“An adaptive generalized interpolation material point method for simulating elastoplastic materials” by Gao, Tampubolon, Jiang and Sifakis
Conference:
Type(s):
Title:
- An adaptive generalized interpolation material point method for simulating elastoplastic materials
Session/Category Title: Fluids in Particular
Presenter(s)/Author(s):
Abstract:
We present an adaptive Generalized Interpolation Material Point (GIMP) method for simulating elastoplastic materials. Our approach allows adaptive refining and coarsening of different regions of the material, leading to an efficient MPM solver that concentrates most of the computation resources in specific regions of interest. We propose a C1 continuous adaptive basis function that satisfies the partition of unity property and remains non-negative throughout the computational domain. We develop a practical strategy for particle-grid transfers that leverages the recently introduced SPGrid data structure for storing sparse multi-layered grids. We demonstrate the robustness and efficiency of our method on the simulation of various elastic and plastic materials. We also compare key kernel components to uniform grid MPM solvers to highlight performance benefits of our method.
References:
1. M. Aanjaneya, M. Gao, H. Liu, C. Batty, and E. Sifakis. 2017. Power Diagrams and Sparse Paged Grids for High Resolution Adaptive Liquids. ACM Trans Graph. 36, 4 (July 2017).
2. B. Adams, M. Pauly, R. Keiser, and L. Guibas. 2007. Adaptively sampled particle fluids. In ACM Trans Graph, Vol. 26. ACM, 48.
3. S. M. Andersen and L. Andersen. 2007. Material-Point Method Analysis of Bending in Elastic Beams. In Inter Conf Civil, Struct Env Eng Comp.
4. R. Ando, N. Thurey and R. Tsuruno. 2012. Preserving fluid sheets with adaptively sampled anisotropic particles. IEEE Trans Vis Comp Graph 18, 8 (2012), 1202–1214.
5. R. Ando, N. Thurey, and C. Wojtan. 2013. Highly adaptive liquid simulations on tetrahedral meshes. ACM Trans Graph 32, 4 (2013), 103:1–103:10.
6. S. G. Bardenhagen and E. M. Kober. 2004. The generalized interpolation material point method. Comp Mod in Eng and Sci 5, 6 (2004), 477–496.
7. A. Bargteil, C. Wojtan, J. Hodgins, and G. Turk. 2007. A finite element method for animating large viscoplastic flow. ACM Trans Graph 26, 3 (2007).
8. C. Batty, S. Xenos, and B. Houston. 2010. Tetrahedral Embedded Boundary Methods for Accurate and Flexible Adaptive Fluids. In Proc of Eurographics.
9. J. Bonet and R. Wood. 2008. Nonlinear continuum mechanics for finite element analysis. Cambridge University Press.
10. J. Brackbill, D. Kothe, and H. Ruppel. 1988. FLIP: A low-dissipation, PIC method for fluid flow. Comp Phys Comm 48 (1988), 25–38. Cross Ref
11. R. Bridson. 2008. Fluid simulation for Comp Graph. Taylor & Francis.
12. S. Capell, S. Green, B. Curless, Tom D., and Z. Popović. 2002. A multiresolution framework for dynamic deformations. In Proc of the 2002 ACM SIGGRAPH/Eurographics Symp on Comp Anim. ACM, 41–47.
13. N. Chentanez and M. Müller. 2011. Real-time Eulerian water simulation using a restricted tall cell grid. ACM Trans on Graph (TOG) 30, 4 (2011), 82.
14. J. M. Cohen, S. Tariq, and S. Green. 2010. Interactive fluid-particle simulation using translating Eulerian grids. In Proc of the 2010 ACM SIGGRAPH Symp on Interactive 3D Graph and Games. ACM, 15–22.
15. N. Daphalapurkar, H. Lu, D. Coker, and R. Komanduri. 2007. Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method. Int J Fract 143, 1 (2007), 79–102. Cross Ref
16. 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 (July 2016).
17. G. Debunne, M. Desbrun, A. Barr, and M-P. Cani. 1999. Interactive multiresolution Anim of deformable models. In Comp Anim and SimulationâĂŹ99. Springer, 133–144.
