“Meshless animation of fracturing solids” by Pauly, Keiser, Adams, Dutré, Gross, et al. …

We present a new meshless animation framework for elastic and plastic materials that fracture. Central to our method is a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques. We explicitly model advancing crack fronts and associated fracture surfaces embedded in the simulation volume. When cutting through the material, crack fronts directly affect the coupling between simulation nodes, requiring a dynamic adaptation of the nodal shape functions. We show how local visibility tests and dynamic caching lead to an efficient implementation of these effects based on point collocation. Complex fracture patterns of interacting and branching cracks are handled using a small set of topological operations for splitting, merging, and terminating crack fronts. This allows continuous propagation of cracks with highly detailed fracture surfaces, independent of the spatial resolution of the simulation nodes, and provides effective mechanisms for controlling fracture paths. We demonstrate our method for a wide range of materials, from stiff elastic to highly plastic objects that exhibit brittle and/or ductile fracture.

1. Alexa, M., and Adamson, A. 2004. On normals and projection operators for surfaces defined by point sets. In Proceedings of Eurographics Symposium on Point-Based Graphics, 150–155. Google ScholarDigital Library
2. Anderson, T. L. 1995. Fracture Mechanics. CRC Press.Google Scholar
3. Belytschko. T., Lu. Y., and Gu, L. 1994. Element-free galerkin methods. Int. J. Numer. Meth. Engng 37, 229–256.Google ScholarCross Ref
4. Belytschko. T., Krongauz, Y., Organ, D., Fleming, M., and Krysl, P. 1996. Meshless methods: An overview and recent developments. Comp. Meth. in Appl. Mech. Eng. 139, 3.Google ScholarCross Ref
5. Belytschko. T., Chen, H., Xu, J., and Zi, G. 2003. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int. J. Numer. Meth. Engng 58, 1873–1905.Google ScholarCross Ref
6. Bielser. D., Glardon, P., Teschner, M., and Gross, M. 2003. A state machine for real-time cutting of tetrahedral meshes. In Pacific Graphics, 377–386. Google ScholarDigital Library
7. Carlson, M., Mucha, P., Van Horn III, B., and Turk, G. 2002. Melting and flowing. In Proceedings of the 2002 ACM SIGGRAPH Symposium on Computer Animation. Google ScholarDigital Library
8. Chang, J., and Zhang, J. J. 2004. Mesh-free deformations. In Comp. Anim. Virtual Worlds. 211–218. Google ScholarDigital Library
9. Chung, T. J. 1996. Applied Continuum Mechanics. Cambridge Univ. Press, NY.Google Scholar
10. Debunne, G., Desbrun, M., Cani, M.-P., and Barr, A. 2001. Dynamic real-time deformations using space & time adaptive sampling. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH 2001, 31–36. Google ScholarDigital Library
11. Desbrun, M., and Cani, M.-P. 1995. Animating soft substances with implicit surfaces. In Computer Graphics Proceedings, ACM SIGGRAPH, 287–290. Google ScholarDigital Library
12. Desbrun, M., and Cani, M.-P. 1996. Smoothed particles: A new paradigm for animating highly deformable bodies. In 6th Eurographics Workshop on Computer Animation and Simulation ’96, 61–76. Google ScholarDigital Library
13. Desbrun, M., and Cani, M.-P. 1999. Space-time adaptive simulation of highly deformable substances. Tech. rep., INRIA Nr. 3829.Google Scholar
14. Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual simulation of smoke. In SIGGRAPH 2001, Computer Graphics Proceedings, ACM Press / ACM SIGGRAPH, E. Fiume, Ed., 15–22. Google ScholarDigital Library
15. Feldman, B. E., O’Brien, J. F., and Arikan, O. 2003. Animating suspended particle explosions. In Proceedings of ACM SIGGRAPH 2003, 708–715. Google ScholarDigital Library
16. Fernandez-Mendez, S., and Huerta, A. 2004. Imposing essential boundary conditions in mesh-free methods. Computer Methods in Applied Mechanics and Engineering 193, 1257–1275.Google ScholarCross Ref
17. Fries, T. P., and Matthies, H. G. 2003. Classification and overview of meshfree methods. Tech. rep., TU Brunswick, Germany Nr. 2003–03.Google Scholar
18. Guibas, L. J., and Marimont, D. H. 1995. Rounding arrangements dynamically. In SCG ’95: Proceedings of the eleventh annual symposium on Computational geometry, ACM Press, 190–199. Google ScholarDigital Library
