“Silly rubber: an implicit material point method for simulating non-equilibrated viscoelastic and elastoplastic solids” by Fang, Li, Gao and Jiang
Conference:
Type:
Session Title:
- MPM and Collision
Title:
- Silly rubber: an implicit material point method for simulating non-equilibrated viscoelastic and elastoplastic solids
Presenter(s)/Author(s):
Abstract:
Simulating viscoelastic polymers and polymeric fluids requires a robust and accurate capture of elasticity and viscosity. The computation is known to become very challenging under large deformations and high viscosity. Drawing inspirations from return mapping based elastoplasticity treatment for granular materials, we present a finite strain integration scheme for general viscoelastic solids under arbitrarily large deformation and non-equilibrated flow. Our scheme is based on a predictor-corrector exponential mapping scheme on the principal strains from the deformation gradient, which closely resembles the conventional treatment for elastoplasticity and allows straightforward implementation into any existing constitutive models. We develop a new Material Point Method that is fully implicit on both elasticity and inelasticity using augmented Lagrangian optimization with various preconditioning strategies for highly efficient time integration. Our method not only handles viscoelasticity but also supports existing elastoplastic models including Drucker-Prager and von-Mises in a unified manner. We demonstrate the efficacy of our framework on various examples showing intricate and characteristic inelastic dynamics with competitive performance.
References:
1. 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). Google ScholarDigital Library
2. H. Barreiro, I. García-Fernández, I. Alduán, and M. Otaduy. 2017. Conformation constraints for efficient viscoelastic fluid simulation. ACM Trans Graph 36, 6 (2017). Google ScholarDigital Library
3. C. Batty, F. Bertails, and R. Bridson. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Trans Graph 26, 3 (2007). Google ScholarDigital Library
4. C. Batty and R. Bridson. 2008. Accurate viscous free surfaces for buckling, coiling, and rotating liquids. Proc ACM SIGGRAPH/Eurograph Symp Comp Anim (2008), 219–228. Google ScholarDigital Library
5. C. Batty and B. Houston. 2011. A simple finite volume method for adaptive viscous liquids. In Symp on Comp Anim. 111–118. Google ScholarDigital Library
6. C. Batty, A. Uribe, B. Audoly, and E. Grinspun. 2012. Discrete viscous sheets. ACM Trans Graph 31, 4 (2012), 113. Google ScholarDigital Library
7. J. Bonet and R. Wood. 2008. Nonlinear continuum mechanics for finite element analysis.Google Scholar
8. S. Bouaziz, S. Martin, T. Liu, L. Kavan, and M. Pauly. 2014. Projective dynamics: fusing constraint projections for fast simulation. ACM Trans Graph 33, 4 (2014), 154. Google ScholarDigital Library
9. S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein, et al. 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends® in Machine learning 3, 1 (2011), 1–122. Google ScholarDigital Library
10. G. Brown, M. Overby, Z. Forootaninia, and R. Narain. 2018. Accurate dissipative forces in optimization integrators. In SIGGRAPH Asia 2018 Papers. Google ScholarDigital Library
11. M. Carlson, P. Mucha, R.B. Van Horn, and G. Turk. 2002. Melting and Flowing. In Proc of the 2002 ACM SIGGRAPH/EuroGraph Symp on Comp Anim (SCA ’02). 167–174. Google ScholarDigital Library
12. N. Chentanez, M. Müller, and M. Macklin. 2016. Real-time simulation of large elastoplastic deformation with shape matching. In Symp on Comp Anim. 159–167. Google ScholarDigital Library