18. C. Dick, J. Georgii, and R. Westermann. 2011. A hexahedral multigrid approach for simulating cuts in deformable objects. IEEE Trans on Vis and Comp Graph 17, 11 (2011), 1663–1675.
19. R. E. English, L. Qiu, Y. Yu, and R. Fedkiw. 2013. Chimera grids for water simulation. In Proc of the 12th ACM SIGGRAPH/Eurographics Symp on Comp Anim. ACM, 85–94.
20. F. Ferstl, R. Ando, C. Wojtan, R. Westermann, and N. Thuerey. 2016. Narrow band FLIP for liquid simulations. In Comp Graph Forum, Vol. 35. Wiley Online Library, 225–232.
21. T. Fries, A. Byfut, A. Alizada, K. Cheng, and A. Schröder. 2011. Hanging nodes and XFEM. Int J Numer Meth Eng 86, 4-5 (2011), 404–430. Cross Ref
22. M. Gao, A. Pradhana, C.Jiang, and E. Sifakis. 2017. Supplemental Document: An Adaptive Generalized Interpolation Material Point Method for Simulating Elastoplastic Materials. (2017).
23. E. Grinspun, P. Krysl, and P. Schröder. 2002. CHARMS: a simple framework for adaptive simulation. ACM Trans on Graph (TOG) 21, 3 (2002), 281–290.
24. B. Houston, M. B. Nielsen, C. Batty, O. Nilsson, and K. Museth. 2006. Hierarchical RLE level set: A compact and versatile deformable surface representation. ACM Trans on Graph (TOG) 25, 1 (2006), 151–175.
25. T. Hughes. 2012. The finite element method: linear static and dynamic finite element analysis. Courier Corporation.
26. G. Irving, E. Guendelman, F. Losasso, and R. Fedkiw. 2006. Efficient simulation of large bodies of water by coupling two and three dimensional techniques. In ACM Trans on Graph (TOG), Vol. 25. ACM, 805–811.
27. C. Jiang, T. Gast, and J. Teran. 2017. Anisotropic elastoplasticity for cloth, knit and hair frictional contact. ACM Trans Graph 36, 4 (2017).
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.
29. C. Jiang, C. Schroeder, J. Teran, A. Stomakhin, and A. Selle. 2016. The Material Point Method for Simulating Continuum Materials. In ACM SIGGRAPH 2016 Course. 24:1–24:52.
30. P. Kaufmann, S. Martin, M. Botsch, and M. Gross. 2009. Flexible simulation of deformable models using discontinuous Galerkin FEM. Graphical Models 71, 4 (2009), 153–167.
31. G. Klár, T. Gast, A. Pradhana, C. Fu, C. Schroeder, C. Jiang, and J. Teran. 2016. Drucker-Prager Elastoplasticity for Sand Anim. ACM Trans Graph 35, 4 (July 2016).
32. F. Labelle and J. R. Shewchuk. 2007. Isosurface stuffing: fast tetrahedral meshes with good dihedral angles. In ACM Trans on Graph (TOG), Vol. 26. ACM, 57.
33. G. Legrain, R. Allais, and P. Cartraud. 2011. On the use of the extended finite element method with quadtree/octree meshes. Int J Numer Meth Eng 86, 6 (2011), 717–743. Cross Ref
34. Y.P. Lian, P.F. Yang, X. Zhang, F. Zhang, Y. Liu, and P. Huang. 2015. A mesh-grading material point method and its parallelization for problems with localized extreme deformation. Comp Meth App Mech Eng 289 (2015), 291 — 315. Cross Ref
35. Y. Lian, X. Zhang, F. Zhang, and X. Cui. 2014. Tied interface grid material point method for problems with localized extreme deformation. Int J Imp Eng 70 (2014), 50–61. Cross Ref
36. H. Liu, N. Mitchell, M. Aanjaneya, and E. Sifakis. 2016. A scalable schur-complement fluids solver for heterogeneous compute platforms. ACM Trans on Graph (TOG) 35, 6 (2016), 201.
37. F. Losasso, F. Gibou, and R. Fedkiw. 2004. Simulating water and smoke with an octree data structure. In ACM Trans Graph, Vol. 23. ACM, 457–462.
