Breannan Smith, Fernando de Goes, Theodore Kim
Non-linear hyperelastic energies play a key role in capturing the fleshy appearance of virtual characters. Real-world, volume-preserving biological tissues have Poisson’s ratios near 1/2, but numerical simulation within this regime is notoriously challenging. In order to robustly capture these visual characteristics, we present a novel version of Neo-Hookean elasticity. Our model maintains the fleshy appearance of the Neo-Hookean model, exhibits superior volume preservation, and is robust to extreme kinematic rotations and inversions. We obtain closed-form expressions for the eigenvalues and eigenvectors of all of the system’s components, which allows us to directly project the Hessian to semi-positive-definiteness, and also leads to insights into the numerical behavior of the material. These findings also inform the design of more sophisticated hyperelastic models, which we explore by applying our analysis to Fung and Arruda-Boyce elasticity. We provide extensive comparisons against existing material models.
Stable Neo-Hookean Flesh Simulation
Chuyuan Fu, Qi Guo, Theodore Gast, Chenfanfu Jiang, Joseph Teran
Recently the Affine Particle-In-Cell (APIC) Method was proposed by Jiang et al.[2015; 2017b] to improve the accuracy of the transfers in Particle-In-Cell (PIC) [Harlow 1964] techniques by augmenting each particle with a locally
affine, rather than locally constant description of the velocity. This reduced the dissipation of the original PIC without suffering from the noise present in the historic alternative, Fluid-Implicit-Particle (FLIP) [Brackbill and Ruppel 1986]. We present a generalization of APIC by augmenting each particle with a more general local function. By viewing the grid-to-particle transfer as a linear and angular momentum conserving projection of the particle-wise local grid velocities onto a reduced basis, we greatly improve the energy and vorticity conservation over the original APIC. Furthermore, we show that the cost of the generalized projection is negligible over APIC when using a particular class of local polynomial functions. Lastly, we note that our method retains the filtering property of APIC and PIC and thus has similar robustness to noise.
A Polynomial Particle-In-Cell Method
Tao Yang, Jian Chang, Ming C. Lin, Ralph R. Martin, Jian J. Zhang, and Shi-Min Hu
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 interactions. Our multi-phase, multi-material system is 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 that are challenging to simulate. Examples are provided to demonstrate the capabilities and effectiveness of this approach.
A Unified Particle System Framework for Multi-Phase, Multi-Material Visual Simulations
Sadashige Ishida, Masafumi Yamamoto, Ryoichi Ando, Toshiya Hachisuka
Simulating the behavior of soap films and foams is a challenging task. A direct numerical simulation of films and foams via the Navier-Stokes equations is still computationally too expensive. We propose an alternative formulation inspired by geometric flow. Our model exploits the fact, according to Plateau’s laws, that the steady state of a film is a union of constant mean curvature surfaces and minimal surfaces. Such surfaces are also well known as the steady state solutions of certain curvature flows. We show a link between the Navier-Stokes equations and a recent variant of mean curvature flow, called hyperbolic mean curvature flow, under the assumption of constant air pressure per enclosed region. We thus introduce hyperbolic mean curvature flow to describe film dynamics. Instead of using hyperbolic mean curvature flow as is, we propose to replace curvature by the gradient of the surface area functional. This formulation enables us to robustly handle non-manifold configurations; such junctions connecting multiple films are intractable with the traditional formulation using curvature. We also add explicit volume preservation to hyperbolic mean curvature flow, which in fact corresponds to the pressure term of the Navier-Stokes equations. Our method is simple, fast, robust, and consistent with Plateau’s laws, which are all due to our reformulation of film dynamics as a geometric flow.
A Hyperbolic Geometric Flow for Evolving Films and Foams
Ming Gao, Andre Pradhana Tampubulon, Chenfanfu Jiang, Eftychios Sifakis
We present an adaptive Generalized Interpolation Material Point (GIMP) method for simulating elastoplastic materials. Our approach allows adaptive refining and coarsening of different regions of the material, leading to an efficient MPM solver that concentrates most of the computation resources in specific regions of interest. We propose a C1 continuous adaptive basis function that satisfies the partition of unity property and remains nonnegative throughout the computational domain. We develop a practical strategy for particle-grid transfers that leverages the recently introduced SPGrid data structure for storing sparse multi-layered grids. We demonstrate the robustness and efficiency of our method on the simulation of various elastic and plastic materials. We also compare key kernel components to uniform grid MPM solvers to highlight performance benefits of our method.
