Stable and realistic crack pattern generation using a cracking node method
Juan ZHANG, Fuqing DUAN, Mingquan ZHOU, Dongcan JIANG, Xuesong WANG, Zhongke WU, Youliang HUANG, Guoguang DU, Shaolong LIU, Pengbo ZHOU, Xiangang SHANG
Stable and realistic crack pattern generation using a cracking node method
This paper presents a method for simulating surface crack patterns appearing in ceramic glaze, glass, wood and mud. It uses a physically and heuristically combined method to model this type of crack pattern. A stress field is defined heuristically over the triangle mesh of an object. Then, a first-order quasi-static cracking node method (CNM) is used to model deformation. A novel combined stress and energy combined crack criterion is employed to address crack initiation and propagation separately according to physics. Meanwhile, a highest-stress-first rule is applied in crack initiation, and a breadth-first rule is applied in crack propagation. Finally, a local stress relaxation step is employed to evolve the stress field and avoid shattering artifacts. Other related issues are also discussed, such as the elimination of quadrature sub-cells, the prevention of parallel cracks and spurious crack procession. Using this method, a variety of crack patterns observed in the real world can be reproduced by changing a set of parameters. Consequently, our method is robust because the computational mesh is independent of dynamic cracks and has no sliver elements. We evaluate the realism of our results by comparing them with photographs of realworld examples. Further, we demonstrate the controllability of our method by varying different parameters.
crack pattern generation / fracture simulation / physically-based / extend finite element method / crack node method
[1] |
O’Brien J F, Hodgins J K. Graphical modeling and animation of brittle fracture. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. 1999, 137–146
CrossRef
Google scholar
|
[2] |
Pfaff T, Narain R, de Joya J M, O’Brien J F. Adaptive tearing and cracking of thin sheets. ACM Transactions on Graphics, 2014, 33(4): 1–9
CrossRef
Google scholar
|
[3] |
Song J H, Belytschko T. Cracking node method for dynamic fracture with finite elements. International Journal for Numerical Methods in Engineering, 2009, 77(3): 360–385
CrossRef
Google scholar
|
[4] |
Molino N, Bao Z, Fedkiw R. A virtual node algorithm for changing mesh topology during simulation. ACM Transactions on Graphics, 2004, 23(3): 385
CrossRef
Google scholar
|
[5] |
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620
CrossRef
Google scholar
|
[6] |
Melenk J, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 289–314
CrossRef
Google scholar
|
[7] |
Rabczuk T. Computational methods for fracture in brittle and quasibrittle solids: state-of-the-art review and future perspectives. Applied Mathematics, 2013, 2013: 1–38
|
[8] |
Lindblad A, Turkiyyah G. A physically-based framework for real-time haptic cutting and interaction with 3D continuum models. In: Proceedings of ACM Symposium on Solid and Physical Modeling. 2007, 421–429
CrossRef
Google scholar
|
[9] |
Chao S. Simulation for cutting deformable model based on X-FEM. In: Proceedings of International Conference on Intelligent Computing and Cognitive Informatics. 2010, 436–439
CrossRef
Google scholar
|
[10] |
Kaufmann P, Martin S, Botsch M, Grinspun E, Gross M. Enrichment textures for detailed cutting of shells. ACM Transactions on Graphics, 2009, 28(3): 50
CrossRef
Google scholar
|
[11] |
Jeřábková L, Kuhlen T. Stable cutting of deformable objects in virtual environments using XFEM. IEEE Computer Graphics and Applications, 2009, 29(2): 61–71
CrossRef
Google scholar
|
[12] |
Turkiyyah G M, Karam W B, Ajami Z, Nasri A. Mesh cutting during real-time physical simulation. In: Proceedings of SIAM/ACM Joint Conference on Geometric and Physical Modeling. 2009, 159–168
CrossRef
Google scholar
|
[13] |
Iben H N, O’Brien J F. Generating surface crack patterns. Graphical Models, 2009, 71(6): 198–208
CrossRef
Google scholar
|
[14] |
Muguercia L, Bosch C, Patow G. Fracture modeling in computer graphics. Computers Graphics, 2014, 45: 86–100
CrossRef
Google scholar
|
[15] |
Terzopoulos D, Platt J, Fleischert K. Elastically deformable models. Computer Graphics, 1987, 21(4): 205–214
CrossRef
Google scholar
|
[16] |
Terzopoulos D, Fleischer K. Modeling inelastic deformation: viscolelasticity, plasticity, fracture. ACM SIGGRAPH Computer Graphics, 1988, 22(4): 269–278
CrossRef
