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A Hybrid Material Point Method for Frictional Contact with Diverse Materials

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Published:26 July 2019Publication History
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Abstract

We present a new hybrid Lagrangian Material Point Method for simulating elastic objects like hair, rubber, and soft tissues that utilizes a Lagrangian mesh for internal force computation and an Eulerian mesh for self collision as well as coupling with external materials. While recent Material Point Method (MPM) techniques allow for natural simulation of hyperelastic materials represented with Lagrangian meshes, they utilize an updated Lagrangian discretization where the Eulerian grid degrees of freedom are used to take variations of the potential energy. This often coarsens the degrees of freedom of the Lagrangian mesh and can lead to artifacts. We develop a hybrid approach that retains Lagrangian degrees of freedom while still allowing for natural coupling with other materials simulated with traditional MPM, e.g. sand, snow, etc. Furthermore, while recent MPM advances allow for resolution of frictional contact with codimensional simulation of hyperelasticity, they do not generalize to the case of volumetric materials. We show that our hybrid approach resolves these issues. We demonstrate the efficacy of our technique with examples that involve elastic soft tissues coupled with kinematic skeletons, extreme deformation, and coupling with multiple elastoplastic materials. Our approach also naturally allows for two-way rigid body coupling.

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References

  1. T. Belytschko, W. Liu, B. Moran, and K. Elkhodary. 2013. Nonlinear finite elements for continua and structures. John Wiley and sons.Google ScholarGoogle Scholar
  2. Miklós Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete viscous threads. In ACM Transactions on Graphics (TOG), Vol. 29. ACM, 116. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Miklós Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, and Eitan Grinspun. 2008. Discrete elastic rods. ACM transactions on graphics (TOG) 27, 3 (2008), 63. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. F. Bertails, B. Audoly, M. Cani, B. Querleux, F. Leroy, and J. Lévêque. 2006. Super-helices for Predicting the Dynamics of Natural Hair. ACM Trans Graph 25, 3 (2006), 1180--1187. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. J. Bonet and R. Wood. 2008. Nonlinear continuum mechanics for finite element analysis. Cambridge University Press.Google ScholarGoogle Scholar
  6. J. Brackbill and H. Ruppel. 1986. FLIP: A method for adaptively zoned, Particle-In-Cell calculations of fluid flows in two dimensions. J Comp Phys 65 (1986), 314--343. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. R. Bridson, R. Fedkiw, and J. Anderson. 2002. Robust Treatment of Collisions, Contact and Friction for Cloth Animation. ACM Trans Graph 21, 3 (2002), 594--603. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. G. Daviet and F. Bertails-Descoubes. 2016. A Semi-implicit Material Point Method for the Continuum Simulation of Granular Materials. ACM Trans Graph 35, 4 (2016), 102:1--102:13. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Y. Fan, J. Litven, D. Levin, and D. Pai. 2013. Eulerian-on-lagrangian Simulation. ACM Trans Graph 32, 3 (2013), 22:1--22:9. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Y. Fan, J. Litven, and D. Pai. 2014. Active Volumetric Musculoskeletal Systems. ACM Trans Graph 33, 4 (2014), 152:1--152:9. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Y. Fang, Y. Hu, S. Hu, and C. Jiang. 2018. A temporally adaptive material point method with regional time stepping. In Computer Graph Forum, Vol. 37. Wiley Online Library, 195--204.Google ScholarGoogle Scholar
