skip to main content
research-article

A Unified Particle-Based Solver for Non-Newtonian Behaviors Simulation

Published: 12 December 2023 Publication History

Abstract

In this article, we present a unified framework to simulate non-Newtonian behaviors. We combine viscous and elasto-plastic stress into a unified particle solver to achieve various non-Newtonian behaviors ranging from fluid-like to solid-like. Our constitutive model is based on a Generalized Maxwell model, which incorporates viscosity, elasticity and plasticity in one non-linear framework by a unified way. On the one hand, taking advantage of the viscous term, we construct a series of strain-rate dependent models for classical non-Newtonian behaviors such as shear-thickening, shear-thinning, Bingham plastic, etc. On the other hand, benefiting from the elasto-plastic model, we empower our framework with the ability to simulate solid-like non-Newtonian behaviors, i.e., visco-elasticity/plasticity. In addition, we enrich our method with a heat diffusion model to make our method flexible in simulating phase change. Through sufficient experiments, we demonstrate a wide range of non-Newtonian behaviors ranging from viscous fluid to deformable objects. We believe this non-Newtonian model will enhance the realism of physically-based animation, which has great potential for computer graphics.

References

[1]
D. Stora, P. O. Agliati, M. P. Cani, F. Neyret, and J. D. Gascuel, “Animating lava flows,” in Proc. Graph. Interface Conf., 1999, pp. 203–210.
[2]
A. Peer, M. Ihmsen, J. Cornelis, and M. Teschner, “An implicit viscosity formulation for SPH fluids,” ACM Trans. Graph., vol. 34, no. 4, pp. 1–10, 2015.
[3]
R. Goldade, Y. Wang, M. Aanjaneya, and C. Batty, “An adaptive variational finite difference framework for efficient symmetric octree viscosity,” ACM Trans. Graph., vol. 38, no. 4, pp. 1–14, 2019.
[4]
A. Stomakhin, C. Schroeder, C. Jiang, L. Chai, J. Teran, and A. Selle, “Augmented MPM for phase-change and varied materials,” ACM Trans. Graph., vol. 33, no. 4, pp. 1–11, 2014.
[5]
H. Su, T. Xue, C. Han, C. Jiang, and M. Aanjaneya, “A unified second-order accurate in time MPM formulation for simulating viscoelastic liquids with phase change,” ACM Trans. Graph., vol. 40, no. 4, pp. 1–18, 2021.
[6]
D. Koschier, J. Bender, B. Solenthaler, and M. Teschner, “A survey on SPH methods in computer graphics,” Comput. Graph. Forum, vol. 41, no. 2, pp. 737–760, 2022.
[7]
M. Carlson, P. J. Mucha, R. B. Van Horn, and G. Turk, “Melting and flowing,” in Proc. ACM SIGGRAPH/Eurographics Symp. Comput. Animation, 2002, pp. 167–174.
[8]
C. Batty and R. Bridson, “Accurate viscous free surfaces for buckling, coiling, and rotating liquids,” in Proc. ACM/Eurographics Symp. Comput. Animation, 2008, pp. 219–228.
[9]
E. Larionov, C. Batty, and R. Bridson, “Variational stokes: A unified pressure-viscosity solver for accurate viscous liquids,” ACM Trans. Graph., vol. 36, no. 4, pp. 1–11, 2017.
[10]
H. Shao, L. Huang, and D. L. Michels, “A fast unsmoothed aggregation algebraic multigrid framework for the large-scale simulation of incompressible flow,” ACM Trans. Graph., vol. 41, no. 4, pp. 1–18, 2022.
[11]
M. Müller, R. Keiser, A. Nealen, M. Pauly, M. Gross, and M. Alexa, “Point based animation of elastic, plastic and melting objects,” in Proc. ACM SIGGRAPH/Eurographics Symp. Comput. Animation, 2004, pp. 141–151.
[12]
B. Solenthaler, J. Schläfli, and R. Pajarola, “A unified particle model for fluid–solid interactions,” Comput. Animation Virtual Worlds, vol. 18, no. 1, pp. 69–82, 2007.
[13]
J. J. Monaghan, “Smoothed particle hydrodynamics,” Annu. Rev. Astron. Astrophys., vol. 30, no. 1, pp. 543–574, 1992.
