“A finite element method for animating large viscoplastic flow” by Bargteil, Wojtan, Hodgins and Turk

We present an extension to Lagrangian finite element methods to allow for large plastic deformations of solid materials. These behaviors are seen in such everyday materials as shampoo, dough, and clay as well as in fantastic gooey and blobby creatures in special effects scenes. To account for plastic deformation, we explicitly update the linear basis functions defined over the finite elements during each simulation step. When these updates cause the basis functions to become ill-conditioned, we remesh the simulation domain to produce a new high-quality finite-element mesh, taking care to preserve the original boundary. We also introduce an enhanced plasticity model that preserves volume and includes creep and work hardening/softening. We demonstrate our approach with simulations of synthetic objects that squish, dent, and flow. To validate our methods, we compare simulation results to videos of real materials.

1. Alliez, P., Cohen-Steiner, D., Yvinec, M., and Desbrun, M. 2005. Variational tetrahedral meshing. ACM Trans. Graph. 24, 3, 617–625. Google ScholarDigital Library
2. Bargteil, A. W., Goktekin, T. G., O’Brien, J. F., and Strain, J. A. 2006. A semi-Lagrangian contouring method for fluid simulation. ACM Trans. Graph. 25, 1, 19–38. Google ScholarDigital Library
3. Borouchaki, H., Laug, P., Cherouat, A., and Saanouni, K. 2005. Adaptive remeshing in large plastic strain with damage. International Journal for Numerical Methods in Engineering 63, 1 (February), 1–36.Google ScholarCross Ref
4. Bridson, R., Fedkiw, R., and Anderson, J. 2002. Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. Graph. 21, 3, 594–603. Google ScholarDigital Library
5. Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of clothing with folds and wrinkles. In The Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 28–36. Google ScholarDigital Library
6. Brochu, T. 2006. Fluid Animation with Explicit Surface Meshes and Boundary-Only Dynamics. Master’s thesis, University of British Columbia.Google Scholar
7. Cheng, S.-W., Dey, T. K., Edelsbrunner, H., Facello, M. A., and Teng, S.-H. 1999. Sliver exudation. In The Proceedings of the Symposium on Computational Geometry, 1–13. Google ScholarDigital Library
8. Clavet, S., Beaudoin, P., and Poulin, P. 2005. Particle-based viscoelastic fluid simulation. In The Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 219–228. Google ScholarDigital Library
9. Desbrun, M., and Gascuel, M.-P. 1995. Animating soft substances with implicit surfaces. In The Proceedings of ACM SIGGRAPH, 287–290. Google ScholarDigital Library
10. Dey, T., Edelsbrunner, H., Guha, S., and Nekhayev, D. V. 1999. Topology preserving edge contraction. Publ. Inst. Math. (Beograd) (N.S.) 66, 23–45.Google Scholar
11. Enright, D. P., Marschner, S. R., and Fedkiw, R. P. 2002. Animation and rendering of complex water surfaces. ACM Trans. Graph. 21, 3, 736–744. Google ScholarDigital Library
12. Goktekin, T. G., Bargteil, A. W., and O’Brien, J. F. 2004. A method for animating viscoelastic fluids. ACM Trans. Graph. 23, 3, 463–468. Google ScholarDigital Library
13. Hieber, S. E., and Koumoutsakos, P. 2005. A Lagrangian particle level set method. J. Comp. Phys. 210, 1, 342–367. Google ScholarDigital Library
14. Hill, R. 1950. The Mathematical Theory of Plasticity. Oxford University Press, Inc.Google Scholar
15. Hudson, B., Miller, G., and Phillips, T. 2006. Sparse Voronoi Refinement. In The Proceedings of the 15th International Meshing Roundtable.Google Scholar
16. Irving, G., Teran, J., and Fedkiw, R. 2004. Invertible finite elements for robust simulation of large deformation. In The Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 131–140. Google ScholarDigital Library
17. Keiser, R., Adams, B., Gasser, D., Bazzi, P., Dutré, P., and Gross, M. 2005. A unified Lagrangian approach to solid-fluid animation. In The Proceedings of Eurographics Symposium on Point-based Graphics, 125–133. Google ScholarCross Ref
18. Klingner, B. M., Feldman, B. E., Chentanez, N., and O’Brien, J. F. 2006. Fluid animation with dynamic meshes. ACM Trans. Graph. 25, 3, 820–825. Google ScholarDigital Library
19. Labelle, F. 2006. Sliver removal by lattice refinement. In The Proceedings of the ACM Symposium on Computational Geometry, 347–356. Google ScholarDigital Library
20. Losasso, F., Shinar, T., Selle, A., and Fedkiw, R. 2006. Multiple interacting liquids. ACM Trans. Graph. 25, 3, 812–819. Google ScholarDigital Library
21. Mauch, S., Noels, L., Zhao, Z., and Radovitzky, R. 2006. Lagrangian simulation of penetration environments via mesh healing and adaptive optimization. In The Proceedings of the 25th Army Science Conference.Google Scholar
22. Müller, M., and Gross, M. 2004. Interactive virtual materials. In The Proceedings of Graphics Interface, 239–246. Google ScholarDigital Library
23. Müller, M., Dorsey, J., McMillan, L., Jagnow, R., and Cutler, B. 2002. Stable real-time deformations. In The Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 49–54. Google ScholarDigital Library
24. Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., and Alexa, M. 2004. Point based animation of elastic, plastic and melting objects. In The Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 141–151. Google ScholarDigital Library
25. O’Brien, J. F., Bargteil, A. W., and Hodgins, J. K. 2002. Graphical modeling and animation of ductile fracture. ACM Trans. Graph. 21, 3, 291–294. Google ScholarDigital Library
26. Pauly, M., Keiser, R., Adams, B., Dutré;, P., Gross, M., and Guibas, L. J. 2005. Meshless animation of fracturing solids. ACM Trans. Graph. 24, 3, 957–964. Google ScholarDigital Library
27. Shewchuk, J. R. 2002. What is a good linear element? Interpolation, Conditioning, and Quality Measures. In 11th Int. Meshing Roundtable, 115–126.Google Scholar
28. Shewchuk, R. 2005. Star splaying: an algorithm for repairing Delaunay triangulations and convex hulls. In The Proceedings of the Symposium on Computational Geometry, 237–246. Google ScholarDigital Library
29. Simo, J., and Hughes, T. 1998. Computational Inelasticity. Springer-Verlag.Google Scholar
30. Terzopoulos, D., and Fleischer, K. 1988. Modeling inelastic deformation: Viscoelasticity, plasticity, fracture. In The Proceedings of ACM SIGGRAPH, 269–278. Google ScholarDigital Library
31. Terzopoulos, D., Platt, J., and Fleischer, K. 1989. Heating and melting deformable models (from goop to glop). In The Proceedings of Graphics Interface, 219–226.Google Scholar
32. Zhu, Y., and Bridson, R. 2005. Animating sand as a fluid. ACM Trans. Graph, 24, 3, 965–972. Google ScholarDigital Library