38. J. Ma, H. Lu, and R. Komanduri. 2006. Structured mesh reinement in generalized interpolation material point (GIMP) method for simulation of dynamic problems. Comp Model Eng & Sci 12, 3 (2006), 213.
39. J. Ma, H. Lu, B. Wang, S. Roy, R. Hornung, A. Wissink, and R. Komanduri. 2005. Multiscale simulations using generalized interpolation material point (GIMP) method and SAMRAI parallel processing. Comp Model Eng & Sci 8, 2 (2005), 135–152.
40. P-L. Manteaux, C. Wojtan, R. Narain, S. Redon, F. Faure, and M-P. Cani. 2016. Adaptive physically based models in Comp Graph. In Comp Graph Forum. Wiley Online Library.
41. C. Mast. 2013. Modeling landslide-induced flow interactions with structures using the Material Point Method. Ph.D. Dissertation.
42. K. Museth. 2013. VDB: High-resolution sparse volumes with dynamic topology. ACM Trans on Graph (TOG) 32, 3 (2013), 27.
43. M. A. Otaduy, D. Germann, S. Redon, and M. Gross. 2007. Adaptive deformations with fast tight bounds. In Proc of the 2007 ACM SIGGRAPH/Eurographics Symp on Comp Anim. Eurographics Association, 181–190.
44. S. Patel, A. Chu, J. Cohen, and F. Pighin. 2005. Fluid simulation via disjoint translating grids. In ACM SIGGRAPH 2005 Sketches. ACM, 139.
45. 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/Eurographics Symp Comp Anim. 157–163.
46. M. Seiler, D. Steinemann, J. Spillmann, and M. Harders. 2011. Robust interactive cutting based on an adaptive octree simulation mesh. The Vis Comp 27, 6–8 (2011), 519–529.
47. R. Setaluri, M. Aanjaneya, S. Bauer, and E. Sifakis. 2014. SPGrid: A Sparse Paged Grid Structure Applied to Adaptive Smoke Simulation. ACM Trans Graph 33, 6, Article 205 (Nov. 2014), 205:1–205:12 pages.
48. 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). Article 20, 50 pages.
49. E. Sifakis, T. Shinar, G. Irving, and R. Fedkiw. 2007. Hybrid simulation of deformable solids. In Proc ACM SIGGRAPH/Eurographics Symp Comp Anim. 81–90.
50. B. Solenthaler and M. Gross. 2011. Two-scale particle simulation. In ACM Tran Graph, Vol. 30. ACM, 81.
51. M. Steffen, R. M. Kirby, and M. Berzins. 2008. Analysis and reduction of quadrature errors in the material point method (MPM). Int J Numer Meth Eng 76, 6 (2008), 922–948. Cross Ref
52. D. Steinemann, M. A. Otaduy, and M. Gross. 2008. Fast adaptive shape matching deformations. In Proc of the 2008 ACM SIGGRAPH/Eurographics Symp on Comp Anim. Eurographics Association, 87–94.
53. A. Stomakhin, R. Howes, C. Schroeder, and J. Teran. 2012. Energetically consistent invertible elasticity. In Proc Symp Comp Anim. 25–32.
54. 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.
55. 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.
56. D. Sulsky, S. Zhou, and H. Schreyer. 1995. Application of a particle-in-cell method to solid mechanics. Comp Phys Comm 87, 1 (1995), 236–252. Cross Ref
57. 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).
58. H. Tan and J. A. Nairn. 2002. Hierarchical, adaptive, material point method for dynamic energy release rate calculations. Comp Meth App Mech Eng 191, 19âĂŞ20 (2002), 2123 — 2137.
59. M. Wicke, D. Ritchie, B. Klingner, S. Burke, J. Shewchuk, and J. O’Brien. 2010. Dynamic local remeshing for elastoplastic simulation. ACM Trans Graph 29, 4 (2010), 49:1–11.
60. C. Wojtan and G. Turk. 2008. Fast viscoelastic behavior with thin features. ACM Trans Graph 27, 3 (2008), 1–8.
61. 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.
62. Y. Zhu and R. Bridson. 2005. Animating sand as a fluid. ACM Trans Graph 24, 3 (2005), 965–972.
