Locking-free Simulation of Isometric Thin Plates

TL;DR

This paper introduces a meshless isometry constraint method for simulating very thin, inextensible materials like cloth or paper, avoiding membrane locking and enabling efficient, accurate dynamics simulation.

Contribution

It presents a novel meshless isometry constraint formulation based on moving-least-squares averaging, which prevents locking and integrates easily into existing dynamics frameworks.

Findings

The proposed constraints effectively prevent membrane locking.

The method can be integrated into standard Lagrangian dynamics.

Simulations demonstrate improved accuracy for thin, inextensible materials.

Abstract

To efficiently simulate very thin, inextensible materials like cloth or paper, it is tempting to replace force-based thin-plate dynamics with hard isometry constraints. Unfortunately, naive formulations of the constraints induce membrane locking---artificial stiffening of bending modes due to the inability of discrete kinematics to reproduce exact isometries. We propose a simple set of meshless isometry constraints, based on moving-least-squares averaging of the strain tensor, which do not lock, and which can be easily incorporated into standard constrained Lagrangian dynamics integration.