BFEMP: Interpenetration-free MPM–FEM coupling with barrier contact

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