Abstract
Recent years have witnessed the rapid deployment of numerous physics-based modeling and simulation algorithms and techniques for fluids, solids, and their delicate coupling in computer animation. However, it still remains a challenging problem to model the complex elastic-viscoplastic behaviors during fluid–solid phase transitions and facilitate their seamless interactions inside the same framework. In this article, we propose a practical method capable of simulating granular flows, viscoplastic liquids, elastic-plastic solids, rigid bodies, and interacting with each other, to support novel phenomena all heavily involving realistic phase transitions, including dissolution, melting, cooling, expansion, shrinking, and so on. At the physics level, we propose to combine and morph von Mises with Drucker–Prager and Cam–Clay yield models to establish a unified phase-field-driven EVP model, capable of describing the behaviors of granular, elastic, plastic, viscous materials, liquid, non-Newtonian fluids, and their smooth evolution. At the numerical level, we derive the discretization form of Cahn–Hilliard and Allen–Cahn equations with the material point method to effectively track the phase-field evolution, so as to avoid explicit handling of the boundary conditions at the interface. At the application level, we design a novel heuristic strategy to control specialized behaviors via user-defined schemes, including chemical potential, density curve, and so on. We exhibit a set of numerous experimental results consisting of challenging scenarios to validate the effectiveness and versatility of the new unified approach. This flexible and highly stable framework, founded upon the unified treatment and seamless coupling among various phases, and effective numerical discretization, has its unique advantage in animation creation toward novel phenomena heavily involving phase transitions with artistic creativity and guidance.
- 2018. MLS pressure boundaries for divergence-free and viscous SPH fluids. Comput. Graph. 76 (2018), 37–46.
DOI: Google ScholarCross Ref . - 2007. A finite element method for animating large viscoplastic flow. ACM Trans. Graph. 26, 3 (
Jul. 2007), 16–es.DOI: Google ScholarDigital Library . - 2017. Divergence-free SPH for incompressible and viscous fluids. IEEE Trans. Vis. Comput. Graph. 23, 3 (2017), 1193–1206.
DOI: Google ScholarDigital Library . - 1998. Nonlinear continuum mechanics for finite element analysis. Nucl. Fusion 38 (1998), 776–776.Google ScholarCross Ref .
- 1958. Free energy of a nonuniform system. I. interfacial free energy. J. Chem. Phys. 28, 2 (1958), 258–267.Google ScholarCross Ref .
- 1972. Rheological equations from molecular network theories. Trans. Soc. Rheol. 16, 1 (1972), 99–127.Google ScholarCross Ref .
- 2020. A moving least square reproducing kernel particle method for unified multiphase continuum simulation. ACM Trans. Graph. 39, 6, Article
176 (Nov. 2020), 15 pages.DOI: Google ScholarDigital Library . - 2019. A thermomechanical material point method for baking and cooking. ACM Trans. Graph. 38, 6, Article
192 (Nov. 2019), 14 pages.DOI: Google ScholarDigital Library . - 2019. Silly rubber: An implicit material point method for simulating non-equilibrated viscoelastic and elastoplastic solids. ACM Trans. Graph. 38, 4, Article
118 (Jul. 2019), 13 pages.DOI: Google ScholarDigital Library . - 2020. IQ-MPM: An interface quadrature material point method for non-sticky strongly two-way coupled nonlinear solids and fluids. ACM Trans. Graph. 39, 4, Article
51 (Jul. 2020), 16 pages.DOI: Google ScholarDigital Library . - 2018. A multi-scale model for simulating liquid-fabric interactions. ACM Trans. Graph. 37, 4, Article
51 (Jul. 2018), 16 pages.DOI: Google ScholarDigital Library . - 2021. Revisiting integration in the material point method: A scheme for easier separation and less dissipation. ACM Trans. Graph. 40, 4, Article
109 (Jul. 2021), 16 pages.DOI: Google ScholarDigital Library . - 2017. A polynomial particle-in-cell method. ACM Trans. Graph. 36, 6, Article
222 (Nov. 2017), 12 pages.DOI: Google ScholarDigital Library . - 2018a. Animating fluid sediment mixture in particle-laden flows. ACM Trans. Graph. 37, 4, Article
149 (Jul. 2018), 11 pages.DOI: Google ScholarDigital Library . - 2018b. GPU optimization of material point methods. ACM Trans. Graph. 37, 6, Article
254 (Dec. 2018), 12 pages.DOI: Google ScholarDigital Library . - 2004. A method for animating viscoelastic fluids. ACM Trans. Graph. 23, 3 (
Aug. 2004), 463–468.DOI: Google ScholarDigital Library . - 2019. A hybrid material point method for frictional contact with diverse materials. Proc. ACM Comput. Graph. Interact. Tech. 2, 2, Article
17 (Jul. 2019), 24 pages.DOI: Google ScholarDigital Library . - 1926. Konsistenzmessungen von gummi-benzollösungen. Koll.-Zeitschr. 39, 4 (1926), 291–300.Google Scholar .
