“Mixing sauces: a viscosity blending model for shear thinning fluids” by Nagasawa, Suzuki, Seto, Okada and Yue

  • ©

Conference:


Type(s):


Title:

    Mixing sauces: a viscosity blending model for shear thinning fluids

Session/Category Title:   Fluids I


Presenter(s)/Author(s):



Abstract:


    The materials around us usually exist as mixtures of constituents, each constituent with possibly a different elasto-viscoplastic property. How can we describe the material property of such a mixture is the core question of this paper. We propose a nonlinear blending model that can capture intriguing flowing behaviors that can differ from that of the individual constituents (Fig. 1). We used a laboratory device, rheometer, to measure the flowing properties of various fluid-like foods, and found that an elastic Herschel-Bulkley model has nice agreements with the measured data even for the mixtures of these foods. We then constructed a blending model such that it qualitatively agrees with the measurements and is closed in the parameter space of the elastic Herschel-Bulkley model. We provide validations through comparisons between the measured and estimated properties using our model, and comparisons between simulated examples and captured footages. We show the utility of our model for producing interesting behaviors of various mixtures.

References:


    1. American Society for Testing and Materials 2016. ASTM D7152 11: Standard Practice for Calculating Viscosity of a Blend of Petroleum Products. American Society for Testing and Materials.Google Scholar
    2. Ryoichi Ando, Nils Thürey, and Chris Wojtan. 2013. Highly Adaptive Liquid Simulations on Tetrahedral Meshes. ACM Transactions on Graphics (Proc. of SIGGRAPH 2013) 32, 4 (2013), 103:1–103:10. Google ScholarDigital Library
    3. Svante Arrhenius. 1887. Über die Dissociation der in Wasser gelösten Stoffe. Zeitschrift für Physikalische Chemie 1U, 1 (1887), 631–648.Google ScholarCross Ref
    4. Fabio Bacchini, Vyacheslav Olshevsky, Stefaan Poedts, and Giovanni Lapenta. 2017. A new Particle-in-Cell method for modeling magnetized fluids. Computer Physics Communications 210 (2017), 79–91.Google ScholarCross Ref
    5. Scott G. Bardenhagen and Edward M. Kober. 2004. The Generalized Interpolation Material Point Method. CMES: Computer Modeling in Engineering and Sciences 5, 6 (2004), 477–495.Google Scholar
    6. Adam W. Bargteil, Chris Wojtan, Jessica K. Hodgins, and Greg Turk. 2007. A Finite Element Method for Animating Large Viscoplastic Flow. ACM Transactions on Graphics (Proc. of SIGGRAPH 2007) 26, 3 (2007), 16:1–8. Google ScholarDigital Library
    7. Héctor Barreiro, Ignacio García-Fernández, Iván Alduán, and Miguel A. Otaduy. 2017. Conformation Constraints for Efficient Viscoelastic Fluid Simulation. ACM Transactions on Graphics (Proc. of SIGGRAPH Asia 2017) 36, 6 (2017), 221:1–11. Google ScholarDigital Library
    8. Christopher Batty, Florence Bertails, and Robert Bridson. 2007. A Fast Variational Framework for Accurate Solid-fluid Coupling. ACM Transactions on Graphics (Proc. of SIGGRAPH 2007) 26, 3 (2007), 100:1–7. Google ScholarDigital Library
    9. Christopher Batty, Andres Uribe, Basile Audoly, and Eitan Grinspun. 2012. Discrete Viscous Sheets. ACM Transactions on Graphics (Proc. of SIGGRAPH Asia 2012) 31, 4 (2012), 113:1–7. Google ScholarDigital Library
    10. Markus Becker, Markus Ihmsen, and Matthias Teschner. 2009. Corotated SPH for Deformable Solids. In Eurographics Workshop on Natural Phenomena, Eric Galin and Jens Schneider (Eds.). The Eurographics Association, 27–34. Google ScholarDigital Library
