Daniel Ram
Chenfanfu Jiang
Alexey Stomakhin
ABSTRACT
We present a new Material Point Method (MPM) for simulating viscoelastic fluids, foams and sponges. We design our discretization from the upper convected derivative terms in the evolution of the left Cauchy-Green elastic strain tensor. We combine this with an Oldroyd-B model for plastic flow in a complex viscoelastic fluid. While the Oldroyd-B model is traditionally used for viscoelastic fluids, we show that its interpretation as a plastic flow naturally allows us to simulate a wide range of complex material behaviors. In order to do this, we provide a modification to the traditional Oldroyd-B model that guarantees volume preserving plastic flows. Our plasticity model is remarkably simple (foregoing the need for the singular value decomposition (SVD) of stresses or strains). Lastly, we show that implicit time stepping can be achieved in a manner similar to [Stomakhin et al. 2013] and that this allows for high resolution simulations at practical simulation times.
Supplemental Material
Available for Download
- Bargteil, A., Wojtan, C., Hodgins, J., and Turk, G. 2007. A finite element method for animating large viscoplastic flow. ACM Trans. Graph. 26, 3. Google Scholar
Digital Library
- Batty, C., and Bridson, R. 2008. Accurate viscous free surfaces for buckling, coiling, and rotating liquids. In Proc 2008 ACM/Eurographics Symp Comp Anim, 219--228. Google ScholarDigital Library
- Batty, C., and Houston, B. 2011. A simple finite volume method for adaptive viscous liquids. In Proc 2011 ACM SIGGRAPH/Eurograp Symp Comp Anim, 111--118. Google ScholarDigital Library
- Batty, C., Uribe, A., Audoly, B., and Grinspun, E. 2012. Discrete viscous sheets. 113:1--113:7.Google Scholar
- Becker, M., Ihmsen, M., and Teschner, M. 2009. Corotated sph for deformable solids. In Eurographics Conf. Nat. Phen., 27--34. Google ScholarDigital Library
- Bonet, J., and Wood, R. 1997. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press.Google Scholar
- Carlson, M., Mucha, P., Horn, R. V., and Turk, G. 2002. Melting and flowing. In ACM SIGGRAPH/Eurographics Symp. Comp. Anim., 167--174. Google ScholarDigital Library
- Chang, Y., Bao, K., Liu, Y., Zhu, J., and Wu, E. 2009. A particle-based method for viscoelastic fluids animation. In ACM Symp. Virt. Real. Soft. Tech., 111--117. Google ScholarDigital Library
- Chao, I., Pinkall, U., Sanan, P., and Schröder, P. 2010. A simple geometric model for elastic deformations. In ACM Transactions on Graphics (TOG), vol. 29, ACM, 38. Google ScholarDigital Library
- Desbrun, M., and Gascuel, M. 1996. Smoothed particles: A new paradigm for animating highly deformable bodies. In Eurographics Workshop Comp. Anim. Sim., 61--76. Google ScholarDigital Library
- Gast, T., Schroeder, C., Stomakhin, A., Jiang, C., and Teran, J. 2015. Optimization integrator for large time steps. IEEE Trans. Vis. Comp. Graph. (in review).Google ScholarDigital Library
- Gerszewski, D., Bhattacharya, H., and Bargteil, A. 2009. A point-based method for animating elastoplastic solids. In Proc ACM SIGGRAPH/Eurograph Symp Comp Anim, 133--138. Google ScholarDigital Library
- Goktekin, T., Bargteil, A., and O'Brien, J. 2004. A method for animating viscoelastic fluids. ACM Trans. Graph. 23, 3, 463--468. Google ScholarDigital Library
- Hiemenz, P., and Rajagopalan, R. 1997. Principles of Colloid and Surface Chemistry. Marcel Dekker.Google Scholar
- Jiang, C., Schroeder, C., Selle, A., Teran, J., and Stomakhin, A. 2015. The affine particle-in-cell method. ACM Trans. Graph. (to appear). Google ScholarDigital Library
- Keiser, R., Adams, B., Gasser, D., Bazzi, P., Dutré, P., and Gross, M. 2005. A unified lagrangian approach to solid-fluid animation. In Eurographics/IEEE VGTC Conf. Point-Based Graph., 125--133. Google ScholarDigital Library
- Larson, R. G. 1999. The Structure and Rheology of Complex Fluids. Oxford University Press: New York.Google Scholar
- Losasso, F., Irving, G., Guendelman, E., and Fedkiw, R. 2006. Melting and burning solids into liquids and gases. IEEE Trans. Vis. Comp. Graph. 12, 343--352. Google ScholarDigital Library
