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

TL;DR

This paper introduces an improved three-dimensional multi-mesh material point method with a new contact algorithm that enhances energy conservation, accurately models contact forces, and effectively handles collision, sliding, and friction in various impact simulations.

Contribution

The paper presents a novel 3D multi-mesh material point method with an improved contact algorithm that better conserves energy and models contact forces compared to previous methods.

Findings

Enhanced energy conservation in collision simulations.

More accurate modeling of normal and tangential contact forces.

Validated effectiveness through diverse numerical impact experiments.

Abstract

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.