BFEMP：无互穿MPM-FEM耦合与屏障接触
BFEMP: Interpenetration-Free MPM-FEM Coupling with Barrier Contact
摘要：
本文介绍了BFEMP，一种新的方法，整体耦合的材料点法（MPM）与有限元法（FEM）通过障碍能量为基础的颗粒-网格摩擦接触，使用变分时步公式。耦合系统的全隐式时间积分被转化为一个障碍增广的无约束非线性最优化问题。采用改进的线搜索牛顿法，严格防止材料点穿透有限元域，确保收敛性和可行性，无论时间步长或网格分辨率。所提出的耦合方案也减少到一个新的方法施加可分离的摩擦运动边界的MPM时，所有的节点位移在有限元域中规定的Dirichlet边界条件。与标准隐式时间积分相比，与接触处理相关联的额外算法组件仅依赖于单点段（或3D中的点三角形）几何查询，其稳健地处理用余维1单纯形表示的任意FEM网格边界。实验和分析表明，所提出的方法的鲁棒性和准确性。
英文摘要：
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.
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