[14]
M. Müller, D. Charypar, and M. Gross, “Particle-based fluid simulation for interactive applications,” in Proc. ACM SIGGRAPH/Eurographics Symp. Comput. Animation, 2003, pp. 154–159.
[15]
B. Zhu, M. Lee, E. Quigley, and R. Fedkiw, “Codimensional non-newtonian fluids,” ACM Trans. Graph., vol. 34, no. 4, pp. 1–9, 2015.
[16]
M. Becker and M. Teschner, “Weakly compressible SPH for free surface flows,” in Proc. ACM SIGGRAPH/Eurographics Symp. Comput. Animation, 2007, pp. 209–217.
[17]
B. Solenthaler and R. Pajarola, “Predictive-corrective incompressible SPH,” in Proc. ACM SIGGRAPH, 2009, pp. 1–6.
[18]
M. Ihmsen, J. Cornelis, B. Solenthaler, C. Horvath, and M. Teschner, “Implicit incompressible SPH,” IEEE Trans. Vis. Comput. Graph., vol. 20, no. 3, pp. 426–435, Mar. 2014.
[19]
J. Bender and D. Koschier, “Divergence-free SPH for incompressible and viscous fluids,” IEEE Trans. Vis. Comput. Graph., vol. 23, no. 3, pp. 1193–1206, Mar. 2017.
[20]
D. Koschier, J. Bender, B. Solenthaler, and M. Teschner, “Smoothed particle hydrodynamics techniques for the physics based simulation of fluids and solids,” in Proc. Eurographics, 2019, pp. 1–41.
[21]
H. Schechter and R. Bridson, “Ghost SPH for animating water,” ACM Trans. Graph., vol. 31, no. 4, pp. 1–8, 2012.
[22]
T. Takahashi, Y. Dobashi, I. Fujishiro, T. Nishita, and M. C. Lin, “Implicit formulation for SPH-based viscous fluids,” Comput. Graph. Forum, vol. 34, no. 2, pp. 493–502, 2015.
[23]
A. Peer and M. Teschner, “Prescribed velocity gradients for highly viscous SPH fluids with vorticity diffusion,” IEEE Trans. Vis. Comput. Graph., vol. 23, no. 12, pp. 2656–2662, Dec. 2017.
[24]
M. Weiler, D. Koschier, M. Brand, and J. Bender, “A physically consistent implicit viscosity solver for SPH fluids,” Comput. Graph. Forum, vol. 37, no. 2, pp. 145–155, 2018.
[25]
L. F. de Souza Andrade, M. Sandim, F. Petronetto, P. Pagliosa, and A. Paiva, “Particle-based fluids for viscous jet buckling,” Comput. Graph., vol. 52, pp. 106–115, 2015.
[26]
Y. Gao, S. Li, A. Hao, and H. Qin, “Simulating multi-scale, granular materials and their transitions with a hybrid Euler-Lagrange solver,” IEEE Trans. Vis. Comput. Graph., vol. 27, no. 12, pp. 4483–4494, Dec. 2021.
[27]
D. Terzopoulos, J. Platt, and K. Fleischer, “Heating and melting deformable models,” J. Visual. Comput. Animation, vol. 2, no. 2, pp. 68–73, 1991.
[28]
F. Losasso, T. Shinar, A. Selle, and R. Fedkiw, “Multiple interacting liquids,” ACM Trans. Graph., vol. 25, no. 3, pp. 812–819, 2006.
[29]
M. Fujisawa and K. T. Miura, “Animation of ice melting phenomenon based on thermodynamics with thermal radiation,” in Proc. 5th Int. Conf. Comput. Graph. Interactive Techn. Aust. Southeast Asia, 2007, pp. 249–256.
[30]
T. G. Goktekin, A. W. Bargteil, and J. F. O’Brien, “A method for animating viscoelastic fluids,” ACM Trans. Graph., vol. 23, no. 3, pp. 463–468, 2004.
[31]
Y. Gao, S. Li, H. Qin, Y. Xu, and A. Hao, “An efficient FLIP and shape matching coupled method for fluid–solid and two-phase fluid simulations,” Vis. Comput., vol. 35, no. 12, pp. 1741–1753, 2019.
[32]
M. Becker, M. Ihmsen, and M. Teschner, “Corotated SPH for deformable solids,” in Proc. 5th Eurographics Conf. Natural Phenomena, 2009, pp. 27–34.
[33]
J. F. O’Brien, A. W. Bargteil, and J. K. Hodgins, “Graphical modeling and animation of ductile fracture,” in Proc. 29th Annu. Conf. Comput. Graph. Interactive Techn., 2002, pp. 291–294.
[34]
A. Stomakhin, C. Schroeder, L. Chai, J. Teran, and A. Selle, “A material point method for snow simulation,” ACM Trans. Graph., vol. 32, no. 4, pp. 1–10, 2013.
[35]