- 2018. A moving least squares material point method with displacement discontinuity and two-way rigid body coupling. ACM Trans. Graph. 37, 4, Article
150 (Jul. 2018), 14 pages.DOI: Google ScholarDigital Library . - 2017. Anisotropic elastoplasticity for cloth, knit and hair frictional contact. ACM Trans. Graph. 36, 4, Article
152 (Jul. 2017), 14 pages.DOI: Google ScholarDigital Library . - 2015. The affine particle-in-cell method. ACM Trans. Graph. 34, 4, Article
51 (Jul. 2015), 10 pages.DOI: Google ScholarDigital Library . - 2016. Drucker-prager elastoplasticity for sand animation. ACM Trans. Graph. 35, 4, Article
103 (Jul. 2016), 12 pages.DOI: Google ScholarDigital Library . - 2017. Variational stokes: A unified pressure-viscosity solver for accurate viscous liquids. ACM Trans. Graph. 36, 4, Article
101 (Jul. 2017), 11 pages.DOI: Google ScholarDigital Library . - 2022b. Stability and convergence analysis for the implicit-explicit method to the Cahn-Hilliard equation. Math. Comp. 91, 334 (2022), 785–809.Google ScholarCross Ref .
- 2022a. Efficient kinetic simulation of two-phase flows. ACM Trans. Graph. 41, 4, Article
114 (Jul. 2022), 17 pages.DOI: Google ScholarDigital Library . - 2004. Interaction of fluids with deformable solids. Comput. Anim. Virt. Worlds 15, 3-4 (2004), 159–171.Google ScholarDigital Library .
- 2013. OpenVDB: An open-source data structure and toolkit for high-resolution volumes. In ACM SIGGRAPH 2013 Courses (SIGGRAPH ’13). Association for Computing Machinery, New York, NY, USA, Article
19 , 1 pages.DOI: Google ScholarDigital Library . - 2019. Mixing sauces: A viscosity blending model for shear thinning fluids. ACM Trans. Graph. 38, 4, Article
95 (Jul. 2019), 17 pages.DOI: Google ScholarDigital Library . - 1950. On the formulation of rheological equations of state. Proc. Roy. Soc. Lond. Ser. A: Math. Phys. Sci. 200, 1063 (1950), 523–541.Google ScholarCross Ref .
- 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). Association for Computing Machinery, New York, NY, 157–163.
DOI: Google ScholarDigital Library . - 2014. Multiple-fluid SPH simulation using a mixture model. ACM Trans. Graph. 33, 5, Article
171 (Sep. 2014), 11 pages.DOI: Google ScholarDigital Library . - 2021. Unified particle system for multiple-fluid flow and porous material. ACM Trans. Graph. 40, 4, Article
118 (Jul. 2021), 14 pages.DOI: Google ScholarDigital Library . - 1968. On the Generalized Stress-Strain Behavior of Wet Clays. Cambridge University Press, Cambridge. 535–609 pages.Google Scholar .
- 2014. SPGrid: A sparse paged grid structure applied to adaptive smoke simulation. ACM Trans. Graph. 33, 6, Article
205 (Nov. 2014), 12 pages.DOI: Google ScholarDigital Library . - 2006. Computational Inelasticity. Vol. 7. Springer Science & Business Media, New York.Google Scholar .
- 2018. Stable neo-hookean flesh simulation. ACM Trans. Graph. 37, 2, Article
12 (Mar. 2018), 15 pages.DOI: Google ScholarDigital Library . - 2007. A unified particle model for fluid-solid interactions. Comput. Animat. Virt. Worlds 18, 1 (2007), 69–82.