13. 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
14. D. Dinev, T. Liu, and L. Kavan. 2018a. Stabilizing Integrators for Real-Time Physics. ACM Trans. Graph. (2018). Google ScholarDigital Library
15. D. Dinev, T. Liu, J. Li, B. Thomaszewski, and L. Kavan. 2018b. FEPR: Fast Energy Projection for Real-time Simulation of Deformable Objects. ACM Trans. Graph. 37, 4 (July 2018), 79:1–79:12. Google ScholarDigital Library
16. J. Eckstein. 1994. Parallel alternating direction multiplier decomposition of convex programs. J of Optimization Theory and Applications 80, 1 (1994), 39–62. Google ScholarDigital Library
17. Y. Fang, Y. Hu, S. Hu, and C. Jiang. 2018. A temporally adaptive material point method with regional time stepping. In Comp Graph forum, Vol. 37. 195–204.Google Scholar
18. Y. Fang, M. Li, M. Gao, and C. Jiang. 2019. Silly Rubber: supplemental document. (2019).Google Scholar
19. Y. Fei, C. Batty, E. Grinspun, and C. Zheng. 2018. A Multi-scale Model for Simulating Liquid-fabric Interactions. ACM Trans. Graph. 37, 4 (Aug. 2018), 51:1–51:16. Google ScholarDigital Library
20. M. Fortin and A. Fortin. 1989. A new approach for the FEM simulation of viscoelastic flows. J of non-newtonian fluid Mech 32, 3 (1989), 295–310.Google Scholar
21. M. Fortin and R. Glowinski. 1983. Chapter III on decomposition-coordination methods using an augmented lagrangian. In Studies in Math and Its Appl. Vol. 15. 97–146.Google Scholar
22. 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. Google ScholarDigital Library
23. M. Gao, A. Pradhana, C. Jiang, and E. Sifakis. 2017. An adaptive generalized interpolation material point method for simulating elastoplastic materials. ACM Trans Graph 36, 6 (2017), 223. Google ScholarDigital Library
24. M. Gao, X. Wang, K. Wu, A. Pradhana, E. Sifakis, C. Yuksel, and C. Jiang. 2018b. GPU Optimization of Material Point Methods. ACM Trans Graph (2018), 254:1–254:12. Google ScholarDigital Library
25. T. Gast, C. Schroeder, A. Stomakhin, C. Jiang, and J. Teran. 2015. Optimization Integrator for Large Time Steps. IEEE Trans Vis Comp Graph 21, 10 (2015), 1103–1115. Google ScholarDigital Library
26. J. Gaume, T. Gast, J. Teran, A. van Herwijnen, and C. Jiang. 2018. Dynamic anticrack propagation in snow. Nature Comm 9, 1 (2018), 3047.Google ScholarCross Ref
27. D. Gerszewski, H. Bhattacharya, and A. Bargteil. 2009. A point-based method for animating elastoplastic solids. In Symp on Comp Anim. 133–138. Google ScholarDigital Library
28. T. Goktekin, A. Bargteil, and J. O’Brien. 2004. A method for animating viscoelastic fluids. ACM Trans Graph 23, 3 (2004), 463–468. Google ScholarDigital Library
29. T. Goldstein, B. O’Donoghue, S. Setzer, and R. Baraniuk. 2014. Fast alternating direction optimization methods. SIAM J on Imag Scis 7, 3 (2014), 1588–1623.Google ScholarCross Ref
30. S. Govindjee and S. Reese. 1997. A presentation and comparison of two large deformation viscoelasticity models. J of Eng Mat and technology 119, 3 (1997), 251–255.Google Scholar
31. 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 ScholarDigital Library
32. X. He, H. Wang, and E. Wu. 2018. Projective peridynamics for modeling versatile elastoplastic materials. IEEE Trans Vis and Comp Graph 24, 9 (2018), 2589–2599.Google ScholarCross Ref
33. G.T. Houlsby and A.M. Puzrin. 2007. Principles of hyperplasticity: an approach to plasticity theory based on thermodynamic principles.Google Scholar
34. 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. Google ScholarDigital Library
35. 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 ScholarDigital Library
