Skip to main content
Top

2019 | OriginalPaper | Chapter

Integrating Peridynamics with Material Point Method for Elastoplastic Material Modeling

Authors : Yao Lyu, Jinglu Zhang, Jian Chang, Shihui Guo, Jian Jun Zhang

Published in: Advances in Computer Graphics

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We present a novel integral-based Material Point Method (MPM) using state based peridynamics structure for modeling elastoplastic material and fracture animation. Previous partial derivative based MPM studies face challenges of underlying instability issues of particle distribution and the complexity of modeling discontinuities. To alleviate these problems, we integrate the strain metric in the basic elastic constitutive model by using material point truss structure, which outweighs differential-based methods in both accuracy and stability. To model plasticity, we incorporate our constitutive model with deviatoric flow theory and a simple yield function. It is straightforward to handle the problem of cracking in our hybrid framework. Our method adopts two time integration ways to update crack interface and fracture inner parts, which overcome the unnecessary grid duplication. Our work can create a wide range of material phenomenon including elasticity, plasticity, and fracture. Our framework provides an attractive method for producing elastoplastic materials and fracture with visual realism and high stability.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
2.
go back to reference Bottcher, G., Allerkamp, D., Wolter, F.E.: Virtual reality systems modelling haptic two-finger contact with deformable physical surfaces. In: 2007 International Conference on Cyberworlds (CW 2007), pp. 292–299. IEEE (2007) Bottcher, G., Allerkamp, D., Wolter, F.E.: Virtual reality systems modelling haptic two-finger contact with deformable physical surfaces. In: 2007 International Conference on Cyberworlds (CW 2007), pp. 292–299. IEEE (2007)
3.
go back to reference Chen, W., Zhu, F., Zhao, J., Li, S., Wang, G.: Peridynamics-based fracture animation for elastoplastic solids. In: Computer Graphics Forum, vol. 37, pp. 112–124. Wiley Online Library (2018) Chen, W., Zhu, F., Zhao, J., Li, S., Wang, G.: Peridynamics-based fracture animation for elastoplastic solids. In: Computer Graphics Forum, vol. 37, pp. 112–124. Wiley Online Library (2018)
4.
go back to reference Gao, M., Tampubolon, A.P., Jiang, C., Sifakis, E.: An adaptive generalized interpolation material point method for simulating elastoplastic materials. ACM Trans. Graph. (TOG) 36(6), 223 (2017) Gao, M., Tampubolon, A.P., Jiang, C., Sifakis, E.: An adaptive generalized interpolation material point method for simulating elastoplastic materials. ACM Trans. Graph. (TOG) 36(6), 223 (2017)
5.
go back to reference Gerszewski, D., Bhattacharya, H., Bargteil, A.W.: A point-based method for animating elastoplastic solids. In: Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 133–138. ACM (2009) Gerszewski, D., Bhattacharya, H., Bargteil, A.W.: A point-based method for animating elastoplastic solids. In: Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 133–138. ACM (2009)
6.
go back to reference He, X., Wang, H., Wu, E.: Projective peridynamics for modeling versatile elastoplastic materials. IEEE Trans. Vis. Comput. Graph. 24(9), 2589–2599 (2018)CrossRef He, X., Wang, H., Wu, E.: Projective peridynamics for modeling versatile elastoplastic materials. IEEE Trans. Vis. Comput. Graph. 24(9), 2589–2599 (2018)CrossRef
7.
go back to reference Homel, M.A., Herbold, E.B.: Field-gradient partitioning for fracture and frictional contact in the material point method. Int. J. Num. Methods Eng. 109(7), 1013–1044 (2017)MathSciNetCrossRef Homel, M.A., Herbold, E.B.: Field-gradient partitioning for fracture and frictional contact in the material point method. Int. J. Num. Methods Eng. 109(7), 1013–1044 (2017)MathSciNetCrossRef