Google scholar
|
[17] |
Wu J, Westermann R, Dick C. A survey of physically based simulation of cuts in deformable bodies. Computer Graphics Forum, 2015, 34(6): 161–187
CrossRef
Google scholar
|
[18] |
Norton A, Turk G, Bacon B, Gerth J, Sweeney P. Animation of fracture by physical modeling. The Visual Computer, 1991, 7(4): 210–219
CrossRef
Google scholar
|
[19] |
Lloyd B A, Szekely G, Harders M. Identification of spring parameters for deformable object simulation. IEEE Transactions on Visualization and Computer Graphics, 2007, 13(5): 1081–1094
CrossRef
Google scholar
|
[20] |
Natsupakpong S, Çavu ¸soğlu M C. Determination of elasticity parameters in lumped element (mass-spring) models of deformable objects. Graphical Models, 2010, 72(6): 61–73
CrossRef
Google scholar
|
[21] |
Liu T T, Bargteil A W, O’Brien J F, Kavan L. Fast simulation of massspring systems. ACM Transactions on Graphics, 2013, 32(6): 214
CrossRef
Google scholar
|
[22] |
Kot M, Nagahashi H, Szymczak P. Elastic moduli of simple mass spring models. The Visual Computer, 2015, 31(10): 1339–1350
CrossRef
Google scholar
|
[23] |
Levine J A, Bargteil A W, Corsi C, Tessendorf J, Geist R. A peridynamic perspective on spring-mass fracture? In: Proceedings of the ACMSIGGRAPH/Eurographics Symposium on Computer Animation. 2014, 47–55
|
[24] |
O’Brien J F, Bargteil A W, Hodgins J K. Graphical modeling and animation of ductile fracture. ACM Transactions on Graphics, 2002, 21(3): 291–294
CrossRef
Google scholar
|
[25] |
Bao Z S, Hong J M, Teran J, Fedkiw R. Fracturing rigid materials. IEEE Transactions on Visualization and Computer Graphics, 2007, 13(2): 370–378
CrossRef
Google scholar
|
[26] |
Busaryev O, Dey T K, Wang H. Adaptive fracture simulation of multilayered thin plates. ACM Transactions on Graphics, 2013, 32(4): 52
CrossRef
Google scholar
|
[27] |
Matthias M, Gross M, Müller M. Interactive virtual materials. In: Proceedings of Graphics Interface. 2004, 239–246
|
[28] |
James D L, Pai D K. Artdefo: accurate real time deformable objects. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. 1999, 65–72
CrossRef
Google scholar
|
[29] |
Kielhorn L. A time-domain symmetric Galerkin BEM for viscoelastodynamics. Dissertation for the Doctoral Degree. Graz: Graz University of Technology, 2009
|
[30] |
Zhu Y, Bridson R, Greif C. Simulating rigid body fracture with surface meshes. ACM Transactions on Graphics, 2015, 34(4): 150
CrossRef
Google scholar
|
[31] |
Hahn D, Wojtan C. High-resolution brittle fracture simulation with boundary elements. ACM Transactions on Graphics, 2015, 34(4): 151
CrossRef
Google scholar
|
[32] |
Müller M, Keiser R, Nealen A, Pauly M, Gross M, Alexa M. Point based animation of elastic, plastic and melting objects. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 2004, 141–151
|
[33] |
Pauly M, Keiser R, Adams B, Dutré P, Gross M, Guibas L J. Meshless animation of fracturing solids. ACM Transactions on Graphics, 2005, 24(3): 957–964
CrossRef
Google scholar
|
[34] |
Solenthaler B, Schläfli J, Pajarola R. A unified particle model for fluidsolid interactions. Computer Animation and Virtual Worlds, 2007, 18(1): 69–82
CrossRef
Google scholar
|
[35] |
Li C, Wang C B, Qin H. Novel adaptive SPH with geometric subdivision for brittle fracture animation of anisotropic materials. The Visual Computer, 2015, 31(6): 937–946
CrossRef
Google scholar
|
[36] |
Liu N, He X W, Li S, Wang G P. Meshless simulation of brittle fracture. Computer Animation and Virtual Worlds, 2011, 22(2-3): 115–124
CrossRef
Google scholar
|
[37] |
Hesham O. Fast meshless simulation of anisotropic tearing in elastic solids. Dissertation for the Doctoral Degree. Ottawa: Carleton University, 2011
|
[38] |
Sifakis E, Der K G, Fedkiw R. Arbitrary cutting of deformable tetrahedralized objects. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 2007, 73–80
|
[39] |
Wang Y T, Jiang C, Schroeder C, Teran J. An adaptive virtual node algorithm with robust mesh cutting. In: Proceedings of ACM SIGGRAPH/ Eurographics Symposium on Computer Animation. 2014, 77–85
|
[40] |
Glondu L, Marchal M, Dumont G. Real-time simulation of brittle fracture using modal analysis. IEEE Transactions on Visualization and Computer Graphics, 2013, 19(2): 201–209
CrossRef
Google scholar
|
[41] |
Hirota K, Tanoue Y, Kaneko T. Generation of crack patterns with a physical model. The Visual Computer, 1998, 14(3): 126–137
CrossRef
Google scholar
|
[42] |
Hirota K, Tanoue Y, Kaneko T. Simulation of three-dimensional cracks. The Visual Computer, 2000, 16(7): 371–378