    11. Markus Becker and Matthias Teschner. 2007. Weakly Compressible SPH for Free Surface Flows. In Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’07). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 209–217. http://dl.acm.org/citation.cfm?id=1272690.1272719 Google ScholarDigital Library
    12. Jan Bender and Dan Koschier. 2015. Divergence-free Smoothed Particle Hydrodynamics. In Proceedings of the 14th ACM SIGGRAPH / Eurographics Symposium on Computer Animation (SCA ’15). ACM, New York, NY, USA, 147–155. Google ScholarDigital Library
    13. Miklós Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete Viscous Threads. ACM Transactions on Graphics (Proc. of SIGGRAPH 2010) 29, 4 (2010), 116:1–10. Google ScholarDigital Library
    14. Haimasree Bhattacharya, Yue Gao, and Adam W. Bargteil. 2015. A Level-Set Method for Skinning Animated Particle Data. IEEE Transactions on Visualization and Computer Graphics 21, 3 (March 2015), 315–327.Google ScholarDigital Library
    15. Eugene C. Bingham and Delbert F. Brown. 1932. The Mixture Law. Journal of Rheology 3, 1 (1932), 95–112.Google ScholarCross Ref
    16. Tyson Brochu, Christopher Batty, and Robert Bridson. 2010. Matching Fluid Simulation Elements to Surface Geometry and Topology. ACM Transactions on Graphics (Proc. of SIGGRAPH 2010) 29, 4 (2010), 47:1–9. Google ScholarDigital Library
    17. John W. Cahn and John E. Hilliard. 1958. Free Energy of a Nonuniform System. I. Interfacial Free Energy. The Journal of Chemical Physics 28, 2 (1958), 258–267.Google ScholarCross Ref
    18. Mark Carlson, Peter J. Mucha, and Greg Turk. 2004. Rigid Fluid: Animating the Interplay Between Rigid Bodies and Fluid. ACM Transactions on Graphics (Proc. of SIGGRAPH 2004) 23, 3 (2004), 377–384. Google ScholarDigital Library
    19. Mark Carlson, Peter J. Mucha, R. Brooks Van Horn, III, and Greg Turk. 2002. Melting and Flowing. In Proceedings of the 2002 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’02). ACM, New York, NY, USA, 167–174. Google ScholarDigital Library
    20. Pierre J. Carreau. 1972. Rheological Equations from Molecular Network Theories. Transactions of the Society of Rheology 16, 1 (1972), 99–127.Google ScholarCross Ref
    21. Yuanzhang Chang, Kai Bao, Youquan Liu, Jian Zhu, and Enhua Wu. 2009. A Particle-based Method for Viscoelastic Fluids Animation. In Proceedings of the 16th ACM Symposium on Virtual Reality Software and Technology (VRST ’09). ACM, 111–117. Google ScholarDigital Library
    22. Pascal Clausen, Martin Wicke, Jonathan R. Shewchuk, and James F. O’Brien. 2013. Simulating Liquids and Solid-liquid Interactions with Lagrangian Meshes. ACM Transactions on Graphics 32, 2 (2013), 17:1–15. Google ScholarDigital Library
    23. Simon Clavet, Philippe Beaudoin, and Pierre Poulin. 2005. Particle-based Viscoelastic Fluid Simulation. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’05). ACM, New York, NY, USA, 219–228. Google ScholarDigital Library
    24. Paul W. Cleary, Soon Hyoung Pyo, Mahesh Prakash, and Bon Ki Koo. 2007. Bubbling and Frothing Liquids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2007) 26, 3 (2007), 97:1–6. Google ScholarDigital Library
    25. Peter A. Cundall and Otto D. L. Strack. 1979. A discrete numerical model for granular assemblies. Géotechnique 29, 1 (1979), 47–65.Google ScholarCross Ref
    26. Gilles Daviet and Florence Bertails-Descoubes. 2016. A Semi-implicit Material Point Method for the Continuum Simulation of Granular Materials. ACM Transactions on Graphics (Proc. of SIGGRAPH 2016) 35, 4 (2016), 102:1–13. Google ScholarDigital Library
    27. Daniel C. Drucker and William Prager. 1952. Soil mechanics and plastic analysis for limit design. Quart. Appl. Math. 10, 2 (1952), 157–165.Google ScholarCross Ref