  12. Y. Fei, C. Batty, E. Grinspun, and C. Zheng. 2018. A multi-scale model for simulating liquid-fabric interactions. ACM Trans Graph 37, 4 (2018), 51:1--51:16. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. C. Fu, Q. Guo, T. Gast, C.Jiang, and J. Teran. 2017. A Polynomial Particle-in-cell Method. ACM Trans Graph 36, 6 (Nov. 2017), 222:1--222:12. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. M. Gao, A. Pradhana, X. Han, Q. Guo, G. Kot, E. Sifakis, and C.Jiang. 2018a. Animating fluid sediment mixture in particle-laden flows. ACM Trans Graph 37, 4 (2018), 149:1--149:11. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. M. Gao, A. Tampubolon, C. Jiang, and E. Sifakis. 2017. An adaptive generalized interpolation material point method for simulating elastoplastic materials. ACM Trans Graph 36, 6 (2017), 223:1--223:12. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. M. Gao, X. Wang, Kui K.Wu, A. Pradhana, E. Sifakis, C. Yuksel, and C. Jiang. 2018b. GPU optimization of material point methods. In SIGGRAPH Asia 2018 Technical Papers (SIGGRAPH Asia '18). ACM, New York, NY, USA, Article 254, 12 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. J. Gaume, T. Gast, J. Teran, A. van Herwijnen, and C. Jiang. 2018. Dynamic anticrack propagation in snow. Nature Com 9, 1 (2018), 3047.Google ScholarGoogle ScholarCross RefCross Ref
  18. A. Golas, R. Narain, and M. Lin. 2014. Continuum modeling of crowd turbulence. Phys Rev E 90 (2014), 042816. Issue 4. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. J. E. Guilkey and J. A. Weiss. 2003. Implicit time integration for the material point method: Quantitative and algorithmic comparisons with the finite element method. Int J Numer Meth Eng 57, 9 (2003), 1323--1338.Google ScholarGoogle ScholarCross RefCross Ref
  20. Q. Guo, X. Han, C. Fu, T. Gast, R. Tamstorf, and J. Teran. 2018. A material point method for thin shells with frictional contact. ACM Trans Graph 37, 4 (2018), 147. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. C. Hammerquist and J. Nairn. 2017. A new method for material point method particle updates that reduces noise and enhances stability. Comp Meth App Mech Eng 318 (2017), 724 -- 738.Google ScholarGoogle ScholarCross RefCross Ref
  22. F. Harlow. 1964. The particle-in-cell method for numerical solution of problems in fluid dynamics. Meth Comp Phys 3 (1964), 319--343.Google ScholarGoogle Scholar
  23. Jan Hegemann, Chenfanfu Jiang, Craig Schroeder, and Joseph M. Teran. 2013. A Level Set Method for Ductile Fracture. In Proc ACM SIGGRAPH/Eurograp Symp Comp Anim. 193--201. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Y. Hu, Y. Fang, Z. Ge, Z. Qu, Y. Zhu, A. Pradhana, and C. Jiang. 2018. A moving least squares material point method with displacement discontinuity and two-way rigid body coupling. ACM Trans Graph 37, 4 (2018), 150:1--150:14. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. P. Huang, X. Zhang, S. Ma, and X. Huang. 2011. Contact algorithms for the material point method in impact and penetration simulation. Int J Num Meth Eng 85, 4 (2011), 498--517.Google ScholarGoogle ScholarCross RefCross Ref
  26. G. Irving, J. Teran, and R. Fedkiw. 2004. Invertible Finite Elements for Robust Simulation of Large Deformation. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim. 131--140. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. C. Jiang, T. Gast, and J. Teran. 2017. Anisotropic elastoplasticity for cloth, knit and hair frictional contact. ACM Trans Graph 36, 4 (2017), 152. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. C. Jiang, C. Schroeder, A. Selle, J. Teran, and A. Stomakhin. 2015. The Affine Particle-In-Cell Method. ACM Trans Graph 34, 4 (2015), 51:1--51:10. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Chenfanfu Jiang, Craig Schroeder, Joseph Teran, Alexey Stomakhin, and Andrew Selle. 2016. The Material Point Method for Simulating Continuum Materials. In ACM SIGGRAPH 2016 Course. 24:1--24:52. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. G. Klár, T. Gast, A. Pradhana, C. Fu, C. Schroeder, C. Jiang, and J. Teran. 2016. Drucker-prager Elastoplasticity for Sand Animation. ACM Trans Graph 35, 4 (2016), 103:1--103:12. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. D. Levin, J. Litven, G.Jones, S. Sueda, and D. Pai. 2011. Eulerian Solid Simulation with Contact. ACM Trans Graph 30, 4 (2011), 36:1--36:10. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. D. Li, S. Sueda, D. Neog, and D. Pai. 2013. Thin Skin Elastodynamics. ACM Trans Graph 32, 4 (2013), 49:1--49:10. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. A. McAdams, A. Selle, K. Ward, E. Sifakis, and J. Teran. 