Alexey Stomakhin, Russell Howes, Craig Schroeder, Joseph Teran
We provide a smooth extension of arbitrary isotropic hyperelastic energy density functions to inverted confi gurations. This extension is designed to improve robustness for elasticity simulations with extremely large deformations and is analogous to the extension given to the first Piola-Kircho ff stress in [ITF04]. We show that our energy-based approach is signi ficantly more robust to large deformations than the first Piola-Kircho ff . Furthermore, we show that the robustness and stability of a hyper-elastic model can be predicted from a characteristic contour, which we call its primary contour. The extension to inverted con figurations is de fined via extrapolation from a convex threshold surface that lies in the uninverted portion of the principal stretches space. The extended hyperelastic energy density yields continuous stress and unambiguous stress derivatives in all inverted con figurations, unlike in [TSIF05]. We show that our invertible energy-density-based approach outperforms the popular hyperelastic corotated model, and we also show how to use the primary contour methodology to improve the robustness of this model to large deformations.