    28. Sachith Dunatunga and Ken Kamrin. 2015. Continuum modelling and simulation of granular flows through their many phases. Journal of Fluid Mechanics 779 (2015), 483–513.Google ScholarCross Ref
    29. Douglas Enright, Stephen Marschner, and Ronald Fedkiw. 2002. Animation and Rendering of Complex Water Surfaces. ACM Transactions on Graphics (Proc. of SIGGRAPH 2002) 21, 3 (2002), 736–744. Google ScholarDigital Library
    30. Yu Fang, Yuanming Hu, Shi-Min Hu, and Chenfanfu Jiang. 2018. A Temporally Adaptive Material Point Method with Regional Time Stepping. Computer Graphics Forum 37, 8 (2018), 195–204.Google ScholarCross Ref
    31. Florian Ferstl, Ryoichi Ando, Chris Wojtan, Rüdiger Westermann, and Nils Thuerey. 2016. Narrow Band FLIP for Liquid Simulations. Computer Graphics Forum 35, 2 (2016), 225–232.Google ScholarCross Ref
    32. Nick Foster and Ronald Fedkiw. 2001. Practical Animation of Liquids. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01). ACM, New York, NY, USA, 23–30. Google ScholarDigital Library
    33. Nick Foster and Dimitri Metaxas. 1996. Realistic Animation of Liquids. Graphical Models and Image Processing 58, 5 (1996), 471–483. Google ScholarDigital Library
    34. Chuyuan Fu, Qi Guo, Theodore Gast, Chenfanfu Jiang, and Joseph Teran. 2017. A Polynomial Particle-in-cell Method. ACM Transactions on Graphics (Proc. of SIGGRAPH Asia 2017) 36, 6 (2017), 222:1–12. Google ScholarDigital Library
    35. Ming Gao, Andre Pradhana, Xuchen Han, Qi Guo, Grant Kot, Eftychios Sifakis, and Chenfanfu Jiang. 2018. Animating Fluid Sediment Mixture in Particle-laden Flows. ACM Transactions on Graphics (Proc. of SIGGRAPH 2018) 37, 4 (2018), 149:1–11. Google ScholarDigital Library
    36. Ming Gao, Andre Pradhana, Chenfanfu Jiang, and Eftychios Sifakis. 2017. An Adaptive Generalized Interpolation Material Point Method for Simulating Elastoplastic Materials. ACM Transactions on Graphics (Proc. of SIGGRAPH Asia 2017) 36, 6 (2017), 223:1–12. Google ScholarDigital Library
    37. Ming Gao, Xinlei Wang, Kui Wu, Andre Pradhana, Eftychios Sifakis, Cem Yuksel, and Chenfanfu Jiang. 2018. GPU Optimization of Material Point Methods. ACM Transactions on Graphics (Proc. of SIGGRAPH Asia 2018) 37, 6 (2018), 254:1–12. Google ScholarDigital Library
    38. Dan Gerszewski, Haimasree Bhattacharya, and Adam W. Bargteil. 2009. A Point-based Method for Animating Elastoplastic Solids. In Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’09). ACM, 133–138. Google ScholarDigital Library
    39. Tolga G. Goktekin, Adam W. Bargteil, and James F. O’Brien. 2004. A Method for Animating Viscoelastic Fluids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2004) 23, 3 (2004), 463–468. Google ScholarDigital Library
    40. Xiaowei He, Huamin Wang, and Enhua Wu. 2018. Projective Peridynamics for Modeling Versatile Elastoplastic Materials. IEEE Transactions on Visualization and Computer Graphics 24, 9 (2018), 2589–2599.Google ScholarCross Ref
    41. Winslow H. Herschel and Ronald Bulkley. 1926. Konsistenzmessungen von Gummi-Benzollösungen. Kolloid-Zeitschrift & Zeitschrift für Polymere 39, 4 (1926), 291–300.Google ScholarCross Ref
    42. Jeong-Mo Hong and Chang-Hun Kim. 2005. Discontinuous Fluids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2005) 24, 3 (2005), 915–920. Google ScholarDigital Library
    43. 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 Transactions on Graphics (Proc. of SIGGRAPH 2018) 37, 4 (2018), 150:1–14. Google ScholarDigital Library
