  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.
