Abstract
This paper provides a formal connexion between springs and continuum mechanics in the context of two-dimensional and three dimensional hyperelasticity. First, we establish the equivalence between surface and volumetric St Venant-Kirchhoff materials defined on linear triangles and tetrahedra with tensile, bending and volumetric biquadratics springs. Those springs depend on the variation of square edge length while traditional or quadratic springs depend on the change in edge length. However, we establish that for small deformations, biquadratic springs can be approximated with quadratic springs with different stiffnesses. This work leads to an efficient implementation of St Venant-Kirchhoff materials that can cope with compressible strains. It also provides expressions to compute spring stiffnesses on triangular and tetrahedral meshes.
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References
Barbič, J., James, D.L.: Real-time subspace integration for St. Venant-Kirchhoff deformable models. ACM TOG (SIGGRAPH 2005) 24(3), 982–990 (2005)
Bianchi, G., Solenthaler, B., Székely, G., Harders, M.: Simultaneous topology and stiffness identification for mass-spring models based on fem reference deformations. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 293–301. Springer, Heidelberg (2004)
Cotin, S., Delingette, H., Ayache, N.: A hybrid elastic model allowing real-time cutting, deformations and force-feedback for surgery training and simulation. The Visual Computer 16(8), 437–452 (2000)
Delingette, H.: Triangular springs for modeling nonlinear membranes. IEEE Transactions on Visualization and Computer Graphics 14(2), 329–341 (2008)
Irving, G., Teran, J., Fedkiw, R.: Tetrahedral and hexahedral invertible finite elements. Graph. Models 68(2), 66–89 (2006)
Lloyd, B., Szekely, G., Harders, M.: Identification of spring parameters for deformable object simulation. IEEE Transactions on Visualization and Computer Graphics 13(5), 1081–1094 (2007)
Nealen, A., Muller, M., Keiser, R., Boxerman, E., Carlson, M.: Physically based deformable models in computer graphics. Technical report, Eurographics State of the Art, Dublin, Ireland (September 2005)
Nesme, M., Payan, Y., Faure, F.: Efficient, physically plausible finite elements. In: Dingliana, J., Ganovelli, F. (eds.) Eurographics (short papers) (august 2005)
Picinbono, G., Delingette, H., Ayache, N.: Non-Linear Anisotropic Elasticity for Real-Time Surgery Simulation. Graphical Models 65(5), 305–321 (2003)
Terzopoulos, D., Platt, J., Barr, A., Fleischer, K.: Elastically deformable models. In: Computer Graphics (SIGGRAPH 1987), vol. 21, pp. 205–214 (1987)
Van Gelder, A.: Approximate simulation of elastic membranes by triangulated spring meshes. Journal of Graphics Tools: JGT 3(2), 21–41 (1998)
Waters, K., Terzopoulos, D.: Modeling and animating faces using scanned data. The Journal of Visualization and Computer Animation 2, 129–131 (1991)
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Delingette, H. (2008). Biquadratic and Quadratic Springs for Modeling St Venant Kirchhoff Materials. In: Bello, F., Edwards, P.J.E. (eds) Biomedical Simulation. ISBMS 2008. Lecture Notes in Computer Science, vol 5104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70521-5_5
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DOI: https://doi.org/10.1007/978-3-540-70521-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70520-8
Online ISBN: 978-3-540-70521-5
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