8.
go back to reference Jiang, C., Gast, T., Teran, J.: Anisotropic elastoplasticity for cloth, knit and hair frictional contact. ACM Trans. Graph. (TOG) 36(4), 152 (2017) Jiang, C., Gast, T., Teran, J.: Anisotropic elastoplasticity for cloth, knit and hair frictional contact. ACM Trans. Graph. (TOG) 36(4), 152 (2017)
9.
go back to reference Jiang, C., Schroeder, C., Selle, A., Teran, J., Stomakhin, A.: The affine particle-in-cell method. ACM Trans. Graph. (TOG) 34(4), 51 (2015)MATH Jiang, C., Schroeder, C., Selle, A., Teran, J., Stomakhin, A.: The affine particle-in-cell method. ACM Trans. Graph. (TOG) 34(4), 51 (2015)MATH
10.
go back to reference Jiang, C., Schroeder, C., Teran, J., Stomakhin, A., Selle, A.: The material point method for simulating continuum materials. In: ACM SIGGRAPH 2016 Courses, p. 24. ACM (2016) Jiang, C., Schroeder, C., Teran, J., Stomakhin, A., Selle, A.: The material point method for simulating continuum materials. In: ACM SIGGRAPH 2016 Courses, p. 24. ACM (2016)
11.
go back to reference Levin, D.I., Litven, J., Jones, G.L., Sueda, S., Pai, D.K.: Eulerian solid simulation with contact. ACM Trans. Graph. (TOG) 30(4), 36 (2011)CrossRef Levin, D.I., Litven, J., Jones, G.L., Sueda, S., Pai, D.K.: Eulerian solid simulation with contact. ACM Trans. Graph. (TOG) 30(4), 36 (2011)CrossRef
12.
go back to reference Levine, J.A., Bargteil, A.W., Corsi, C., Tessendorf, J., Geist, R.: A peridynamic perspective on spring-mass fracture. In: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 47–55. Eurographics Association (2014) Levine, J.A., Bargteil, A.W., Corsi, C., Tessendorf, J., Geist, R.: A peridynamic perspective on spring-mass fracture. In: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 47–55. Eurographics Association (2014)
13.
go back to reference Liang, Y., Benedek, T., Zhang, X., Liu, Y.: Material point method with enriched shape function for crack problems. Comput. Methods Appl. Mech. Eng. 322, 541–562 (2017)MathSciNetCrossRef Liang, Y., Benedek, T., Zhang, X., Liu, Y.: Material point method with enriched shape function for crack problems. Comput. Methods Appl. Mech. Eng. 322, 541–562 (2017)MathSciNetCrossRef
14.
go back to reference O’brien, J.F., Bargteil, A.W., Hodgins, J.K.: Graphical modeling and animation of ductile fracture. ACM Trans. Graph. (TOG) 21, 291–294 (2002) O’brien, J.F., Bargteil, A.W., Hodgins, J.K.: Graphical modeling and animation of ductile fracture. ACM Trans. Graph. (TOG) 21, 291–294 (2002)
15.
go back to reference Salsedo, F., et al.: Architectural design of the HAPTEX system. In: submitted to the Proceedings of this Conference (2005) Salsedo, F., et al.: Architectural design of the HAPTEX system. In: submitted to the Proceedings of this Conference (2005)
16.
go back to reference Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48(1), 175–209 (2000)MathSciNetCrossRef Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48(1), 175–209 (2000)MathSciNetCrossRef
17.
go back to reference Silling, S.A., Askari, A.: Peridynamic model for fatigue cracking. SAND2014-18590. Sandia National Laboratories, Albuquerque (2014) Silling, S.A., Askari, A.: Peridynamic model for fatigue cracking. SAND2014-18590. Sandia National Laboratories, Albuquerque (2014)
18.
go back to reference Silling, S.A., Epton, M., Weckner, O., Xu, J., Askari, E.: Peridynamic states and constitutive modeling. J. Elast. 88(2), 151–184 (2007)MathSciNetCrossRef Silling, S.A., Epton, M., Weckner, O., Xu, J., Askari, E.: Peridynamic states and constitutive modeling. J. Elast. 88(2), 151–184 (2007)MathSciNetCrossRef
19.
go back to reference Silling, S.A., Askari, A.: Practical peridynamics. Technical report, Sandia National Lab. (SNL-NM), Albuquerque, NM, United States (2014) Silling, S.A., Askari, A.: Practical peridynamics. Technical report, Sandia National Lab. (SNL-NM), Albuquerque, NM, United States (2014)
