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Stable and realistic crack pattern generation using a cracking node method

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Abstract

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 real-world examples. Further, we demonstrate the controllability of our method by varying different parameters.

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References

  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

    Google Scholar 

  2. Pfaff T, Narain R, de Joya JM, O’Brien J F. Adaptive tearing and cracking of thin sheets. ACM Transactions on Graphics, 2014, 33(4): 1–9

    Article  MATH  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

    Article  MathSciNet  MATH  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

    Article  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

    Article  MATH  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

    Article  MathSciNet  MATH  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

    MathSciNet  MATH  Google Scholar 

  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

    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

    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

    Article  Google Scholar 

  11. Jerábková L, Kuhlen T. Stable cutting of deformable objects in virtual environments using XFEM. IEEE Computer Graphics and Applications, 2009, 29(2): 61–71

    Article  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

    Google Scholar 

  13. Iben H N, O’Brien J F. Generating surface crack patterns. Graphical Models, 2009, 71(6): 198–208

    Article  Google Scholar 

  14. Muguercia L, Bosch C, Patow G. Fracture modeling in computer graphics. Computers Graphics, 2014, 45: 86–100

    Article  Google Scholar 

  15. Terzopoulos D, Platt J, Fleischert K. Elastically deformable models. Computer Graphics, 1987, 21(4): 205–214

    Article  Google Scholar 

  16. Terzopoulos D, Fleischer K. Modeling inelastic deformation: viscolelasticity, plasticity, fracture. ACM SIGGRAPH Computer Graphics, 1988, 22(4): 269–278

    Article  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

    Article  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

    Article  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

    Article  Google Scholar 

  20. Natsupakpong S, Çavusoglu M C. Determination of elasticity parameters in lumped element (mass-spring) models of deformable objects. Graphical Models, 2010, 72(6): 61–73

    Article  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

    Google Scholar 

  22. Kot M, Nagahashi H, Szymczak P. Elastic moduli of simple mass spring models. The Visual Computer, 2015, 31(10): 1339–1350

    Article  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

    Google Scholar 

  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

    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

    Article  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

    Article  MATH  Google Scholar 

  27. Matthias M, Gross M, Müller M. Interactive virtual materials. In: Proceedings of Graphics Interface. 2004, 239–246

    Google Scholar 

  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

    Google Scholar 

  29. Kielhorn L. A time-domain symmetric Galerkin BEM for viscoelastodynamics. Dissertation for the Doctoral Degree. Graz: Graz University of Technology, 2009

    Google Scholar 

  30. Zhu Y, Bridson R, Greif C. Simulating rigid body fracture with surface meshes. ACM Transactions on Graphics, 2015, 34(4): 150

    MATH  Google Scholar 

  31. Hahn D, Wojtan C. High-resolution brittle fracture simulation with boundary elements. ACM Transactions on Graphics, 2015, 34(4): 151

    Article  MATH  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

    Google Scholar 

  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

    Article  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

    Article  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

    Article  Google Scholar 

  36. Liu N, He XW, Li S, Wang G P. Meshless simulation of brittle fracture. Computer Animation and Virtual Worlds, 2011, 22(2-3): 115–124

    Article  Google Scholar 

  37. Hesham O. Fast meshless simulation of anisotropic tearing in elastic solids. Dissertation for the Doctoral Degree. Ottawa: Carleton University, 2011

    Google Scholar 

  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

    Google Scholar 

  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

    Google Scholar 

  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

    Article  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

    Article  Google Scholar 

  42. Hirota K, Tanoue Y, Kaneko T. Simulation of three-dimensional cracks. The Visual Computer, 2000, 16(7): 371–378

    Article  MATH  Google Scholar 

  43. Gobron S, Chiba N. Crack pattern simulation based on 3D surface cellular automata. The Visual Computer, 2001, 17(5): 287–309

    Article  MATH  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

    Google Scholar 

  45. Federl P. Modeling fracture formation on growing surfaces. Dissertation for the Doctoral Degree. Calgary: University of Calgary, 2003

    Google Scholar 

  46. Paquette E, Poulin P, Drettakis G. The simulation of paint cracking and peeling. In: Proceedings of the Graphics Interface. 2002, 59–68

    Google Scholar 

  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

    Article  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

    Article  MATH  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

    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

    Article  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

    Google Scholar 

  52. Martinet A, Galin E, Desbenoit B, Akkouche S. Procedural modeling of cracks and fractures. In: Proceedings of Shape Modelling Applications. 2004, 346–349

    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

    Google Scholar 

  54. Hsieh H H, Tai WK. 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

    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

    Article  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

    Google Scholar 

  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

    Google Scholar 

  58. Liu S G, Chen D. Computer simulation of batik printing patterns with cracks. Textile Research Journal, 2015, 85(18): 1972–1984

    Article  Google Scholar 

  59. Gross D, Seelig T. Fracture Mechanics: With an Introduction to Micromechanics. Springer Science & Business Media, 2011