    44. Markus Ihmsen, Jens Cornelis, Barbara Solenthaler, Christopher Horvath, and Matthias Teschner. 2014. Implicit Incompressible SPH. IEEE Transactions on Visualization and Computer Graphics 20, 3 (March 2014), 426–435. Google ScholarDigital Library
    45. Geoffrey Irving, Joseph M. Teran, and Ronald P. Fedkiw. 2004. Invertible Finite Elements for Robust Simulation of Large Deformation. In Proceedings of the 2004 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’04). Eurographics Association, 131–140. Google ScholarDigital Library
    46. Chenfanfu Jiang, Theodore Gast, and Joseph Teran. 2017. Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact. ACM Transactions on Graphics (Proc. of SIGGRAPH 2017) 36, 4 (2017), 152:1–14. Google ScholarDigital Library
    47. Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin.Google Scholar
    48. 2015 The Affine Particle-in-cell Method. ACM Transactions on Graphics (Proc. of SIGGRAPH 2015) 34, 4 (2015), 51:1–10. Google ScholarDigital Library
    49. Chenfanfu Jiang, Craig Schroeder, Joseph Teran, Alexey Stomakhin, and Andrew Selle.Google Scholar
    50. 2016 The Material Point Method for Simulating Continuum Materials. In ACM SIGGRAPH 2016 Courses (SIGGRAPH ’16). ACM, New York, NY, USA, Article 24, 52 pages. Google ScholarDigital Library
    51. Ben Jones, Stephen Ward, Ashok Jallepalli, Joseph Perenia, and Adam W. Bargteil. 2014. Deformation Embedding for Point-based Elastoplastic Simulation. ACM Transactions on Graphics 33, 2 (2014), 21:1–9. Google ScholarDigital Library
    52. Harry C. Jones and Eugene C. Bingham. 1905. Conductivity and viscosity of solutions of certain salts in mixtures of acetone with methyl alcohol, with ethyl alcohol and water. American Chemical Journal 34 (1905), 481–554.Google Scholar
    53. James Kendall and Kenneth Potter Monroe. 1917. THE VISCOSITY OF LIQUIDS. II. THE VISCOSITY-COMPOSITION CURVE FOR IDEAL LIQUID MIXTURES.1. Journal of the American Chemical Society 39, 9 (1917), 1787–1802.Google ScholarCross Ref
    54. Byungmoon Kim. 2010. Multi-phase Fluid Simulations Using Regional Level Sets. ACM Transactions on Graphics (Proc. of SIGGRAPH Asia 2010) 29, 6 (2010), 175:1–8. Google ScholarDigital Library
    55. Gergely Klár, Theodore Gast, Andre Pradhana, Chuyuan Fu, Craig Schroeder, Chenfanfu Jiang, and Joseph Teran. 2016. Drucker-prager Elastoplasticity for Sand Animation. ACM Transactions on Graphics (Proc. of SIGGRAPH 2016) 35, 4 (2016), 103:1–12. Google ScholarDigital Library
    56. Egor Larionov, Christopher Batty, and Robert Bridson. 2017. Variational Stokes: A Unified Pressure-viscosity Solver for Accurate Viscous Liquids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2017) 36, 4 (2017), 101:1–11. Google ScholarDigital Library
    57. E. L. Lederer. 1931. Zur Theorie der Viskosität von Flüssigkeiten. Kolloid Beihefte 34, 5–9 (1931), 270–338.Google Scholar
    58. Toon Lenaerts, Bart Adams, and Philip Dutré. 2008. Porous Flow in Particle-based Fluid Simulations. ACM Transactions on Graphics (Proc. of SIGGRAPH 2008) 27, 3 (2008), 49:1–8. Google ScholarDigital Library
    59. Frank Losasso, Geoffrey Irving, Eran Guendelman, and Ronald Fedkiw. 2006a. Melting and burning solids into liquids and gases. IEEE Transactions on Visualization and Computer Graphics 12, 3 (2006), 343–352. Google ScholarDigital Library
    60. Frank Losasso, Tamar Shinar, Andrew Selle, and Ronald Fedkiw. 2006b. Multiple Interacting Liquids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2006) 25, 3 (2006), 812–819. Google ScholarDigital Library
    61. Miles Macklin and Matthias Müller. 2013. Position Based Fluids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2013) 32, 4 (2013), 104:1–12. Google ScholarDigital Library
