Biquadratic and Quadratic Springs for Modeling St Venant Kirchhoff Materials

  • Hervé Delingette
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5104)


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.


Elastic Force Deformable Model Tetrahedral Mesh Surgery Simulation Shape Vector 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hervé Delingette
    • 1
  1. 1.Asclepios Research ProjectINRIA Sophia-AntipolisSophia-AntipolisFrance

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