Approximate simulation of elastic membranes by triangulated spring meshes
Journal of Graphics Tools
Non-linear anisotropic elasticity for real-time surgery simulation
Graphical Models - Special issue on SMI 2002
Real-Time subspace integration for St. Venant-Kirchhoff deformable models
ACM SIGGRAPH 2005 Papers
Tetrahedral and hexahedral invertible finite elements
Graphical Models - Special issue on SCA 2004
Triangular Springs for Modeling Nonlinear Membranes
IEEE Transactions on Visualization and Computer Graphics
Identification of Spring Parameters for Deformable Object Simulation
IEEE Transactions on Visualization and Computer Graphics
Shell model for reconstruction and real-time simulation of thin anatomical structures
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
Acquisition of elastically deformable object model based on measurement
EuroHaptics'12 Proceedings of the 2012 international conference on Haptics: perception, devices, mobility, and communication - Volume Part I
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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.