DOI: Google ScholarCross Ref . - 2013. A material point method for snow simulation. ACM Trans. Graph. 32, 4, Article
102 (Jul. 2013), 10 pages.DOI: Google ScholarDigital Library . - 2014. Augmented MPM for phase-change and varied materials. ACM Trans. Graph. 33, 4, Article
138 (Jul. 2014), 11 pages.DOI: Google ScholarDigital Library . - 2021. A unified second-order accurate in time MPM formulation for simulating viscoelastic liquids with phase change. ACM Trans. Graph. 40, 4, Article
119 (Jul. 2021), 18 pages.DOI: Google ScholarDigital Library . - 1993. A particle method for history-dependent materials. Computer Methods Appl. Mech. Eng. 118 (1993), 179–196.Google ScholarCross Ref .
- 2021. A material point method for nonlinearly magnetized materials. ACM Trans. Graph. 40, 6, Article
205 (Dec. 2021), 13 pages.DOI: Google ScholarDigital Library . - 2017. Multi-species simulation of porous sand and water mixtures. ACM Trans. Graph. 36, 4, Article
105 (Jul. 2017), 11 pages.DOI: Google ScholarDigital Library . - 1988. Modeling inelastic deformation: Viscolelasticity, plasticity, fracture. SIGGRAPH Comput. Graph. 22, 4 (
Jun. 1988), 269–278.DOI: Google ScholarDigital Library . - 2019. Simulation and visualization of ductile fracture with the material point method. Proc. ACM Comput. Graph. Interact. Tech. 2, 2, Article
18 (jul 2019), 20 pages.DOI: Google ScholarDigital Library . - 2020. A massively parallel and scalable multi-GPU material point method. ACM Trans. Graph. 39, 4, Article
30 (Jul. 2020), 15 pages.DOI: Google ScholarDigital Library . - 2018. A physically consistent implicit viscosity solver for SPH fluids. Comput. Graph. Forum 37, 2 (2018), 145–155.
DOI: Google ScholarCross Ref . - 2020. AnisoMPM: Animating anisotropic damage mechanics. ACM Trans. Graph. 39, 4, Article
37 (Jul. 2020), 16 pages.DOI: Google ScholarDigital Library . - 2019. CD-MPM: Continuum damage material point methods for dynamic fracture animation. ACM Trans. Graph. 38, 4, Article
119 (Jul. 2019), 15 pages.DOI: Google ScholarDigital Library . - 2020. A novel discretization and numerical solver for non-fourier diffusion. ACM Trans. Graph. 39, 6, Article
178 (Nov. 2020), 14 pages.DOI: Google ScholarDigital Library . - 2016. Multiphase SPH simulation for interactive fluids and solids. ACM Trans. Graph. 35, 4, Article
79 (Jul. 2016), 11 pages.DOI: Google ScholarDigital Library . - 2018. MPM simulation of interacting fluids and solids. Comput. Graph. Forum 37, 8 (2018), 183–193.
DOI: Google ScholarCross Ref . - 2017. A unified particle system framework for multi-phase, multi-material visual simulations. ACM Trans. Graph. 36, 6, Article
224 (Nov. 2017), 13 pages.DOI: Google ScholarDigital Library . - 2015. Fast multiple-fluid simulation using Helmholtz free energy. ACM Trans. Graph. 34, 6, Article
201 (Oct. 2015), 11 pages.DOI: Google ScholarDigital Library . - 2015. Continuum foam: A material point method for shear-dependent flows. ACM Trans. Graph. 34, 5, Article
160 (Nov. 2015), 20 pages.DOI: Google ScholarDigital Library . - 2018. Hybrid grains: Adaptive coupling of discrete and continuum simulations of granular media. ACM Trans. Graph. 37, 6, Article
283 (Dec. 2018), 19 pages.DOI: Google ScholarDigital Library . - 2015. Codimensional non-newtonian fluids. ACM Trans. Graph. 34, 4, Article
115 (Jul. 2015), 9 pages.DOI: Google ScholarDigital Library .
Index Terms
- A Unified MPM Framework Supporting Phase-field Models and Elastic-viscoplastic Phase Transition
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