“A material point method for thin shells with frictional contact” by Guo, Han, Fu, Gast, Tamstorf, et al. …

  • ©Qi Guo, Xuchen Han, Chuyuan Fu, Theodore Gast, Rasmus Tamstorf, and Joseph Teran



Entry Number: 147

Session Title:

    Disorder Matter: From Shells to Rods and Grains


    A material point method for thin shells with frictional contact




    We present a novel method for simulation of thin shells with frictional contact using a combination of the Material Point Method (MPM) and subdivision finite elements. The shell kinematics are assumed to follow a continuum shell model which is decomposed into a Kirchhoff-Love motion that rotates the mid-surface normals followed by shearing and compression/extension of the material along the mid-surface normal. We use this decomposition to design an elastoplastic constitutive model to resolve frictional contact by decoupling resistance to contact and shearing from the bending resistance components of stress. We show that by resolving frictional contact with a continuum approach, our hybrid Lagrangian/Eulerian approach is capable of simulating challenging shell contact scenarios with hundreds of thousands to millions of degrees of freedom. Without the need for collision detection or resolution, our method runs in a few minutes per frame in these high resolution examples. Furthermore we show that our technique naturally couples with other traditional MPM methods for simulating granular and related materials.


    1. T. Belytschko, W. Liu, B. Moran, and K. Elkhodary. 2013. Nonlinear finite elements for continua and structures. John Wiley and sons.Google Scholar
    2. J. Bonet and R. Wood. 2008. Nonlinear continuum mechanics for finite element analysis. Cambridge University Press.Google Scholar
    3. 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 ScholarDigital Library
    4. R. Bridson, S. Marino, and R. Fedkiw. 2003. Simulation of Clothing with Folds and Wrinkles. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim (SCA ’03). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 28–36. Google ScholarDigital Library
    5. Edwin Catmull and James Clark. 1978. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-aided design 10, 6 (1978), 350–355.Google Scholar
    6. B. Chen and M. Govindaraj. 1995. A Physically Based Model of Fabric Drape Using Flexible Shell Theory. Text Res J 65, 6 (1995), 324–330.Google ScholarCross Ref
    7. F. Cirak and M. Ortiz. 2001. Fully C1-conforming subdivision elements for finite deformation thin-shell analysis. Int J Num Meth Eng 51, 7 (2001), 813–833.Google ScholarCross Ref
    8. F. Cirak, M. Ortiz, and P. Schröder. 2000. Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Int J Num Meth Eng 47, 12 (2000), 2039–2072.Google ScholarCross Ref
    9. David Clyde. 2017. Numerical Subdivision Surfaces for Simulation and Data Driven Modeling of Woven Cloth. Ph.D. Dissertation. University of California, Los Angeles.Google Scholar
    10. D. Clyde, J. Teran, and R. Tamstorf. 2017. Modeling and data-driven parameter estimation for woven fabrics. In Proc ACM SIGGRAPH/Eurograp Symp Comp Anim (SCA ’17). ACM, New York, NY, USA, 17:1–17:11. Google ScholarDigital Library
    11. J. Collier, B. Collier, G. O’Toole, and S. Sargand. 1991. Drape prediction by means of finite-element analysis. J Textile Inst 82, 1 (1991), 96–107.Google ScholarCross Ref
    12. 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 ScholarDigital Library
    13. R. Echter, B. Oesterle, and M. Bischoff. 2013. A hierarchic family of isogeometric shell finite elements. Comp Meth App Mech Eng 254 (2013), 170 — 180.Google ScholarCross Ref
    14. J. Eischen, S. Deng, and T. Clapp. 1996. Finite-element modeling and control of flexible fabric parts. IEEE Comp Graph App 16, 5 (1996), 71–80. Google ScholarDigital Library
    15. O. Etzmuss, J. Gross, and W. Strasser. 2003a. Deriving a particle system from continuum mechanics for the animation of deformable objects. IEEE Trans Vis Comp Graph 9, 4 (Oct. 2003), 538–550. Google ScholarDigital Library