2009. Detail Preserving Continuum Simulation of Straight Hair. ACM Trans Graph 28, 3 (2009), 62:1--62:6. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. M. Müller, N. Chentanez, T. Kim, and M. Macklin. 2015. Air Meshes for Robust Collision Handling. ACM Trans. Graph. 34, 4 (2015), 133:1--133:9. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. R. Narain, A. Golas, S. Curtis, and M. Lin. 2009. Aggregate Dynamics for Dense Crowd Simulation. ACM Trans Graph 28, 5 (2009), 122:1--122:8. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. D. Ram, T. Gast, C. Jiang, C. Schroeder, A. Stomakhin, J. Teran, and P. Kavehpour. 2015. A material point method for viscoelastic fluids, foams and sponges. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim. 157--163. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. E. Sifakis and J. Barbic. 2012. FEM simulation of 3D deformable solids: a practitioner's guide to theory, discretization and model reduction. In ACM SIGGRAPH 2012 Courses (SIGGRAPH '12). ACM, New York, NY, USA, 20:1--20:50. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. E. Sifakis, S. Marino, and J. Teran. 2008. Globally Coupled Collision Handling Using Volume Preserving Impulses. In Proc 2008 ACM SIGGRAPH/Eurographics Symp Comp Anim. 147--153. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. E. Sifakis, T. Shinar, G. Irving, and R. Fedkiw. 2007. Hybrid simulation of deformable solids. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim. Eurographics Association, 81--90. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. A. Stomakhin, R. Howes, C. Schroeder, and J. Teran. 2012. Energetically consistent invertible elasticity. In Proc Symp Comp Anim. 25--32. Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. A. Stomakhin, C. Schroeder, L. Chai, J. Teran, and A. Selle. 2013. A Material Point Method for snow simulation. ACM Trans Graph 32, 4 (2013), 102:1--102:10. Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. A. Stomakhin, C. Schroeder, C. Jiang, L. Chai, J. Teran, and A. Selle. 2014. Augmented MPM for phase-change and varied materials. ACM Trans Graph 33, 4 (2014), 138:1--138:11. Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. D. Sulsky, Z. Chen, and H. Schreyer. 1994. A particle method for history-dependent materials. Comp Meth App Mech Eng 118, 1 (1994), 179--196.Google ScholarGoogle ScholarCross RefCross Ref
  44. A. P. Tampubolon, T. Gast, G. Klár, C. Fu, J. Teran, C. Jiang, and K. Museth. 2017. Multi-species simulation of porous sand and water mixtures. ACM Trans Graph 36, 4 (2017). Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. Y. Teng, D. Levin, and T. Kim. 2016. Eulerian Solid-fluid Coupling. ACM Trans Graph 35, 6 (2016), 200:1--200:8. Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. K. Wu and C. Yuksel. 2016. Real-time Hair Mesh Simulation. In ACM SIGGRAPH Symp Int 3D Graph Games. ACM. Google ScholarGoogle ScholarDigital LibraryDigital Library
  47. Y. Yue, B. Smith, C. Batty, C. Zheng, and E. Grinspun. 2015. Continuum foam: a material point method for shear-dependent flows. ACM Trans Graph 34, 5 (2015), 160:1--160:20. Google ScholarGoogle ScholarDigital LibraryDigital Library
  48. Y. Yue, B. Smith, P. Chen, M. Chantharayukhonthorn, K. Kamrin, and E. Grinspun. 2018. Hybrid grains: adaptive coupling of discrete and continuum simulations of granular media. ACM Trans Graph 37, 6 (2018), 283:1--283:19. Google ScholarGoogle ScholarDigital LibraryDigital Library
  49. F. Zhu, J. Zhao, S. Li, Y. Tang, and G. Wang. 2017. Dynamically enriched MPM for invertible elasticity. In Comp Graph Forum, Vol. 36. Wiley Online Library, 381--392. Google ScholarGoogle ScholarDigital LibraryDigital Library

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    • Published in

      cover image Proceedings of the ACM on Computer Graphics and Interactive Techniques
      Proceedings of the ACM on Computer Graphics and Interactive Techniques  Volume 2, Issue 2
      July 2019
      239 pages
      EISSN:2577-6193
      DOI:10.1145/3352480
      Issue’s Table of Contents

      Copyright © 2019 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 26 July 2019
      Published in pacmcgit Volume 2, Issue 2

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