  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.