19. Hirota, K., Tanoue, Y., and Kaneko, T. 1998. Generation of crack patterns with a physical model. Vis. Comput. 14, 126–137.Google ScholarCross Ref
20. James, D. L., and Pai, D. K. 1999. Artdefo, accurate real time deformable objects. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH 99, 65–72. Google ScholarDigital Library
21. Keiser, R., Müller, M., Heidelberger, B., Teschner, M., and Gross, M. 2004. Contact handling for deformable point-based objects. In Proceedings of VMV.Google Scholar
22. Krysl, P., and Belytschko, T. 1999. The element free galerkin method for dynamic propagation of arbitrary 3-d cracks. Int. J. Numer. Meth. Engng 44, 767–800.Google ScholarCross Ref
23. Lancaster, P., and Salkauskas. K. 1981. Surfaces generated by moving least squares methods. Mathematics of Computation 87, 141–158.Google ScholarCross Ref
24. Liu, G. R. 2002. Mesh-Free Methods. CRC Press.Google Scholar
25. Molino, N., Bao, Z., and Fedkiw, R. 2004. A virtual node algorithm for changing mesh topology during simulation. ACM Trans. Graph. 23, 3, 385–392. Google ScholarDigital Library
26. Müller, M., and Gross. M. 2004. Interactive virtual materials. In Proceedings of the 2004 conference on Graphics interface, Canadian Human-Computer Communications Society, 239–246. Google ScholarDigital Library
27. Müller, M., McMillan, L., Dorsey, J., and Jagnow, R. 2001. Real-time simulation of deformation and fracture of stiff materials. EUROGRAPHICS 2001 Computer Animation and Simulation Workshop, 27–34. Google ScholarDigital Library
28. Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., and Alexa, M. 2004. Point based animation of elastic, plastic and melting objects. Proceedings of 2004 ACM SIGGRAPH Symposium on Computer Animation, 141–151. Google ScholarDigital Library
29. Nguyen, D. Q., Fedkiw, R., and Jensen, H. W. 2002. Physically based modeling and animation of fire. In Proceedings of the 29th annual conference on Computer graphics and interactive techniques. ACM Press, 721–728. Google ScholarDigital Library
30. O’BRIEN, J. F., AND HODGINS, J. K. 1999. Graphical modeling and animation of brittle fracture. In Proceedings of SIGGRAPH 1999, 287–296. Google ScholarDigital Library
31. O’BRIEN, J. F., BARGTEIL, A. W., AND HODGINS, J. K. 2002. Graphical modeling and animation of ductile fracture. In Proceedings of SIGGRAPH 2002, 291–294. Google ScholarDigital Library
32. Organ, D., Fleming, M., Terry. T., and Belytschko, T. 1996. Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Computational Mechanics 18, 1–11.Google ScholarCross Ref
33. Ortiz, M., and Pandolfi, A. 1999. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int. J. Num. Meth. Eng. 44, 1267–1282.Google ScholarCross Ref
34. Pauly, M., Keiser, R., Kobbelt, L. P., and Gross, M. 2003. Shape modeling with point-sampled geometry. ACM Trans. Graph. 22, 3, 641–650. Google ScholarDigital Library
35. Smith, J., Witkin, A., and Baraff, D. 2000. Fast and controllable simulation of the shattering of brittle objects. In Graphics Interface, 27–34.Google Scholar
36. Sukumar, N., Mos, N., Moran, B., and Belytschko, T. 2000. Extended finite element method for three-dimensional crack modeling. International Journal for Numerical Methods in Engineering 48, 11, 1549–1570.Google ScholarCross Ref
37. Terzopoulos, D., and Fleischer, K. 1988. Modeling inelastic deformation: viscolelasticity, plasticity, fracture. In Proceedings of the 15th annual conference on Computer graphics and interactive techniques, ACM Press, 269–278. Google ScholarDigital Library
38. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH 87, 205–214. Google ScholarDigital Library
39. Teschner, M., Heidelberger, B., Müller, M., Pomeranets, D., and Gross, M. 2003. Optimized spatial hashing for collision detection of deformable objects. In Proc. Vision, Modeling, Visualization VMV, 47–54.Google Scholar
40. Ventura, G., Xu, J., and Belytschko, T. 2002. A vector level set method and new discontinuity approximations for crack growth by efg. International Journal for Numerical Methods in Engineering 54, 923–944.Google ScholarCross Ref
41. Wicke, M., Teschner, M., and Gross, M. 2004. Csg tree rendering of point-sampled objects. In Proceedings of Pacific Graphics 2004. Google ScholarDigital Library
42. Zhang, X., Liu, X.-H., Song, K.-Z., and Lu, M.-W. 2001. Least-squares collocation meshless method. Int. J. Numer Meth. Engng 51, 1089–1100.Google ScholarCross Ref