36. 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
37. 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
38. H. Johnston and J. Liu. 2004. Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term. J of Comp Phys 199, 1 (2004), 221–259. Google ScholarDigital Library
39. B. Jones, S. Ward, A. Jallepalli, J. Perenia, and A. Bargteil. 2014. Deformation embedding for point-based elastoplastic simulation. ACM Trans Graph 33, 2 (2014), 21. Google ScholarDigital Library
40. 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). Google ScholarDigital Library
41. E. Larionov, C. Batty, and R. Bridson. 2017. Variational stokes: a unified pressure-viscosity solver for accurate viscous liquids. ACM Trans Graph 36, 4 (2017), 101. Google ScholarDigital Library
42. Patrick Le Tallec. 1990. Numerical analysis of viscoelastic problems. Vol. 15.Google Scholar
43. J. Li, T. Liu, and L. Kavan. 2018. Laplacian Damping for Projective Dynamics. In VRIPHYS2018: 14th Workshop on Virtual Reality Interaction and Physical Sim. Google ScholarDigital Library
44. T. Liu, A. Bargteil, J. O’Brien, and L. Kavan. 2013. Fast Simulation of Mass-Spring Systems. ACM Trans Graph 32, 6 (2013), 209:1–7. Google ScholarDigital Library
45. T. Liu, S. Bouaziz, and L. Kavan. 2017. Quasi-newton methods for real-time simulation of hyperelastic materials. ACM Trans Graph 36, 4 (2017), 116a.Google ScholarDigital Library
46. F. Losasso, T. Shinar, A. Selle, and R. Fedkiw. 2006. Multiple Interacting Liquids. In ACM SIGGRAPH 2006 Papers (SIGGRAPH ’06). 812–819. Google ScholarDigital Library
47. A. Mielke. 2006. A mathematical framework for generalized standard materials in the rate-independent case. In Multifield Problems in Solid and Fluid Mech. 399–428.Google Scholar
48. K. Museth, J. Lait, J. Johanson, J. Budsberg, R. Henderson, M. Alden, P. Cucka, D. Hill, and A. Pearce. 2013. OpenVDB: an open-source data structure and toolkit for high-resolution volumes. In siggraph 2013 courses. Google ScholarDigital Library
49. 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
50. B Nedjar. 2002a. Frameworks for finite strain viscoelastic-plasticity based on multiplicative decompositions. Part I: Continuum formulations. Comp Meth in App Mech and Eng 191, 15–16 (2002), 1541–1562.Google Scholar
51. B Nedjar. 2002b. Frameworks for finite strain viscoelastic-plasticity based on multiplicative decompositions. Part II: Computational aspects. Comp Meth in App Mech and Eng 191, 15–16 (2002), 1563–1593.Google Scholar
52. Y. Nesterov et al. 2007. Gradient methods for minimizing composite objective function.Google Scholar
53. Michael Ortiz and Laurent Stainier. 1999. The variational formulation of viscoplastic constitutive updates. Comp Meth in App Mech and Eng 171, 3–4 (1999), 419–444.Google ScholarCross Ref
54. M. Overby, G. Brown, J. Li, and R. Narain. 2017. ADMM ⊇ Projective Dynamics: Fast Simulation of Hyperelastic Models with Dynamic Constraints. IEEE Trans. Vis. Comput. Graph. 23, 10 (Oct. 2017), 2222–2234.Google ScholarDigital Library
55. Y. Peng, B. Deng, J. Zhang, F. Geng, W. Qin, and L. Liu. 2018. Anderson Acceleration for Geometry Optimization and Physics Simulation. arXiv (2018).Google Scholar
56. A. Pradhana, 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 ScholarDigital Library
57. 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 ScholarDigital Library
58. N. Rasmussen, D. Enright, D. Nguyen, S. Marino, N. Sumner, W. Geiger, S. Hoon, and R. Fedkiw. 2004. Directable photorealistic liquids. In Proc of the 2004 ACM SIGGRAPH/EuroGraph Symp on Comp Anim. 193–202. Google ScholarDigital Library