- McAdams, A., Zhu, Y., Selle, A., Empey, M., Tamstorf, R., Teran, J., and Sifakis, E. 2011. Efficient elasticity for character skinning with contact and collisions. In ACM Transactions on Graphics (TOG), vol. 30, ACM, 37. Google ScholarDigital Library
- Morrison, I., and Ross, S. 2002. Colloidal Dispersions: Suspensions, Emulsions and Foams. Wiley Interscience.Google Scholar
- Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., and Alexa, M. 2004. Point based animation of elastic, plastic and melting objects. In ACM SIGGRAPH/Eurographics Symp. Comp. Anim., 141--151. Google ScholarDigital Library
- Museth, K. 2014. A flexible image processing approach to the surfacing of particle-based fluid animation (invited talk). In Mathematical Progress in Expressive Image Synthesis I, vol. 4 of Mathematics for Industry. 81--84.Google Scholar
- Paiva, A., Petronetto, F., Lewiner, T., and Tavares, G. 2006. Particle-based non-newtonian fluid animation for melting objects. In Conf. Graph. Patt. Images, 78--85.Google Scholar
- Paiva, A., Petronetto, F., Lewiner, T., and Tavares, G. 2009. Particle-based viscoplastic fluid/solid simulation. Comp. Aided Des. 41, 4, 306--314. Google ScholarDigital Library
- Prudhomme, R., and Kahn, S. 1996. Foams: Theory, Measurements, and Applications. Marcel Dekker.Google Scholar
- Rasmussen, N., Enright, D., Nguyen, D., Marino, S., Sumner, N., Geiger, W., Hoon, S., and Fedkiw, R. 2004. Directable photorealistic liquids. In ACM SIGGRAPH/Eurographics Symp. Comp. Anim., 193--202. Google ScholarDigital Library
- Schramm, L. 1994. Foams: Fundamentals and Applications in the Petroleum Industry. ACS.Google ScholarCross Ref
- Solenthaler, B., Schläfli, J., and Pajarola, R. 2007. A unified particle model for fluid-solid interactions. Comp. Anim. Virt. Worlds 18, 1, 69--82. Google ScholarDigital Library
- Stomakhin, A., Schroeder, C., Chai, L., Teran, J., and Selle, A. 2013. A material point method for snow simulation. ACM Trans. Graph. 32, 4, 102:1--102:10. Google ScholarDigital Library
- Stomakhin, A., Schroeder, C., Jiang, C., Chai, L., Teran, J., and Selle, A. 2014. Augmented mpm for phase-change and varied materials. ACM Trans. Graph. 33, 4, 138:1--138:11. Google ScholarDigital Library
- Teran, J., Fauci, L., and Shelley, M. 2008. Peristaltic pumping and irreversibility of a stokesian viscoelastic fluid. Phys Fl 20, 7.Google ScholarCross Ref
- Terzopoulos, D., and Fleischer, K. 1988. Deformable models. Vis Comp 4, 6, 306--331.Google ScholarCross Ref
- Terzopoulos, D., and Fleischer, K. 1988. Modeling inelastic deformation: Viscolelasticity, plasticity, fracture. SIGGRAPH Comp Graph 22, 4, 269--278. Google ScholarDigital Library
- Wojtan, C., and Turk, G. 2008. Fast viscoelastic behavior with thin features. ACM Trans. Graph. 27, 3, 47:1--47:8. Google ScholarDigital Library
- Wojtan, C., Thürey, N., Gross, M., and Turk, G. 2009. Deforming meshes that split and merge. ACM Trans. Graph. 28, 3, 76:1--76:10. Google ScholarDigital Library
- Yue, Y., Smith, B., Batty, C., Zheng, C., and Grinspun, E. 2015. Continuum foam: A material point method for shear-dependent flows. ACM Trans. Graph..Google ScholarDigital Library
Index Terms
- A material point method for viscoelastic fluids, foams and sponges
Recommendations
The affine particle-in-cell method
Hybrid Lagrangian/Eulerian simulation is commonplace in computer graphics for fluids and other materials undergoing large deformation. In these methods, particles are used to resolve transport and topological change, while a background Eulerian grid is ...
A method for animating viscoelastic fluids
SIGGRAPH '04: ACM SIGGRAPH 2004 PapersThis paper describes a technique for animating the behavior of viscoelastic fluids, such as mucus, liquid soap, pudding, toothpaste, or clay, that exhibit a combination of both fluid and solid characteristics. The technique builds upon prior Eulerian ...
A method for animating viscoelastic fluids
This paper describes a technique for animating the behavior of viscoelastic fluids, such as mucus, liquid soap, pudding, toothpaste, or clay, that exhibit a combination of both fluid and solid characteristics. The technique builds upon prior Eulerian ...
Comments