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.

翻译：体积保持超弹性材料被广泛用于模拟近似不可压缩材料，如橡胶和软组织。然而，由于能量函数的非凸性，在此体系下对体积保持超弹性材料进行数值模拟是众所周知的挑战。在这项工作中，我们指出了牛顿法期间用于将Hessian矩阵投影至半正定的流行特征值截断策略的缺陷。我们为投影牛顿法引入了一种新颖的特征值滤波策略，以在高泊松比（接近0.5）和大初始体积变化下稳定Neo-Hookean能量及其他体积保持变体的优化。我们的方法仅需在现有投影牛顿框架中更改一行代码，即可在稳定性和收敛速度上实现显著提升。我们在多种具有挑战性的示例以及大型数据集上的不同变形上，证明了我们特征值投影方案的有效性和效率。