    62. Hai Mao and Yee-Hong Yang. 2006. Particle-based Immiscible Fluid-fluid Collision. In Proceedings of Graphics Interface 2006 (GI ’06). Canadian Information Processing Society, Toronto, Ont., Canada, Canada, 49–55. http://dl.acm.org/citation.cfm?id=1143079.1143088 Google ScholarDigital Library
    63. Marek Krzysztof Misztal, Kenny Erleben, Adam Bargteil, Jens Fursund, Brian Bunch Christensen, Jakob Andreas Bærentzen, and Robert Bridson. 2014. Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes. IEEE Transactions on Visualization and Computer Graphics 20, 1 (2014), 4–16. Google ScholarDigital Library
    64. Georgios Moutsanidis, David Kamensky, Duan Z. Zhang, Yuri Bazilevs, and Christopher C. Long. 2019. Modeling strong discontinuities in the material point method using a single velocity field. Computer Methods in Applied Mechanics and Engineering 345 (2019), 584–601.Google ScholarCross Ref
    65. Matthias Müller, David Charypar, and Markus Gross. 2003. Particle-based Fluid Simulation for Interactive Applications. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’03). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 154–159. http://dl.acm.org/citation.cfm?id=846276.846298 Google ScholarDigital Library
    66. Matthias Müller, Bruno Heidelberger, Marcus Hennix, and John Ratclif. 2007. Position based dynamics. Journal of Visual Communication and Image Representation 18, 2 (2007), 109–118.Google ScholarDigital Library
    67. Matthias Müller, Simon Schirm, Matthias Teschner, Bruno Heidelberger, and Markus Gross. 2004. Interaction of Fluids with Deformable Solids: Research Articles. Computer Animation and Virtual Worlds 15, 3–4 (July 2004), 159–171. Google ScholarDigital Library
    68. Matthias Müller, Barbara Solenthaler, Richard Keiser, and Markus Gross. 2005. Particle-based Fluid-fluid Interaction. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’05). ACM, New York, NY, USA, 237–244. Google ScholarDigital Library
    69. Rahul Narain, Abhinav Golas, and Ming C. Lin. 2010. Free-flowing Granular Materials with Two-way Solid Coupling. ACM Transactions on Graphics (Proc. of SIGGRAPH Asia 2010) 29, 6 (2010), 173:1–10. Google ScholarDigital Library
    70. Arthur A. Noyes and Willis R. Whitney. 1897. The rate of solution of solid substances in their own sulutions. Journal of the American Chemical Society 19, 12 (1897), 930–934.Google ScholarCross Ref
    71. James G. Oldroyd and Alan Herries Wilson. 1950. On the formulation of rheological equations of state. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 200, 1063 (1950), 523–541.Google ScholarCross Ref
    72. Afonso Paiva, Fabiano Petronetto, Thomas Lewiner, and Geovan Tavares. 2006. Particle-based non-newtonian fluid animation for melting objects. In Proceedings of XIX Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI’06) (SIBGRAPI’06). 78–85.Google ScholarCross Ref
    73. Afonso Paiva, Fabiano Petronetto, Thomas Lewiner, and Geovan Tavares. 2009. Particle-based viscoplastic fluid/solid simulation. Computer-Aided Design 41, 4 (2009), 306–314. Point-based Computational Techniques. Google ScholarDigital Library
    74. Jinho Park, Younghwi Kim, Daehyeon Wi, Nahyup Kang, Sung Yong Shin, and Junyong Noh. 2008. A Unified Handling of Immiscible and Miscible Fluids. Computer Animation and Virtual Worlds 19, 3–4 (2008), 455–467. Google ScholarDigital Library
    75. Andreas Peer, Markus Ihmsen, Jens Cornelis, and Matthias Teschner. 2015. An Implicit Viscosity Formulation for SPH Fluids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2015) 34, 4 (2015), 114:1–10. Google ScholarDigital Library
