标题： 求解碰撞问题的三维多网格材料点法 显示英文标题

标题： Three-dimensional multi-mesh material point method for solving collision problems

摘要： 不同物体间的接触算法在求解碰撞问题中起着重要作用，通常很难处理得非常好。Bardenhagen、Brackbill 和 Sulsky\cite{Bardenhagen2000,Bardenhagen2001}，以及 Hu 和 Chen\cite{Hu_Chen2003}提出了几种针对质点法的接触算法。本文提出了一种改进的三维质点法接触算法。该算法强调系统能量守恒，并准确恢复接触物体之间的反作用力。与 Bardenhagen 的方法相比，无论是法向还是切向接触力，都更适当地通过背景网格的接触节点施加到接触物体上；与 Hu 和 Chen 的方法相比，不仅切向速度，而且法向速度也在各自的独立网格中分别处理。这种处理方式确保了不仅能恢复接触/滑动/分离过程，还能恢复接触物体之间的摩擦力。通过滚动模拟、弹性球碰撞、Taylor 棒冲击和塑性球碰撞等数值实验验证了所提出的接触算法。数值结果显示，采用改进接触算法的多网格质点法更适合解决碰撞问题。 显示英文摘要

摘要： Contact algorithm between different bodies plays an important role in solving collision problems. Usually it is not easy to be treated very well. Several ones for material point method were proposed by Bardenhangen, Brackbill, and Sulsky\cite{Bardenhagen2000,Bardenhagen2001}, Hu and Chen\cite{Hu_Chen2003}. An improved one for three-dimensional material point method is presented in this paper. The improved algorithm emphasizes the energy conservation of the system and faithfully recovers opposite acting forces between contacting bodies. Contrasted to the one by Bardenhagen, both the normal and tangential contacting forces are more appropriately applied to the contacting bodies via the contacting nodes of the background mesh; Contrasted to the one by Hu and Chen, not only the tangential velocities but also the normal ones are handled separately in respective individual mesh. This treatment ensures not only the contact/sliding/separation procedure but also the friction between contacting bodies are recovered. The presented contact algorithm is validated via numerical experiments including rolling simulation, impact of elastic spheres, impact of a Taylor bar and impact of plastic spheres. The numerical results show that the multi-mesh material point method with the improved contact algorithm is more suitable for solving collision problems.