM that prevents interpenetration using barrier energy and a specialized Newton's method, ensuring stability and accuracy in simulations.

Contribution

The paper introduces a barrier energy-based coupling scheme for MPM-FEM that guarantees no interpenetration and handles complex contact scenarios with a modified Newton's method.

Findings

Ensures strict non-penetration in MPM-FEM coupling.

Robustness across various mesh resolutions and time steps.

Accurate simulation results demonstrated through experiments.

Abstract

This paper introduces BFEMP, a new approach for monolithically coupling the Material Point Method (MPM) with the Finite Element Method (FEM) through barrier energy-based particle-mesh frictional contact using a variational time-stepping formulation. The fully implicit time integration of the coupled system is recast into a barrier-augmented unconstrained nonlinear optimization problem. A modified line-search Newton's method is adopted to strictly prevent material points from penetrating the FEM domain, ensuring convergence and feasibility regardless of the time step size or the mesh resolutions. The proposed coupling scheme also reduces to a new approach for imposing separable frictional kinematic boundaries for MPM when all nodal displacements in the FEM domain are prescribed with Dirichlet boundary conditions. Compared to standard implicit time integration, the extra algorithmic components associated with the contact treatment only depend on simple point-segment (or point-triangle in 3D) geometric queries which robustly handle arbitrary FEM mesh boundaries represented with codimension-1 simplices. Experiments and analyses are performed to demonstrate the robustness and accuracy of the proposed method.