A momentum preserving frictional contact algorithm based on affine particle-in-cell grid transfers

TL;DR

This paper introduces a momentum conserving contact algorithm using affine particle-in-cell grid transfers that effectively enforces contact with zero gap and handles friction and separation in solid body simulations.

Contribution

It presents a novel momentum conserving contact algorithm based on APIC, addressing gaps and sticking issues in particle-in-cell methods.

Findings

Ensures conservation of linear and angular momentum during contact.

Achieves contact enforcement at nearly zero gap.

Enables natural separation and friction enforcement between particles.

Abstract

An efficient and momentum conserving algorithm for enforcing contact between solid bodies is proposed. Previous advances in the material point method (MPM) led to a fast and simple, but potentially momentum violating, strategy for enforcing contact. This was achieved through a combination of velocity transfers between background and foreground grids, and a background grid velocity field update. We propose a modified strategy which ensures conservation of both linear and angular momentum with a novel use of the affine particle-in-cell (APIC) method. Two issues common to particle-in-cell based algorithms for contact are also addressed: material bodies tend to stick at a gap which is proportional to the grid spacing; and material points tend to stick together permanently when located within the same grid cell, making material rebound and friction challenging. We show that the use of APIC, combined with a grid transfer and momentum update algorithm results in contact being enforced at essentially zero gap. For the second issue, we propose a novel iterative scheme which allows particles interacting through the background grid to naturally separate after contact and enforce friction, while still satisfying momentum conservation.