    76. Andre Pradhana. 2017. Multiphase Simulation Using Material Point Method. dissertation. UCLA. https://escholarship.org/uc/item/52b8b82qGoogle Scholar
    77. Andre Pradhana, Theodore Gast, Gergely Klár, Chuyuan Fu, Joseph Teran, Chenfanfu Jiang, and Ken Museth. 2017. Multi-species Simulation of Porous Sand and Water Mixtures. ACM Transactions on Graphics (Proc. of SIGGRAPH 2017) 36, 4 (2017), 105:1–11. Google ScholarDigital Library
    78. Daniel Ram, Theodore Gast, Chenfanfu Jiang, Craig Schroeder, Alexey Stomakhin, Joseph Teran, and Pirouz Kavehpour. 2015. A Material Point Method for Viscoelastic Fluids, Foams and Sponges. In Proceedings of the 14th ACM SIGGRAPH / Eurographics Symposium on Computer Animation (SCA ’15). ACM, 157–163. Google ScholarDigital Library
    79. Bo Ren, Chenfeng Li, Xiao Yan, Ming C. Lin, Javier Bonet, and Shi-Min Hu. 2014. Multiple-Fluid SPH Simulation Using a Mixture Model. ACM Transactions on Graphics 33, 5 (2014), 171:1–11. Google ScholarDigital Library
    80. Avi Robinson-Mosher, Tamar Shinar, Jon Gretarsson, Jonathan Su, and Ronald Fedkiw. 2008. Two-way Coupling of Fluids to Rigid and Deformable Solids and Shells. ACM Transactions on Graphics (Proc. of SIGGRAPH 2008) 27, 3 (2008), 46:1–9. Google ScholarDigital Library
    81. Michel (Sr.) Roegiers and Lucien Roegiers. 1946. La viscosité des mélanges de fluides normaux. (1946).Google Scholar
    82. Michael Rusin. 1975. The Structure of Nonlinear Blending Models. Chemical Engineering Science 30, 8 (1975), 937–944.Google ScholarCross Ref
    83. Alireza Sadeghirad, Rebecca M. Brannon, and Jeff Burghardt. 2011. A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations. Internat. J. Numer. Methods Engrg. 86, 12 (2011), 1435–1456.Google ScholarCross Ref
    84. Seung-Ho Shin, Hyeong Ryeol Kam, and Chang-Hun Kim. 2010. Hybrid Simulation of Miscible Mixing with Viscous Fingering. Computer Graphics Forum (Proc. EUROGRAPHICS 2010) 29, 2 (2010), 675–683.Google Scholar
    85. J. 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 66, 2 (feb 1988), 199–219. Google ScholarDigital Library
    86. Juan C. Simo and Thomas J. R. Hughes. 1998. Computational Inelasticity. Springer.Google Scholar
    87. Barbara Solenthaler and Renato B. Pajarola. 2009. Predictive-corrective Incompressible SPH. ACM Transaction on Graphics (Proc. of SIGGRAPH 2009) 28, 3 (2009), 40:1–6. Google ScholarDigital Library
    88. Barbara Solenthaler, Jürg Schläfli, and Renato Pajarola. 2007. A unified particle model for fluid-solid interactions. Computer Animation and Virtual Worlds 18, 1 (2007), 69–82. Google ScholarDigital Library
    89. Jos Stam. 1999. Stable Fluids. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’99). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 121–128. Google ScholarDigital Library
    90. Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, and Andrew Selle. 2013. A Material Point Method for Snow Simulation. ACM Transactions on Graphics (Proc. of SIGGRAPH 2013) 32, 4 (2013), 102:1–10. Google ScholarDigital Library
    91. Alexey Stomakhin, Craig Schroeder, Chenfanfu Jiang, Lawrence Chai, Joseph Teran, and Andrew Selle. 2014. Augmented MPM for phase-change and varied materials. ACM Transactions on Graphics (Proc. of SIGGRAPH 2014) 33, 4 (2014), 138:1–11. Google ScholarDigital Library
    92. 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 (1994), 179–196.Google Scholar
    93. Deborah Sulsky, Shi-Jian Zhou, and Howard L. Schreyer. 1995. Application of a particle-in-cell method to solid mechanics. Computer Physics Communications 87, 1–2 (1995), 236–252.Google ScholarCross Ref
