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.

本文介绍了 BFEMP，这是一种通过势垒将材料点法 (MPM) 与有限元法 (FEM) 整体耦合的新方法使用变分时间步长公式的基于能量的粒子-网格摩擦接触。耦合系统的全隐式时间积分被重新转换为障碍增强无约束非线性优化问题。采用改进的线搜索牛顿法，严格防止材料点穿透有限元域，无论时间步长或网格分辨率如何，都确保收敛性和可行性。当 FEM 域中的所有节点位移都用 Dirichlet 边界条件规定时，所提出的耦合方案也简化为一种为 MPM 施加可分离摩擦运动边界的新方法。与标准的隐式时间积分相比，与接触处理相关的额外算法组件仅依赖于简单的点段（或 3D 中的点三角形）几何查询，这些几何查询可以稳健地处理用 codimension-1 单纯形表示的任意 FEM 网格边界。进行实验和分析以证明所提出方法的鲁棒性和准确性。