Y. Yue, B. Smith, C. Batty, C. Zheng, and E. Grinspun, “Continuum foam: A material point method for shear-dependent flows,” ACM Trans. Graph., vol. 34, no. 5, pp. 1–20, 2015.
[36]
Y. Fang, M. Li, M. Gao, and C. Jiang, “Silly rubber: An implicit material point method for simulating non-equilibrated viscoelastic and elastoplastic solids,” ACM Trans. Graph., vol. 38, no. 4, pp. 1–13, 2019.
[37]
M. Gao et al., “GPU optimization of material point methods,” ACM Trans. Graph., vol. 37, no. 6, pp. 1–12, 2018.
[38]
C. Gissler, A. Henne, S. Band, A. Peer, and M. Teschner, “An implicit compressible SPH solver for snow simulation,” ACM Trans. Graph., vol. 39, no. 4, pp. 1–16, 2020.
[39]
A. W. Bargteil, C. Wojtan, J. K. Hodgins, and G. Turk, “A finite element method for animating large viscoplastic flow,” ACM Trans. Graph., vol. 26, no. 3, pp. 1–8, 2007.
[40]
C. Wojtan and G. Turk, “Fast viscoelastic behavior with thin features,” ACM Trans. Graph., vol. 27, no. 3, pp. 1–8, 2008.
[41]
O. Ozgen, M. Kallmann, and E. Brown, “An SPH model to simulate the dynamic behavior of shear thickening fluids,” Comput. Animation Virtual Worlds, vol. 30, no. 5, pp. 1–18, 2019.
[42]
N. Phan Thien and N. Mai Duy, Understanding Viscoelasticity: An Introduction to Rheology, Berlin, Germany: Springer International Publishing, 2017, pp. 95–111.
[43]
R. P. Chhabra, Non-Newtonian Fluids: An Introduction. New York, NY, USA: Springer, 2010, pp. 3–34.
[44]
M. M. Cross, “Rheology of non-newtonian fluids: A new flow equation for pseudoplastic systems,” J. Colloid Sci., vol. 20, no. 5, pp. 417–437, 1965.
[45]
M. Müller, B. Heidelberger, M. Teschner, and M. Gross, “Meshless deformations based on shape matching,” ACM Trans. Graph., vol. 24, no. 3, pp. 471–478, 2005.
[46]
Y. Gao, S. Li, L. Yang, H. Qin, and A. Hao, “An efficient heat-based model for solid-liquid-gas phase transition and dynamic interaction,” Graphical Models, vol. 94, pp. 14–24, 2017.
[47]
P. W. Cleary and J. J. Monaghan, “Conduction modelling using smoothed particle hydrodynamics,” J. Comput. Phys., vol. 148, no. 1, pp. 227–264, 1999.
[48]
J. Orthmann and A. Kolb, “Temporal blending for adaptive SPH,” Comput. Graph. Forum, vol. 31, no. 8, pp. 2436–2449, 2012.
[49]
P. Bottiglieri, F. De Sio, G. Fasanaro, G. Mojoli, M. Impembo, and D. Castaldo, “Rheological characterization of ketchup,” J. Food Qual., vol. 14, no. 6, pp. 497–512, 1991.

Index Terms

  1. A Unified Particle-Based Solver for Non-Newtonian Behaviors Simulation
          Index terms have been assigned to the content through auto-classification.

          Recommendations

          Comments

          Information & Contributors

          Information

          Published In

          cover image IEEE Transactions on Visualization and Computer Graphics
          IEEE Transactions on Visualization and Computer Graphics  Volume 30, Issue 4
          April 2024
          170 pages

          Publisher

          IEEE Educational Activities Department

          United States

          Publication History

          Published: 12 December 2023

          Qualifiers

          • Research-article

          Contributors

          Other Metrics

          Bibliometrics & Citations

          Bibliometrics

          Article Metrics

          • 0
            Total Citations
          • 0
            Total Downloads
          • Downloads (Last 12 months)0
          • Downloads (Last 6 weeks)0
          Reflects downloads up to 13 Jan 2025

          Other Metrics

          Citations

          View Options

          View options

          Media

          Figures

          Other

          Tables

          Share

          Share

          Share this Publication link

          Share on social media