59. S. Reese and S. Govindjee. 1998. A theory of finite viscoelasticity and numerical aspects. Int J of solids and structures 35, 26–27 (1998), 3455–3482.Google Scholar
60. E. Sifakis and J. Barbič. 2015. Finite Element Method Simulation of 3D Deformable Solids. SIGGRAPH Course 1, 1 (2015), 1–69.Google Scholar
61. J. C. Simo. 1992. Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory. Comp Meth App Mech Eng 99, 1 (1992), 61–112. Google ScholarDigital Library
62. Juan C Simo and Thomas JR Hughes. 2006. Computational inelasticity. Vol. 7.Google Scholar
63. B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd. 2018. OSQP: An Operator Splitting Solver for Quadratic Programs. In Int Conf on Control. 339–339.Google Scholar
64. 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
65. 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. Google ScholarDigital Library
66. 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.Google ScholarCross Ref
67. T. Takahashi, Y. Dobashi, I. Fujishiro, T. Nishita, and M. Lin. 2015. Implicit formulation for SPH-based viscous fluids. In Comp Graph Forum, Vol. 34. 493–502. Google ScholarDigital Library
68. T. Takahashi, T. Nishita, and I. Fujishiro. 2014. Fast simulation of viscous fluids with elasticity and thermal conductivity using position-based dynamics. Comps Graph 43 (2014), 21–30.Google ScholarCross Ref
69. J. Teran, E. Sifakis, G. Irving, and R. Fedkiw. 2005. Robust quasistatic finite elements and flesh simulation. In Symp on Comp Anim. 181–190. Google ScholarDigital Library
70. D. Terzopoulos and K. Fleischer. 1988. Modeling inelastic deformation: viscolelasticity, plasticity, fracture. In ACM Siggraph Comp Graph, Vol. 22. 269–278. Google ScholarDigital Library
71. D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer. 1987. Elastically deformable models. ACM Siggraph Comp Graph 21, 4 (1987), 205–214. Google ScholarDigital Library
72. H.F. Walker and P. Ni. 2011. Anderson acceleration for fixed-point iterations. SIAM J on Numer Analysis 49, 4 (2011), 1715–1735. Google ScholarDigital Library
73. H. Wang and Y. Yang. 2016. Descent methods for elastic body simulation on the GPU. ACM Trans Graph 35, 6 (2016), 212. Google ScholarDigital Library
74. 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. Google ScholarDigital Library
75. B. Wohlberg. 2017. ADMM Penalty Parameter Selection by Residual Balancing. (2017).Google Scholar
76. Chris Wojtan, Nils Thürey, Markus Gross, and Greg Turk. 2009. Deforming meshes that split and merge. In ACM Trans Graph, Vol. 28. 76. Google ScholarDigital Library
77. C. Wojtan and G. Turk. 2008. Fast viscoelastic behavior with thin features. ACM Trans Graph 27, 3 (2008), 47. Google ScholarDigital Library
78. J. Wretborn, R. Armiento, and K. Museth. 2017. Animation of Crack Propagation by Means of an Extended Multi-body Solver for the Material Point Method. Comput. Graph. 69, C (Dec. 2017), 131–139. Google ScholarDigital Library
79. X. Yan, C. Li, X. Chen, and S. Hu. 2018. MPM simulation of interacting fluids and solids. Comp Graph Forum 37, 8 (2018), 183–193.Google ScholarCross Ref
80. 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
81. 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 (2018), 283:1–283:19. Google ScholarDigital Library
82. B. Zhu, M. Lee, E. Quigley, and R. Fedkiw. 2015. Codimensional non-Newtonian fluids. ACM Trans Graph 34, 4 (2015), 115. Google ScholarDigital Library
83. Y. Zhu and R. Bridson. 2005. Animating sand as a fluid. ACM Trans Graph 24, 3 (2005), 965–972. Google ScholarDigital Library