    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

    Article  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

    Google Scholar 

  62. Freund L B. Dynamic Fracture Mechanics. Cambridge: Cambridge University Press, 1990

    Book  MATH  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

    Article  MathSciNet  MATH  Google Scholar 

  64. Fung Y C. A First Course in Continuum Mechanics. Englewood Cliffs, NJ: Prentice-Hall, 1994

    Google Scholar 

  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

    Google Scholar 

  66. Iben H N. Generating Surface Crack Patterns. Dissertation for the Doctoral Degree. Berkeley: University of California, Berkeley, 2007

    Google Scholar 

Download references

Acknowledgements

The authors are sincerely grateful to the referees and anonymous reviewers for their helpful comments and suggestions. The authors also would like to thank the authors of the original studies included in this analysis. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 61572078 and 61170203) and Program for New Century Excellent Talents in University (NCET-13-0051) and Beijing Natural Science Foundation (4152027). The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. College of Computer Science and Technology, Beijing Normal University, Beijing, 100875, China

    Juan Zhang, Fuqing Duan, Mingquan Zhou, Xuesong Wang, Zhongke Wu, Youliang Huang, Guoguang Du, Shaolong Liu, Pengbo Zhou & Xiangang Shang

  2. College of Art and Communication, Beijing Normal University, Beijing, 100875, China

    Pengbo Zhou

  3. School of Electronics Engineering and Computer Science, Peking University, Beijing, 100871, China

    Dongcan Jiang

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  1. Juan Zhang
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Correspondence to Fuqing Duan or Mingquan Zhou.

Additional information

Juan Zhang received the BS and MS degrees in software engineering from Northwest University, China in 2006 and 2009, respectively. She is a PhD candidate in computer application technology at College of Information Science and Technology, Beijing Normal University, China. Her research interests are computer graphics and virtual reality.

Fuqing Duan received the BS and MS degrees in mathematics from Northwest University, China in 1995 and 1998, respectively, and the PhD degree in pattern recognition from the National Laboratory of Pattern Recognition, China in 2006. He is a professor with the College of Information Science and Technology, Beijing Normal University, China. His current research interests include 3D face reconstruction, skull identification, and machine learning and applications. He has authored more than 80 conference and journal articles on related topics.

Mingquan Zhou is a full professor and PhD student supervisor with the College of Information Science and Technology, Beijing Normal University (BNU), China. He is also the director of Engineering Research Center for Virtual Reality Applications, MOE, China and the director of Key Laboratory of Digital Protection and Virtual Reality for Cultural Heritage, BNU. His research interests are computer graphics and virtual reality.

Dongcan Jiang received the BS degree in computer science and technology fromBeijing Normal University, China in 2014. She is a master student in Department of Computer Science, Peking University, China. Her interests are computer graphics, search engine, and Web mining.

Xuesong Wang received the BS and MS degrees in computer software and theory from Northwest University, China in 1999 and 2002, respectively, and the PhD degree in educational technology from Beijing Normal University, China in 2010. His research interests include image processing, virtual reality, information retrieval, and knowledge engineering.

Zhongke Wu is a full professor and the PhD student supervisor with the College of Information Science and Technology, Beijing Normal University (BNU), China. Prior to joining BNU, he was with Nanyang Technological University, Singapore, the Institute National de Recherche en Informatique et en Automatique, France, the Institute of High Performance Computing, Singapore, and the Institute of Software, Chinese Academy of Sciences, China from 1995 to 2006. His research interests are image processing and computer graphics.

Youliang Huang received the ME degree in computer application technology from Beijing Forestry University, China in 2009. He is a PhD candidate in computer application technology at College of Information Science and Technology, Beijing Normal University, China. His research interests are virtual reality, medical image processing, and biological engineering.

Guoguang Du is a PhD candidate in Beijing Key Laboratory of Digital Protection and Virtual Reality for Cultural Heritage, College of Information Science and Technology, Beijing Normal University, China. His research interests are 3D reconstruction, digital geometry processing, virtual reality, and the application areas mainly focus on the digital protection of cultural heritage.

Shaolong Liu is a PhD candidate in computer application technology at College of Information Science and Technology, Beijing Normal University, Beijing, China. His research interests include virtual reality, human computer interaction, and digital art.

Pengbo Zhou received the MS degree in applied mathematics from University of South Brittany, France in 2010. He is a PhD candidate in computer application technology at College of Information Science and Technology, Beijing Normal University, China. His research interests include image processing and virtual reality.

Xiangang Shang received the ME degree in control engineering and control theory from Shandong University of Science and Technology, China in 2005. He is a PhD candidate in computer application technology at College of Information Science and Technology, Beijing Normal University, China. His research interests include medical image processing and virtual reality.

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Zhang, J., Duan, F., Zhou, M. et al. Stable and realistic crack pattern generation using a cracking node method. Front. Comput. Sci. 12, 777–797 (2018). https://doi.org/10.1007/s11704-016-5511-9

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