CrossRef
Google scholar
|
[43] |
Gobron S, Chiba N. Crack pattern simulation based on 3D surface cellular automata. The Visual Computer, 2001, 17(5): 287–309
CrossRef
Google scholar
|
[44] |
Gobron S, Norishige C. Simulation of peeling using 3D-surface cellular automata. In: Proceedings of the 9th Pacific Conference on Computer Graphics and Applications. 2001, 338–347
CrossRef
Google scholar
|
[45] |
Federl P. Modeling fracture formation on growing surfaces. Dissertation for the Doctoral Degree. Calgary: University of Calgary, 2003
|
[46] |
Paquette E, Poulin P, Drettakis G. The simulation of paint cracking and peeling. In: Proceedings of the Graphics Interface. 2002, 59–68
|
[47] |
Valette G, Prévost S, Lucas L, Léonard J. A dynamic model of cracks development based on a 3D discrete shrinkage volume propagation. Computer Graphics Forum, 2008, 27(1): 47–62
CrossRef
Google scholar
|
[48] |
Müller M, Chentanez N, Kim T Y. Real time dynamic fracture with volumetric approximate convex decompositions. ACM Transactions on Graphics, 2013, 32(4): 115
CrossRef
Google scholar
|
[49] |
Raghavachary S. Fracture generation on polygonal meshes using voronoi polygons. In: Proceedings of ACM SIGGRAPH Conference on Abstracts and Applications. 2002, 187–187
CrossRef
Google scholar
|
[50] |
Tang Y, Fang K J, Fu S H, Zhang L B. An improved algorithm for simulating wax-printing patterns. Textile Research Journal, 2011, 81(14): 1510–1520
CrossRef
Google scholar
|
[51] |
Schvartzman S C, Otaduy M A. Fracture animation based on highdimensional voronoi diagrams. In: Proceedings of the 18th Meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. 2014, 15–22
|
[52] |
Martinet A, Galin E, Desbenoit B, Akkouche S. Procedural modeling of cracks and fractures. In: Proceedings of Shape Modelling Applications. 2004, 346–349
CrossRef
Google scholar
|
[53] |
Wyvill B, van Overveld K, Carpendale S. Rendering cracks in batik. In: Proceedings of the 3rd International Symposium on Non-photorealistic Animation and Rendering. 2004, 61–149
CrossRef
Google scholar
|
[54] |
Hsieh H H, Tai W K. A straightforward and intuitive approach on generation and display of crack-like patterns on 3D objects. In: Nishita T, Peng Q S, Seidel H P, eds. Advances in Computer Graphics, Vol 4035. Berlin: Springer Heidelberg, 2006, 554–561
CrossRef
Google scholar
|
[55] |
Lu J Y, Georghiades A S, Glaser A, Wu H Z, Wei L Y, Guo B N, Dorsey J, Rushmeier H. Context-aware textures. ACM Transaction on Graphics, 2007, 26(1): 3
CrossRef
Google scholar
|
[56] |
Wei L Y, Lefebvre S, Kwatra V, Turk G. State of the art in examplebased texture synthesis. In: Proceedings of Eurographicsthe ACM SIGGRAPH/ Eurographics. 2009, 93–117
|
[57] |
Glondu L. Physically-based and real-time simulation of brittle fracture for interactive applications. Dissertation for the Doctoral Degree. Cachan: École normale supérieure de Cachan-ENS Cachan, 2012
|
[58] |
Liu S G, Chen D. Computer simulation of batik printing patterns with cracks. Textile Research Journal, 2015, 85(18): 1972–1984
CrossRef
Google scholar
|
[59] |
Gross D, Seelig T. Fracture Mechanics: With an Introduction to Micromechanics. Springer Science & Business Media, 2011
CrossRef
Google scholar
|
[60] |
Wicke M, Ritchie D, Klingner B M, Burke S, Shewchuk J R, O’Brien J F. Dynamic local remeshing for elastoplastic simulation. ACM Transactions on Graphics, 2010, 29(4): 49
CrossRef
Google scholar
|
[61] |
Koschier D, Lipponer S, Bender J. Adaptive tetrahedral meshes for brittle fracture simulation. In: Proceedings of ACM SIGGRAPH/ Eurographics Symposium on Computer Animation. 2014, 58–66
|
[62] |
Freund L B. Dynamic Fracture Mechanics. Cambridge: Cambridge University Press, 1990
CrossRef
Google scholar
|
[63] |
Ventura G. On the elimination of quadrature subcells for discontinuous functions in the extended finite-element method. International Journal for Numerical Methods in Engineering, 2006, 66(5): 761–795
CrossRef
Google scholar
|
[64] |
Fung Y C. A First Course in Continuum Mechanics. Englewood Cliffs, NJ: Prentice-Hall, 1994
|
[65] |
Rusinkiewicz S. Estimating curvatures and their derivatives on triangle meshes. In: Proceedings of the 2nd International Symposium on 3D Data Processing, Visualization, and Transmission. 2004, 486–493
CrossRef
Google scholar
|
[66] |
Iben H N. Generating Surface Crack Patterns. Dissertation for the Doctoral Degree. Berkeley: University of California, Berkeley, 2007
|
/
〈 | 〉 |