    16. O. Etzmuss, M. Keckeisen, and W. Strasser. 2003b. A fast finite element solution for cloth modeling. In Proc 11th Vac Conf Comp Graph App (PG ’03). IEEE Computer Society, Washington, DC, USA, 244–254. Google ScholarDigital Library
    17. 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 ScholarDigital Library
    18. Y. Fan, J. Litven, and D. Pai. 2014. Active Volumetric Musculoskeletal Systems. ACM Trans Graph 33, 4 (2014), 152:1–152:9. Google ScholarDigital Library
    19. 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 ScholarDigital Library
    20. L. Gan, N. Ly, and G. Steven. 1995. A study of fabric deformation using nonlinear finite elements. Text Res J 65, 11 (1995), 660–668.Google ScholarCross Ref
    21. Y. Gingold, A. Secord, J. Han, E. Grinspun, and D. Zorin. 2004. A discrete model for inelastic deformation of thin shells. In Tech Report: Courant Institute of Mathematical Sciences, New York University.Google Scholar
    22. A. Golas, R. Narain, and M. Lin. 2014. Continuum modeling of crowd turbulence. Phys Rev E 90 (2014), 042816. Issue 4.Google ScholarCross Ref
    23. O. Gonzalez and A. Stuart. 2008. A first course in continuum mechanics. Cambridge University Press.Google Scholar
    24. E. Grinspun, F. Cirak, P. Schröder, and M. Ortiz. 1999. Non-linear mechanics and collisions for subdivision surfaces. Technical report, Caltech Multi-Res Modeling Group (1999).Google Scholar
    25. E. Grinspun, A. Hirani, M. Desbrun, and P. Schröder. 2003. Discrete Shells. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim (SCA ’03). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 62–67. Google ScholarDigital Library
    26. E. Grinspun, P. Krysl, and P. Schröder. 2002. CHARMS: A simple framework for adaptive simulation. ACM Trans Graph 21, 3 (2002), 281–290. Google ScholarDigital Library
    27. E. Grinspun and P. Schröder. 2001. Normal bounds for subdivision-surface interference detection. In IEEE Viz. 333–340. Google ScholarDigital Library
    28. Q. Guo, X. Han, C. Fu, T. Gast, R. Tamstorf, and J. Teran. 2018. A Material Point Method for Thin Shells with Frictional Contact: Supplementary Technical Document. (2018).Google Scholar
    29. D. Harmon, E. Vouga, R. Tamstorf, and E. Grinspun. 2008. Robust Treatment of Simultaneous Collisions. ACM Trans Graph 27, 3 (2008), 23:1–23:4. Google ScholarDigital Library
    30. C. Jiang, T. Gast, and J. Teran. 2017. Anisotropic elastoplasticity for cloth, knit and hair frictional contact. ACM Trans Graph 36, 4 (2017). Google ScholarDigital Library
    31. 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 ScholarDigital Library
    32. C. Kane, E. Repetto, M. Ortiz, and J. Marsden. 1999. Finite element analysis of nonsmooth contact. Comp Meth App Mech Eng 180, 1 (1999), 1 — 26.Google ScholarCross Ref
    33. P. Kaufmann, S. Martin, M. Botsch, and M. Gross. 2009. Implementation of discontinuous Galerkin Kirchhoff-Love shells. ETH Zurich, Department of Computer Science, Technical Report No. 622 (2009).Google Scholar
    34. J. Kiendl, K. Bletzinger, J. Linhard, and R. Wuchner. 2009. Isogeometric shell analysis with Kirchhoff-Love elements. Comp Meth App Mech Eng 198, 49 (2009), 3902 — 3914.Google ScholarCross Ref
    35. J. Kiendl, M. Hsu, M. Wu, and A. Reali. 2015. Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials. Comp Meth App Mech Eng 291, Supplement C (2015), 280–303.Google ScholarCross Ref
    36. 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 ScholarDigital Library
    37. 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 ScholarDigital Library
    38. D. Li, S. Sueda, D. Neog, and D. Pai. 2013. Thin Skin Elastodynamics. ACM Trans Graph 32, 4 (2013), 49:1–49:10. Google ScholarDigital Library
    39. Q. Long, P. Bornemann, and F. Cirak. 2012. Shear flexible subdivision shells. Int J Num Meth Eng 90, 13 (2012), 1549–1577.Google ScholarCross Ref
    40. L. De Lorenzis, P. Wriggers, and T. Hughes. 2014. Isogeometric contact: a review. GAMM-Mitteilungen 37, 1 (2014), 85–123.Google ScholarCross Ref
    41. J. Lu. 2011. Isogeometric contact analysis: Geometric basis and formulation for frictionless contact. Comp Meth App Mech Eng 200, 5 (2011), 726 — 741.Google ScholarCross Ref
    42. J. Lu and C. Zheng. 2014. Dynamic cloth simulation by isogeometric analysis. Comp Meth App Mech Eng 268, Supplement C (2014), 475 — 493.Google ScholarCross Ref
    43. X. Man and C. Swan. 2007. A mathematical modeling framework for analysis of functional clothing. J Eng Fibers Fabrics 2, 3 (2007), 10–28. http://www.jeffjournal.org/papers/Volume2/Swan(6-14R1).pdfGoogle Scholar
    44. S. Martin, P. Kaufmann, M. Botsch, E. Grinspun, and M. Gross. 2010. Unified simulation of elastic rods, shells, and solids. ACM Trans Graph 29, 4 (2010), 39:1–39:10. Google ScholarDigital Library
    45. M. Matzen and M. Bischoff. 2016. A weighted point-based formulation for isogeometric contact. Comp Meth App Mech Eng 308, Supplement C (2016), 73–95.Google ScholarCross Ref
    46. M. Matzen, T. Cichosz, and M. Bischoff. 2013. A point to segment contact formulation for isogeometric, NURBS based finite elements. Comp Meth App Mech Eng 255, Supplement C (2013), 27–39.Google ScholarCross Ref
    47. 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 ScholarDigital Library
    48. R. Mindlin. 1951. Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J App Mech 18 (1951), 31–38.Google ScholarCross Ref
    49. 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 ScholarDigital Library
    50. R. Narain, A. Golas, and M. Lin. 2010. Free-flowing granular materials with two-way solid coupling. ACM Trans Graph 29, 6 (2010), 173:1–173:10. Google ScholarDigital Library
    51. R. Narain, T. Pfaff and J. O’Brien. 2013. Folding and crumpling adaptive sheets. ACM Trans Graph 32, 4 (July 2013), 51:1–51:8. Google ScholarDigital Library
    52. L. Noels and R. Radovitzky. 2008. A new discontinuous Galerkin method for Kirchhoff-Love shells. Comp Meth App Mech Eng 197 (2008), 2901–2929.Google ScholarCross Ref
    53. M. Otaduy, R. Tamstorf, D. Steinemann, and M. Gross. 2009. Implicit Contact Handling for Deformable Objects. Comp Graph Forum 28, 2 (2009).Google Scholar
    54. 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 ScholarDigital Library
    55. J. Simo and D. Fox. 1989. On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization. Comp Meth App Mech Eng 72, 3 (1989), 267 — 304. Google ScholarDigital Library
    56. Jos Stam. 1998. Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values. In Proceedings of the 25th annual conference on Computer graphics and interactive techniques. ACM, 395–404. Google ScholarDigital Library
    57. 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 ScholarDigital Library
    58. M. Tang, H. Wang, L. Tang, R. Tong, and D. Manocha. 2016. CAMA: Contact-Aware Matrix Assembly with Unified Collision Handling for GPU-based Cloth Simulation. Comp Graph Forum 35, 2 (2016), 511–521.Google ScholarCross Ref
    59. A. Temizer, P. Wriggers, and T. Hughes. 2011. Contact treatment in isogeometric analysis with NURBS. Comp Meth App Mech Eng 200, 9 (2011), 1100 — 1112.Google ScholarCross Ref
    60. Y. Teng, D. Levin, and T. Kim. 2016. Eulerian Solid-fluid Coupling. ACM Trans Graph 35, 6 (2016), 200:1–200:8. Google ScholarDigital Library
    61. D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer. 1987. Elastically Deformable Models. SIGGRAPH Comput Graph 21, 4 (1987), 205–214. Google ScholarDigital Library
    62. B. Thomaszewski, M. Wacker, and W. Strasser. 2006. A consistent bending model for cloth simulation with corotational subdivision finite elements. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim. Eurographics Association, 107–116. Google ScholarDigital Library
    63. A. Wawrzinek, K. Hildebrandt, and K. Polthier. 2011. Koiter’s thin shells on Catmull-Clark limit surfaces. In Vision, Modeling, and Visualization (2011), Peter Eisert, Joachim Hornegger, and Konrad Polthier (Eds.). The Eurographics Association.Google Scholar
    64. 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 ScholarDigital Library
    65. Y. Zhu and R. Bridson. 2005. Animating sand as a fluid. ACM Trans Graph 24, 3 (2005), 965–972. Google ScholarDigital Library

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