Physics-Based Animation

Kentaro Nagasawa, Takayuki Suzuki, Ryohei Seto, Masato Okada, Yonghao Yue

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. 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.

Mixing Sauces: A Viscosity Blending Model for Shear Thinning Fluids

L. Huang, T. Hädrich, D. L. Michels

We present an approach to the accurate and efficient large-scale simulation of the complex dynamics of ferrofluids based on physical principles. Ferrofluids are liquids containing magnetic particles that react to an external magnetic field without solidifying. In this contribution, we employ smooth magnets to simulate ferrofluids in contrast to previous methods based on the finite element method or point magnets. We solve the magnetization using the analytical solution of the smooth magnets’ field, and derive the bounded magnetic force formulas addressing particle penetration. We integrate the magnetic field and force evaluations into the fast multipole method allowing for efficient large-scale simulations of ferrofluids. The presented simulations are well reproducible since our approach can be easily incorporated into a framework implementing a Fast Multipole Method and a Smoothed Particle Hydrodynamics fluid solver with surface tension. We provide a detailed analysis of our approach and validate our results against real wet lab experiments. This work can potentially open the door for a deeper understanding of ferrofluids and for the identification of new areas of applications of these materials.

On the Accurate Large-Scale Simulation of Ferrofluids

Yu Fang, Minchen Li, Ming Gao, Chenfanfu Jiang

Simulating viscoelastic polymers and polymeric fluids requires a robust andaccurate capture of elasticity and viscosity. The computation is known to become very challenging under large deformations and high viscosity. Drawing inspirations from return mapping based elastoplasticity treatment for granular materials, we present a finite strain integration scheme for general viscoelastic solids under arbitrarily large deformation and non-equilibrated flow. Our scheme is based on a predictor-corrector exponential mapping scheme on the principal strains from the deformation gradient, which closely resembles the conventional treatment for elastoplasticity and allows straightforward implementation into any existing constitutive models. We develop a new Material Point Method that is fully implicit on both elasticity and inelasticity using augmented Lagrangian optimization with various preconditioning strategies for highly efficient time integration. Our method not only handles viscoelasticity but also supports existing elastoplastic models including Drucker-Prager and von-Mises in a unified manner. We demonstrate the efficacy of our framework on various examples showing intricate and characteristic inelastic dynamics with competitive performance.

Silly Rubber: An Implicit Material Point Method for Simulating Non-equilibrated Viscoelastic and Elastoplastic Solids

Marcel Padilla, Albert Chern, Felix Knöppel, Ulrich Pinkall, Peter Schröder

We introduce variable thickness, viscous vortex filaments. These can model such varied phenomena as underwater bubble rings or the intricate “chandeliers” formed by ink dropping into fluid. Treating the evolution of such filaments as an instance of Newtonian dynamics on a Riemannian configuration manifold we are able to extend classical work in the dynamics of vortex filaments through inclusion of viscous drag forces. The latter must be accounted for in low Reynolds number flows where they lead to significant variations in filament thickness and form an essential part of the observed dynamics. We develop and document both the underlying theory and associated practical numerical algorithms.

On Bubble Rings and Ink Chandeliers

Joshuah Wolper, Yu Fang, Minchen Li, Jiecong Lu, Ming Gao, Chenfanfu Jiang

We present two new approaches for animating dynamic fracture involving large elastoplastic deformation. In contrast to traditional mesh-based tech-
niques, where sharp discontinuity is introduced to split the continuum at crack surfaces, our methods are based on Continuum Damage Mechanics
(CDM) with a variational energy-based formulation for crack evolution. Our first approach formulates the resulting dynamic material damage evolution with a Ginzburg-Landau type phase-field equation and discretizes it with the Material Point Method (MPM), resulting in a coupled momentum/damage solver rooted in phase field fracture: PFF-MPM. Although our PFF-MPM approach achieves convincing fracture with or without plasticity, we also introduce a return mapping algorithm that can be analytically solved for a wide range of general non-associated plasticity models, achieving more than two times speedup over traditional iterative approaches. To demonstrate the efficacy of the algorithm, we also develop a Non-Associated Cam-Clay (NACC) plasticity model with a novel fracture-friendly hardening scheme.Our NACC plasticity paired with traditional MPM composes a second approach to dynamic fracture, as it produces a breadth of organic, brittle material fracture effects on its own. Though NACC and PFF can be combined, we focus on exploring their material effects separately. Both methods can be easily integrated into any existing MPM solver, enabling the simulation of various fracturing materials with extremely high visual fidelity while requiring little additional computational overhead.

CD-MPM: Continuum Damage Material Point Methods for Dynamic Fracture Animation

Ted Kim, Fernando de Goes, Hayley Iben

We present an analysis of anisotropic hyperelasticity, specifically transverse isotropy, that obtains closed-form expressions for the eigendecompositions of many common energies. We then use these to build fast and concise Newton implementations. We leverage our analysis in two separate applications. First, we show that existing anisotropic energies are not inversion-safe, and contain spurious stable states under large deformation. We then propose a new anisotropic strain invariant that enables the formulation of a novel, robust, and inversion-safe energy. The new energy fits completely within our analysis, so closed-form expressions are obtained for its eigensystem as well. Secondly, we use our analysis to rehabilitate badly-conditioned finite elements. Using this method, we can robustly simulate large deformations even when a mesh contains degenerate, zero-volume elements. We accomplish this by swapping the badly-behaved isotropic direction with a well-behaved anisotropic term. We validate our approach on a variety of examples.

Anisotropic elasticity for inversion-safety and element rehabilitation

• Anisotropic Elasticity for Inversion-Safety and Element Rehabilitation
• CD-MPM: Continuum Damage Material Point Methods for Dynamic Fracture Animation
• Silly Rubber: An Implicit Material Point Method for Simulating Non-equilibrated Viscoelastic and Elastoplastic Solids
• Decomposed Optimization Time Integrator for Large-Step Elastodynamics
• Efficient and Conservative Fluids Using Bidirectional Mapping
• On Bubble Rings and Ink Chandeliers
• Mixing Sauces: A Viscosity Blending Model for Shear Thinning Fluids
• On the Accurate Large-scale Simulation of Ferrofluids
• An Adaptive Variational Finite Difference Framework for Efficient Symmetric Octree Viscosity
• REDMAX: Efficient and Flexible Approach for Articulated Dynamics
• Fundamental solutions for water wave animation
• Implicit Untangling: A Robust Solution for Modeling Layered Clothing
• Harmonic Triangulations
• Hand Modeling and Simulation Using Stabilized Magnetic Resonance Imaging

TOG:

• Analytic Eigensystems for Isotropic Distortion Energies
• Editing Fluid Animation using Flow Interpolation
• Interlinked SPH Pressure Solvers for Strong Rigid-Fluid Coupling
• Efficient and Accurate Collision Response for Elastically Deformable Models
• Poly-Spline Finite Element Method

Tetsuya Takahashi, Ming C. Lin.

We present a grid-based fluid solver for simulating viscous materials and their interactions with solid objects. Our method formulates the implicit viscosity integration as a minimization problem with consistently estimated volume fractions to account for the sub-grid details of free surfaces and solid boundaries. To handle the interplay between fluids and solid objects with viscosity forces, we also formulate the two-way fluid-solid coupling as a unified minimization problem based on the variational principle, which naturally enforces the boundary conditions. Our formulation leads to a symmetric positive definite linear system with a sparse matrix regardless of the monolithically coupled solid objects. Additionally, we present a position-correction method using density constraints to enforce the uniform distributions of fluid particles and thus prevent the loss of fluid volumes. We demonstrate the effectiveness of our method in a wide range of viscous fluid scenarios.

A Geometrically Consistent Viscous Fluid Solver with Two-Way Fluid-Solid Coupling

Andreas Enzenhoefer, Nicolas Lefebvre, Sheldon Andrews

Simulating stiff physical systems is a requirement for numerous computer graphics applications, such as VR training for heavy equipment operation. However, iterative linear solvers often perform poorly in such cases, and direct methods involving a factorization of the system matrix are typically preferred for accurate and stable simulations. This can have a detrimental impact on performance, since factorization of the system matrix is costly for complex simulations. In this paper, we present a method for efficiently solving linear systems of stiff physical systems involving contact, where the dynamics are modeled as a mixed linear complementarity problem (MLCP). Our approach is based on a block Bard-type algorithm that applies low-rank downdates to a Cholesky factorization of the system matrix at each pivoting step. Further performance improvements are realized by exploiting low bandwidth characteristics of the factorization. Our method gives up to 3.5 times speed-up versus recomputing the factorization based on the index set. Various challenging scenarios are used to demonstrate the advantages of our approach.

Efficient block pivoting for multibody simulations with contact

Alexander Brown, Gary Ushaw, Graham Morgan

In this paper we propose a solution to delivering scalable real-time physics simulations. Although high performance computing simulations of physics related problems do exist, these are not real-time and do not model the real-time intricate interactions of rigid bodies for visual effect common in video games (favouring accuracy over real-time). As such, this paper presents the first approach to real-time delivery of scalable, commercial grade, video game quality physics. This is achieved by taking the physics engine out of the player’s machine and deploying it across standard cloud based infrastructures. The simulation world is then divided into sections that are then allocated to servers. A server maintains the physics for all simulated objects in its section. Our contribution is the ability to maintain a scalable simulation by allowing object interaction across section boundaries using predictive migration techniques. We allow each object to project an aura that is used to determine object migration across servers to ensure seamless physics interactions between objects. The validity of our results is demonstrated through experimentation and benchmarking. Our approach allows player interaction at any point in real-time (influencing the simulation) in the same manner as any video game. We believe that this is the first successful demonstration of scalable real-time physics

Aura Projection for Scalable Real-Time Physics