Energetically consistent invertible elasticity

  • Authors:

  • Alexey Stomakhin;Russell Howes;Craig Schroeder;Joseph M. Teran

  • Affiliations:

  • Department of Mathematics, University of California, Los Angeles;Department of Mathematics, University of California, Los Angeles;Department of Mathematics, University of California, Los Angeles;Department of Mathematics, University of California, Los Angeles

  • Venue:
  • EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
  • Year:
  • 2012

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Abstract

We provide a smooth extension of arbitrary isotropic hyperelastic energy density functions to inverted configurations. This extension is designed to improve robustness for elasticity simulations with ex- tremely large deformations and is analogous to the extension given to the first Piola-Kirchoff stress in [ITF04]. We show that our energy-based approach is significantly more robust to large deformations than the first Piola-Kirchoff fix. 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 configurations is defined via extrapolation from a convex threshold surface that lies in the uninverted portion of the principal stretches space. The extended hyperelastic energy den- sity yields continuous stress and unambiguous stress derivatives in all inverted configurations, unlike in [TSIF05]. We show that our invertible energy-density-based approach outperforms the popular hy- perelastic corotated model, and we also show how to use the primary contour methodology to improve the robustness of this model to large deformations.