A semi-implicit material point method for the continuum simulation of granular materials

Fig. 1. Frying an egg on a hot pan, achieved by enabling the diffusion of phases but disabling the diffusion of concentrations.We introduce a unified particle framework which integrates the phase-field method with multi-material simulation to allow modeling of both liquids and solids, as well as phase transitions between them. A simple elastoplastic model is used to capture the behavior of various kinds of solids, including deformable bodies, granular materials, and cohesive soils. States of matter or phases, particularly liquids and solids, are modeled using the nonconservative Allen-Cahn equation. In contrast, materials-made of different substances-are advected by the conservative Cahn-Hilliard equation. The distributions of phases and materials are represented by a phase variable and a concentration variable, respectively, allowing us to represent commonly observed fluid-solid i nteractions. T he d ynamics o f a m ulti-phase, multimaterial system are governed by a unified Helmholtz free-energy density. This framework provides the first method in computer graphics capable of modeling a continuous interface between phases. It is versatile and can be readily used in many scenarios challenging to simulate. Examples are provided to demonstrate the capabilities and effectiveness of this approach.

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“…Daviet et al [2016] presented a continuum-based method for simulating non-smooth viscoplastic granular rheology using a material point method.…”

Section: Solid Simulationmentioning

confidence: 99%

A unified particle system framework for multi-phase, multi-material visual simulations

et al. 2017

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“…Ram et al [2015] used the MPM formalism to simulate viscoelastic materials, while Yue et al [2015] applied it for the simulation of foam. More recently, this method has been applied to the simulation of sand [Daviet and Bertails-Descoubes 2016;Klár et al 2016] and the interaction between sand and water [Tampubolon et al 2017]. While MPM has gained popularity due to its high-quality results, it is computationally intensive.…”

Section: Related Workmentioning

confidence: 99%

Conformation constraints for efficient viscoelastic fluid simulation

Barreiro¹,

García-Fernández

Alduán

et al. 2017

ACM Trans. Graph.

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Fig. 1. A complex multiphysics simulation involving viscoelastic fluids, rigid bodies, and deformable bodies. We simulate whipped cream and strawberry syrup e iciently using our novel viscoelasticity model based on conformation constraints. The complete scene consists of 150,000 particles and runs at 1.13 seconds per frame.e simulation of high viscoelasticity poses important computational challenges. One is the di culty to robustly measure strain and its derivatives in a medium without permanent structure. Another is the high sti ness of the governing di erential equations. Solutions that tackle these challenges exist, but they are computationally slow. We propose a constraint-based model of viscoelasticity that enables e cient simulation of highly viscous and viscoelastic phenomena. Our model reformulates, in a constraint-based fashion, a constitutive model of viscoelasticity for polymeric uids, which de nes simple governing equations for a conformation tensor. e model can represent a diverse pale e of materials, spanning elastoplastic, highly viscous, and inviscid liquid behaviors. In addition, we have designed a constrained dynamics solver that extends the position-based dynamics method to handle e ciently both position-based and velocity-based constraints. We show results that range from interactive simulation of viscoelastic e ects to large-scale simulation of high viscosity with competitive performance.

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“…Stomakhin et al (2014) added a heat solver to simulate phase change of materials. Klar et al (2016) and Daviet and Bertails-Descoubes (2016) used MPM together with a DruckerPrager plasticiy model to simulate sand and other granular materials. Yue et al (2015) complemented MPM with a particle re-sampling scheme to handle potential non-uniform particle distributions due to high shearing strain.…”

Section: Related Workmentioning

confidence: 99%

Animation of crack propagation by means of an extended multi-body solver for the material point method

Wretborn

Armiento

Museth

2017

Computers & Graphics

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A semi-implicit material point method for the continuum simulation of granular materials

Abstract: Figure 1: A steel ball impacts a granular bed. Unlike previous approaches, our fully resolved (non-linearized) Drucker-Prager rheology allows us to retrieve a perfectly round crater.

Cited by 89 publications

References 27 publications

A unified particle system framework for multi-phase, multi-material visual simulations

A unified particle system framework for multi-phase, multi-material visual simulations

Conformation constraints for efficient viscoelastic fluid simulation

Animation of crack propagation by means of an extended multi-body solver for the material point method

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