    94. Demetri Terzopoulos and Kurt Fleischer. 1988. Modeling Inelastic Deformation: Viscolelasticity, Plasticity, Fracture. SIGGRAPH Computer Graphics (Proc. of SIGGRAPH 1988) 22, 4 (1988), 269–278. Google ScholarDigital Library
    95. Martin Wicke, Daniel Ritchie, Bryan M. Klingner, Sebastian Burke, Jonathan R. Shewchuk, and James F. O’Brien. 2010. Dynamic Local Remeshing for Elastoplastic Simulation. ACM Transactions on Graphics (Proc. of SIGGRAPH 2010) 29, 4 (2010), 49:1–11. Google ScholarDigital Library
    96. Chris Wojtan, Nils Thürey, Markus Gross, and Greg Turk. 2009. Deforming Meshes That Split and Merge. ACM Transactions on Graphics (Proc. of SIGGRAPH 2009) 28, 3 (2009), 76:1–10. Google ScholarDigital Library
    97. Chris Wojtan and Greg Turk. 2008. Fast Viscoelastic Behavior with Thin Features. ACM Transactions on Graphics (Proc. of SIGGRAPH 2008) 27, 3 (2008), 47:1–8. Google ScholarDigital Library
    98. Joel Wretborn, Rickard Armiento, and Ken Museth. 2017. Animation of Crack Propagation by Means of an Extended Multi-body Solver for the Material Point Method. Computers and Graphics 69, C (2017), 131–139. Google ScholarDigital Library
    99. Xiao Yan, Yun-Tao Jiang, Chen-Feng Li, Ralph R. Martin, and Shi-Min Hu. 2016. Multiphase SPH Simulation for Interactive Fluids and Solids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2016) 35, 4 (2016), 79:1–11. Google ScholarDigital Library
    100. Xiao Yan, Chen-Feng Li, Xiao-Song Chen, and Shi-Min Hu. 2018. MPM simulation of interacting fluids and solids. Computer Graphics Forum 37, 8 (2018), 183–193.Google ScholarCross Ref
    101. 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 Transactions on Graphics (Proc. of SIGGRAPH Asia 2017) 36, 6 (2017), 224:1–13. Google ScholarDigital Library
    102. Tao Yang, Jian Chang, Bo Ren, Ming C. Lin, Jian Jun Zhang, and Shi-Min Hu. 2015. Fast Multiple-fluid Simulation Using Helmholtz Free Energy. ACM Transactions on Graphics (Proc. SIGGRAPH Asia 2015) 34, 6 (2015), 201:1–11. Google ScholarDigital Library
    103. Tao Yang, Ralph R. Martin, Ming C. Lin, Jian Chang, and Shi-Min Hu. 2017. Pairwise Force SPH Model for Real-Time Multi-Interaction Applications. IEEE Transactions on Visualization and Computer Graphics 23, 10 (2017), 2235–2247.Google ScholarDigital Library
    104. Kenji Yasuda. 1979. Investigation of the analogies between viscometric and linear viscoelastic properties of polystyrene fluids. dissertation. Massachusetts Institute of Technology. https://dspace.mit.edu/handle/1721.1/16043Google Scholar
    105. Yonghao Yue, Breannan Smith, Christopher Batty, Changxi Zheng, and Eitan Grinspun. 2015. Continuum Foam: A Material Point Method for Shear-Dependent Flows. ACM Transactions on Graphics 34, 5 (2015), 160:1–20. Google ScholarDigital Library
    106. 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 Transactions on Graphics (Proc. of SIGGRAPH Asia 2018) 37, 6 (2018), 283:1–19. Google ScholarDigital Library
    107. Boris Zhmud. 2014. Viscosity Blending Equations. Lube Magazine 121 (2014), 22–27.Google Scholar
    108. Bo Zhu, Minjae Lee, Ed Quigley, and Ronald Fedkiw. 2015. Codimensional non-Newtonian Fluids. ACM Transactions on Graphics (Proc. of SIGGRAPH 2015) 34, 4 (2015), 115:1–9. Google ScholarDigital Library
    109. Fei Zhu, Jing Zhao, Sheng Li, Yong Tang, and Guoping Wang. 2017. Dynamically Enriched MPM for Invertible Elasticity. Computer Graphics Forum 36, 6 (2017), 381–392. Google ScholarDigital Library
    110. Yongning Zhu and Robert Bridson. 2005. Animating Sand As a Fluid. ACM Transactions on Graphics (Proc. of SIGGRAPH 2005) 24, 3 (2005), 965–972. Google ScholarDigital Library


ACM Digital Library Publication:



Overview Page: