Revisiting integration in the material point method: a scheme for easier separation and less dissipation

Abstract

The material point method (MPM) recently demonstrated its efficacy at simulating many materials and the coupling between them on a massive scale. However, in scenarios containing debris, MPM manifests more dissipation and numerical viscosity than traditional Lagrangian methods. We have two observations from carefully revisiting existing integration methods used in MPM. First, nearby particles would end up with smoothed velocities without recovering momentum for each particle during the particle-grid-particle transfers. Second, most existing integrators assume continuity in the entire domain and advect particles by directly interpolating the positions from deformed nodal positions, which would trap the particles and make them harder to separate. We propose an integration scheme that corrects particle positions at each time step. We demonstrate our method's effectiveness with several large-scale simulations involving brittle materials. Our approach effectively reduces diffusion and unphysical viscosity compared to traditional integrators.

References

1. Ryoichi Ando, Nils Thurey, and Reiji Tsuruno. 2012. Preserving fluid sheets with adaptively sampled anisotropic particles. IEEE Transactions on Visualization and Computer Graphics 18, 8 (2012), 1202--1214.
2. David Baraff and Andrew Witkin. 1998. Large steps in cloth simulation. In Proceedings of the 25th annual conference on Computer graphics and interactive techniques. 43--54.
3. Christopher Batty, Florence Bertails, and Robert Bridson. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans. on Graph. (TOG) (2007).
4. Miklós Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, and Eitan Grinspun. 2008. Discrete Elastic Rods. ACM Trans. on Graph. (TOG) (aug 2008).
5. Florence Bertails, Basile Audoly, Marie-Paule Cani, Bernard Querleux, Frédéric Leroy, and Jean-Luc Lévêque. 2006. Super-helices for predicting the dynamics of natural hair. ACM Trans. on Graph. (TOG) 25, 3 (2006), 1180--1187.
6. Javier Bonet and Richard D Wood. 1997. Nonlinear continuum mechanics for finite element analysis. Cambridge university press.
7. Landon Boyd and Robert Bridson. 2012. MultiFLIP for energetic two-phase fluid simulation. ACM Trans. on Graph. (TOG) 31, 2 (2012), 1--12.
8. Jeremiah U Brackbill and Hans M Ruppel. 1986. FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. Journal of Computational physics 65, 2 (1986), 314--343.
9. Percy Williams Bridgman. 1949. The physics of high pressure. London: Bells and Sons.
10. Robert Bridson. 2015. Fluid simulation for computer graphics. CRC press.
11. R Bridson, S Marino, and R Fedkiw. 2003. Simulation of clothing with folds and wrinkles. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation. 28--36.
12. K Bertram Broberg. 1999. Cracks and fracture. Elsevier.
13. Xiao-Song Chen, Chen-Feng Li, Geng-Chen Cao, Yun-Tao Jiang, and Shi-Min Hu. 2020. A moving least square reproducing kernel particle method for unified multiphase continuum simulation. ACM Trans. on Graph. (TOG) 39, 6 (2020), 1--15.
14. Jens Cornelis, Markus Ihmsen, Andreas Peer, and Matthias Teschner. 2014. IISPH-FLIP for incompressible fluids. In Computer Graphics Forum, Vol. 33. Wiley Online Library, 255--262.
15. Ounan Ding, Tamar Shinar, and Craig Schroeder. 2020. Affine particle in cell method for MAC grids and fluid simulation. J. Comput. Phys. 408 (2020), 109311.
16. Daniel Charles Drucker and William Prager. 1952. Soil mechanics and plastic analysis or limit design. Quarterly of applied mathematics 10, 2 (1952), 157--165.
17. Essex Edwards and Robert Bridson. 2012. A high-order accurate particle-in-cell method. Internat. J. Numer. Methods Engrg. 90, 9 (2012), 1073--1088.
18. Yu Fang, Yuanming Hu, Shi-Min Hu, and Chenfanfu Jiang. 2018. A temporally adaptive material point method with regional time stepping. In Computer graphics forum, Vol. 37. Wiley Online Library, 195--204.
19. Florian Ferstl, Ryoichi Ando, Chris Wojtan, Rüdiger Westermann, and Nils Thuerey. 2016. Narrow band FLIP for liquid simulations. In Computer Graphics Forum, Vol. 35. Wiley Online Library, 225--232.
20. Chuyuan Fu, Qi Guo, Theodore Gast, Chenfanfu Jiang, and Joseph Teran. 2017. A polynomial particle-in-cell method. ACM Trans. on Graph. (TOG) 36, 6 (2017), 1--12.
21. Ming Gao, Andre Pradhana, Xuchen Han, Qi Guo, Grant Kot, Eftychios Sifakis, and Chenfanfu Jiang. 2018a. Animating fluid sediment mixture in particle-laden flows. ACM Trans. on Graph. (TOG) 37, 4 (2018), 1--11.
22. Ming Gao, Andre Pradhana Tampubolon, Chenfanfu Jiang, and Eftychios Sifakis. 2017. An adaptive generalized interpolation material point method for simulating elastoplastic materials. ACM Trans. on Graph. (TOG) 36, 6 (2017), 1--12.
23. Ming Gao, Xinlei Wang, Kui Wu, Andre Pradhana, Eftychios Sifakis, Cem Yuksel, and Chenfanfu Jiang. 2018b. GPU optimization of material point methods. ACM Trans. on Graph. (TOG) 37, 6 (2018), 1--12.
24. Dan Gerszewski and Adam W Bargteil. 2013. Physics-based animation of large-scale splashing liquids. ACM Trans. Graph. 32, 6 (2013), 185--1.
25. Oscar Gonzalez and Andrew M Stuart. 2008. A first course in continuum mechanics. Cambridge University Press.
26. Eitan Grinspun, Anil N Hirani, Mathieu Desbrun, and Peter Schröder. 2003. Discrete shells. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation. Citeseer, 62--67.
27. Qi Guo, Xuchen Han, Chuyuan Fu, Theodore Gast, Rasmus Tamstorf, and Joseph Teran. 2018. A material point method for thin shells with frictional contact. ACM Trans. on Graph. (TOG) 37, 4 (2018), 1--15.
28. Brian Hall. 2015. Lie groups, Lie algebras, and representations: an elementary introduction. Vol. 222. Springer.
29. Chad C Hammerquist and John A Nairn. 2017. A new method for material point method particle updates that reduces noise and enhances stability. Computer methods in applied mechanics and engineering 90 (2017), 1073--1088.
30. X. Han, T. F Gast, Q. Guo, S. Wang, C. Jiang, and J. Teran. 2019. A hybrid material point method for frictional contact with diverse materials. Proceedings of the ACM on Computer Graphics and Interactive Techniques (2019).
31. Francis Harvey Harlow, Martha Evans, and Robert D Richtmyer. 1955. A machine calculation method for hydrodynamic problems. Los Alamos Scientific Laboratory of the University of California.
32. Yuanming Hu, Yu Fang, Ziheng Ge, Ziyin Qu, Yixin Zhu, Andre Pradhana, and Chenfanfu Jiang. 2018. A moving least squares material point method with displacement discontinuity and two-way rigid body coupling. ACM Trans. on Graph. (TOG) (2018).
33. Yuanming Hu, Xinxin Zhang, Ming Gao, and Chenfanfu Jiang. 2019. On hybrid lagrangian-eulerian simulation methods: practical notes and high-performance aspects. In ACM SIGGRAPH 2019 Courses. 1--246.
34. Markus Ihmsen, Jens Cornelis, Barbara Solenthaler, Christopher Horvath, and Matthias Teschner. 2013. Implicit incompressible SPH. IEEE transactions on visualization and computer graphics 20, 3 (2013), 426--435.
35. Chenfanfu Jiang, Theodore Gast, and Joseph Teran. 2017a. Anisotropic elastoplasticity for cloth, knit and hair frictional contact. ACM Trans. on Graph. (TOG) (2017).
36. Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin. 2015. The affine particle-in-cell method. ACM Trans. on Graph. (TOG) (2015).
37. Chenfanfu Jiang, Craig Schroeder, and Joseph Teran. 2017b. An angular momentum conserving affine-particle-in-cell method. J. Comput. Phys. 338 (2017), 137--164.
38. Chenfanfu Jiang, Craig Schroeder, Joseph Teran, Alexey Stomakhin, and Andrew Selle. 2016. The material point method for simulating continuum materials. In ACM SIGGRAPH 2016 Courses. 1--52.
39. Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2010. Efficient Yarn-based Cloth with Adaptive Contact Linearization. ACM Trans. on Graph. (TOG) 29, 4, Article 105 (July 2010), 10 pages.
40. Gergely Klár, Theodore Gast, Andre Pradhana, Chuyuan Fu, Craig Schroeder, Chenfanfu Jiang, and Joseph Teran. 2016. Drucker-prager elastoplasticity for sand animation. ACM Trans. on Graph. (TOG) 35, 4 (2016), 1--12.
41. Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M Kaufman. 2020a. Incremental Potential Contact: Intersection-and Inversion-free, Large-Deformation Dynamics. ACM Trans. on Graph. (TOG) 39, 4 (2020).
42. Minchen Li, Danny M Kaufman, and Chenfanfu Jiang. 2020b. Codimensional Incremental Potential Contact. arXiv preprint arXiv:2012.04457 (2020).
43. A. McAdams, A. Selle, K. Ward, E. Sifakis, and J. Teran. 2009. Detail preserving continuum simulation of straight hair. ACM Trans. on Graph. (TOG) (2009).
44. Neil Molino, Zhaosheng Bao, and Ron Fedkiw. 2004. A virtual node algorithm for changing mesh topology during simulation. ACM Trans. on Graph. (TOG) (2004).
45. FD Murnaghan. 1944. The compressibility of media under extreme pressures. Proceedings of the national academy of sciences of the United States of America (1944).
46. James F O'Brien and Jessica K Hodgins. 1999. Graphical modeling and animation of brittle fracture. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques. 137--146.
47. Takahiro Sato, Christopher Wojtan, Nils Thuerey, Takeo Igarashi, and Ryoichi Ando. 2018. Extended narrow band FLIP for liquid simulations. In Computer Graphics Forum, Vol. 37. Wiley Online Library, 169--177.
48. Andrew Selle, Michael Lentine, and Ronald Fedkiw. 2008. A mass spring model for hair simulation. In ACM SIGGRAPH 2008 papers. 1--11.
49. Eftychios Sifakis and Jernej Barbic. 2012. FEM simulation of 3D deformable solids: a practitioner's guide to theory, discretization and model reduction. In ACM SIGGRAPH 2012 courses. 1--50.
50. Juan C Simo. 1988. A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation. Computer methods in applied mechanics and engineering (1988).
51. A. Stomakhin, C. Schroeder, L. Chai, J. Teran, and A. Selle. 2013. A material point method for snow simulation. ACM Trans. on Graph. (TOG) (2013).
52. Alexey Stomakhin, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, and Andrew Selle. 2014. Augmented MPM for phase-change and varied materials. ACM Trans. on Graph. (TOG) 33, 4 (2014), 1--11.
53. Alexey Stomakhin and Andrew Selle. 2017. Fluxed animated boundary method. ACM Trans. on Graph. (TOG) 36, 4 (2017), 1--8.
54. Deborah Sulsky, Zhen Chen, and Howard L Schreyer. 1994. A particle method for history-dependent materials. Computer methods in applied mechanics and engineering 118, 1-2 (1994), 179--196.
55. Deborah Sulsky, Shi-Jian Zhou, and Howard L Schreyer. 1995. Application of a particle-in-cell method to solid mechanics. Computer physics communications (1995).
56. Andre Pradhana Tampubolon, Theodore Gast, Gergely Klár, Chuyuan Fu, Joseph Teran, Chenfanfu Jiang, and Ken Museth. 2017. Multi-species simulation of porous sand and water mixtures. ACM Trans. on Graph. (TOG) 36, 4 (2017), 1--11.
57. Kiwon Um, Seungho Baek, and JungHyun Han. 2014. Advanced hybrid particle-grid method with sub-grid particle correction. In Computer Graphics Forum, Vol. 33. Wiley Online Library, 209--218.
58. Joshuah Wolper, Yu Fang, Minchen Li, Jiecong Lu, Ming Gao, and Chenfanfu Jiang. 2019. CD-MPM: Continuum damage material point methods for dynamic fracture animation. ACM Trans. on Graph. (TOG) 38, 4 (2019), 1--15.
59. Tao Yang, Jian Chang, Ming C Lin, Ralph R Martin, Jian J Zhang, and Shi-Min Hu. 2017. A unified particle system framework for multi-phase, multi-material visual simulations. ACM Trans. on Graph. (TOG) 36, 6 (2017), 1--13.
60. Yonghao Yue, Breannan Smith, Peter Yichen Chen, Maytee Chantharayukhonthorn, Ken Kamrin, and Eitan Grinspun. 2018. Hybrid grains: adaptive coupling of discrete and continuum simulations of granular media. ACM Trans. on Graph. (TOG) (2018).
61. Yongning Zhu and Robert Bridson. 2005. Animating sand as a fluid. ACM Trans. on Graph. (TOG) 24, 3 (2005), 965--972.

Index Terms

• Computing methodologies

  • Computer graphics

    • Animation

      • Physical simulation