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.
翻译:本文介绍BFEMP, 一种将材料点方法(MPM)与有限元素法(FEM)统一结合的新方法,即使用变式时间步骤配方,通过屏蔽能源基粒子-灰质摩擦接触,将材料点法(MPM)与有限元素法(FEM)统一结合的新方法。完全隐含的时间结合系统被重新粉饰成一个屏障强化的不受限制的非线性优化问题。对牛顿的线搜索方法进行了修改,以严格防止材料点穿透FEM域,确保汇合和可行性,而不管时间步骤大小或网格分辨率如何。拟议的混合方案还减少为在FEM域的所有节点偏移都与Drichlet边界条件挂钩时,为MMMM规定了可分离的摩擦运动界限。与标准隐含时间结合的整合相比,与接触处理相关的额外算构件只取决于简单的点划分(或3D中的点三角点三角)几何测测,以稳健健健地处理带有 Codimension-1 Simplicless。进行实验和分析,以显示拟议方法的精确性和精确性。