20.
go back to reference Stomakhin, A., Howes, R., Schroeder, C., Teran, J.M.: Energetically consistent invertible elasticity. In: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 25–32. Eurographics Association (2012) Stomakhin, A., Howes, R., Schroeder, C., Teran, J.M.: Energetically consistent invertible elasticity. In: Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 25–32. Eurographics Association (2012)
21.
go back to reference Stomakhin, A., Schroeder, C., Chai, L., Teran, J., Selle, A.: A material point method for snow simulation. ACM Trans. Graph. (TOG) 32(4), 102 (2013)CrossRef Stomakhin, A., Schroeder, C., Chai, L., Teran, J., Selle, A.: A material point method for snow simulation. ACM Trans. Graph. (TOG) 32(4), 102 (2013)CrossRef
22.
go back to reference Stomakhin, A., Teran, J., Selle, A.: Augmented material point method for simulating phase changes and varied materials, 2 Jul 2015. US Patent App. 14/323,798 Stomakhin, A., Teran, J., Selle, A.: Augmented material point method for simulating phase changes and varied materials, 2 Jul 2015. US Patent App. 14/323,798
23.
go back to reference Sulsky, D., Chen, Z., Schreyer, H.L.: A particle method for history-dependent materials. Comput. Methods Appl. Mech. Eng. 118(1–2), 179–196 (1994)MathSciNetCrossRef Sulsky, D., Chen, Z., Schreyer, H.L.: A particle method for history-dependent materials. Comput. Methods Appl. Mech. Eng. 118(1–2), 179–196 (1994)MathSciNetCrossRef
24.
go back to reference Sulsky, D., Zhou, S.J., Schreyer, H.L.: Application of a particle-in-cell method to solid mechanics. Comput. Phys. Commun. 87(1–2), 236–252 (1995)CrossRef Sulsky, D., Zhou, S.J., Schreyer, H.L.: Application of a particle-in-cell method to solid mechanics. Comput. Phys. Commun. 87(1–2), 236–252 (1995)CrossRef
25.
go back to reference Tampubolon, A.P., Gast, T., Klár, G., Fu, C., Teran, J., Jiang, C., Museth, K.: Multi-species simulation of porous sand and water mixtures. ACM Trans. Graph. (TOG) 36(4), 105 (2017)CrossRef Tampubolon, A.P., Gast, T., Klár, G., Fu, C., Teran, J., Jiang, C., Museth, K.: Multi-species simulation of porous sand and water mixtures. ACM Trans. Graph. (TOG) 36(4), 105 (2017)CrossRef
26.
go back to reference Terzopoulos, D., Fleischer, K.: Modeling inelastic deformation: viscolelasticity, plasticity, fracture. In: ACM SIGGRAPH Computer Graphics, vol. 22, pp. 269–278. ACM (1988) Terzopoulos, D., Fleischer, K.: Modeling inelastic deformation: viscolelasticity, plasticity, fracture. In: ACM SIGGRAPH Computer Graphics, vol. 22, pp. 269–278. ACM (1988)
27.
go back to reference Terzopoulos, D., Platt, J., Barr, A., Fleischer, K.: Elastically deformable models. ACM SIGGRAPH Comput. Graph. 21(4), 205–214 (1987)CrossRef Terzopoulos, D., Platt, J., Barr, A., Fleischer, K.: Elastically deformable models. ACM SIGGRAPH Comput. Graph. 21(4), 205–214 (1987)CrossRef
28.
go back to reference Xu, L., He, X., Chen, W., Li, S., Wang, G.: Reformulating hyperelastic materials with peridynamic modeling. In: Computer Graphics Forum, vol. 37, pp. 121–130. Wiley Online Library (2018) Xu, L., He, X., Chen, W., Li, S., Wang, G.: Reformulating hyperelastic materials with peridynamic modeling. In: Computer Graphics Forum, vol. 37, pp. 121–130. Wiley Online Library (2018)
29.
go back to reference Zhu, B., Lee, M., Quigley, E., Fedkiw, R.: Codimensional non-Newtonian fluids. ACM Trans. Graph. (TOG) 34(4), 115 (2015)MATH Zhu, B., Lee, M., Quigley, E., Fedkiw, R.: Codimensional non-Newtonian fluids. ACM Trans. Graph. (TOG) 34(4), 115 (2015)MATH
Metadata
Title
Integrating Peridynamics with Material Point Method for Elastoplastic Material Modeling
Authors
Yao Lyu
Jinglu Zhang
Jian Chang
Shihui Guo
Jian Jun Zhang
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-22514-8_19

Premium Partner