Stabler Neo-Hookean Simulation: Absolute Eigenvalue Filtering for Projected Newton

TL;DR

This paper introduces a new eigenvalue filtering technique for projected Newton's method to improve the stability and convergence of volume-preserving hyperelastic material simulations, especially near incompressibility.

Contribution

A novel eigenvalue filtering strategy is proposed to enhance the stability and efficiency of Newton's method for simulating near-incompressible hyperelastic materials.

Findings

Significant improvement in stability and convergence speed.

Effective on challenging examples with high Poisson's ratio.

Requires minimal code modification.

Abstract

Volume-preserving hyperelastic materials are widely used to model near-incompressible materials such as rubber and soft tissues. However, the numerical simulation of volume-preserving hyperelastic materials is notoriously challenging within this regime due to the non-convexity of the energy function. In this work, we identify the pitfalls of the popular eigenvalue clamping strategy for projecting Hessian matrices to positive semi-definiteness during Newton's method. We introduce a novel eigenvalue filtering strategy for projected Newton's method to stabilize the optimization of Neo-Hookean energy and other volume-preserving variants under high Poisson's ratio (near 0.5) and large initial volume change. Our method only requires a single line of code change in the existing projected Newton framework, while achieving significant improvement in both stability and convergence speed. We demonstrate the effectiveness and efficiency of our eigenvalue projection scheme on a variety of challenging examples and over different deformations on a large dataset.