An Adaptive Generalized Interpolation Material Point Method for Simulating Elastoplastic Materials
Richard Jones, Richard Southern
In this paper we present a physically-based model for simulating realistic interactions between liquid droplets in an efficient manner. Our particle-based system recreates the coalescence, separation and fragmentation interactions that occur between colliding liquid droplets and allows systems of droplets to be meaningfully repre- sented by an equivalent number of simulated particles. By consid- ering the interactions specific to liquid droplet phenomena directly, we display novel levels of detail that cannot be captured using other interaction models at a similar scale. Our work combines experi- mentally validated components, originating in engineering, with a collection of novel modifications to create a particle-based interac- tion model for use in the development of mid-to-large scale droplet- based liquid spray effects. We demonstrate this model, alongside a size-dependent drag force, as an extension to a commonly-used ballistic particle system and show how the introduction of these interactions improves the quality and variety of results possible in recreating liquid droplets and sprays, even using these otherwise simple systems.
Physically-Based Droplet Interaction
Sören Pirk, Michał Jarząbek, Torsten Hädrich, Dominik L. Michels, Wojciech Palubicki
We present a novel method for the combustion of botanical tree models. Tree models are represented as connected particles for the branching structure and a polygonal surface mesh for the combustion. Each particle stores biological and physical attributes that drive the kinetic behavior of a plant and the exothermic reaction of the combustion. Coupled with realistic physics for rods, the particles enable dynamic branch motions. We model material properties, such as moisture and charring behavior, and associate them with individual particles. The combustion is efficiently processed in the surface domain of the tree model on a polygonal mesh. A user can dynamically interact with the model by initiating fires and by inducing stress on branches. The flames realistically propagate through the tree model by consuming the available resources. Our method runs at interactive rates and supports multiple tree instances in parallel. We demonstrate the effectiveness of our approach through numerous examples and evaluate its plausibility against the combustion of real wood samples.
Interactive Wood Combustion for Botanical Tree Models
Hector Barreiro, Ignacio Garcia-Fernandez, Ivan Alduan, Miguel A. Otaduy
The simulation of high viscoelasticity poses important computational challenges. One is the difficulty to robustly measure strain and its derivatives in a medium without permanent structure. Another is the high stiffness of the governing differential equations. Solutions that tackle these challenges exist, but they are computationally slow. We propose a constraint-based model of viscoelasticity that enables efficient simulation of highly viscous and viscoelastic phenomena. Our model reformulates, in a constraint-based fashion, a constitutive model of viscoelasticity for polymeric fluids, which defines simple governing equations for a conformation tensor. The model can represent a diverse palette 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 efficiently both position-based and velocity-based constraints. We show results that range from interactive simulation of viscoelastic effects to large-scale simulation of high viscosity with competitive performance
Conformation Constraints for Efficient Viscoelastic Fluid Simulation
Tao Yang, Ralph R. Martin, Ming C. Lin, Jian Chang, and Shi-Min Hu
In this paper, we present a novel pairwise-force smoothed particle hydrodynamics (PF-SPH) model to enable simulation of various interactions at interfaces in real time. Realistic capture of interactions at interfaces is a challenging problem for SPH-based simulations, especially for scenarios involving multiple interactions at different interfaces. Our PF-SPH model can readily handle multiple types of interactions simultaneously in a single simulation; its basis is to use a larger support radius than that used in standard SPH. We adopt a novel anisotropic filtering term to further improve the performance of interaction forces. The proposed model is stable; furthermore, it avoids the particle clustering problem which commonly occurs at the free surface. We show how our model can be used to capture various interactions. We also consider the close connection between droplets and bubbles, and show how to animate bubbles rising in liquid as well as bubbles in air. Our method is versatile, physically plausible and easy-to-implement. Examples are provided to demonstrate the capabilities and effectiveness of our approach.
Pairwise Force SPH Model for Real-Time Multi-Interaction Applications