This paper introduces BFEMP, a new approach for strongly 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.

翻译：本文引入了BFEMP, 这是一种将材料点方法(MPM)与有限元素法(FEM)紧密结合的新方法,即通过使用变式时间步骤配方,通过基于屏障能源的粒子-灰质摩擦接触,将材料点法(MPM)与有限元素法(FEM)紧密结合的新方法。完全隐含的时间整合被重塑为屏障加固的无限制非线优化问题。采用了经修改的线搜索牛顿方法,严格防止材料点穿透FEM域,确保汇合和可行性,而不论时间步数大小或网状分辨率。在FEMM域的所有节点移位都与Drichlet边界条件挂钩时,拟议的组合方案还减少为MMMM规定可分离的摩擦运动界限。与标准隐含时间整合相比,与接触处理相关的额外算法部分只取决于简单的点划分(或3D中的点三角点三角点三角)的几何测量,以稳健的方式处理与共解-1断断断点之间的任意FEMshmsh 边界。进行了实验和分析,以证明拟议方法的稳健和精确性。