Triangular springs for modeling nonlinear membranes

IEEE Transactions on Visualization and Computer Graphics
Hervé Delingette

Abstract

This paper provides a formal connexion between springs and continuum mechanics in the context of one-dimensional and two-dimensional elasticity. In a first stage, the equivalence between tensile springs and the finite element discretization of stretching energy on planar curves is established. Furthermore, when considering a quadratic strain function of stretch, we introduce a new type of springs called tensile biquadratic springs. In a second stage, we extend this equivalence to non-linear membranes (St Venant-Kirchhoff materials) on triangular meshes leading to triangular biquadratic and quadratic springs. Those tensile and angular springs produce isotropic deformations parameterized by Young modulus and Poisson ratios on unstructured meshes in an efficient and simple way. For a specific choice of the Poisson ratio, 0.3, we show that regular spring-mass models may be used realistically to simulate a membrane behavior. Finally, the different spring formulations are tested in pure traction and cloth simulation experiments.

References

May 5, 2005·IEEE Transactions on Visualization and Computer Graphics·Joseph TeranRonald Fedkiw
Mar 3, 2006·IEEE Transactions on Visualization and Computer Graphics·Pascal Volino, Nadia Magnenat-Thalmann

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Citations

Jan 15, 2014·PLoS Computational Biology·Behruz BozorgHenrik Jönsson
Feb 26, 2011·Annals of Biomedical Engineering·Peter E HammerRobert D Howe
Sep 2, 2014·Materials Science & Engineering. C, Materials for Biological Applications·Mingzhu Chen, Fergal J Boyle
Sep 28, 2010·Progress in Biophysics and Molecular Biology·Stéphanie MarchesseauHervé Delingette
Dec 14, 2011·IEEE Transactions on Visualization and Computer Graphics·Gaizka San-VicenteJuan Tomás Celigüeta
Mar 1, 2011·IEEE Computer Graphics and Applications· Dong Ni Pheng-Ann Heng
Sep 14, 2018·Journal of Mathematical Biology·Hadrien OliveriOlivier Ali
Apr 3, 2019·Physical Review. E·Pawel Gniewek, Oskar Hallatschek

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