SIGGRAPH Asia 2023

Non-Newtonian ViRheometry via Similarity Analysis

Mitsuki Hamamichi, Kentaro Nagasawa, Masato Okada, Ryohei Seto, Yonghao Yue

We estimate the three Herschel–Bulkley parameters (yield stress, power-law index, and consistency parameter) for shear-dependent fluid-like materials possibly with large-scale inclusions, for which rheometers may fail to provide a useful measurement. We perform experiments using the unknown material for dam-break (or column collapse) setups and capture video footage. We then use simulations to optimize for the material parameters. For better match up with the simple shear flow encountered in a rheometer, we modify the flow rule for the elasto-viscoplastic Herschel-Bulkley model. Analyzing the loss landscape for optimization, we realize a similarity relation; material parameters far away within this relation would result in matched simulations, making it hard to distinguish the parameters. We found that by exploiting the setup dependency of the similarity relation, we can improve on the estimation using multiple setups, which we propose by analyzing the Hessian of the similarity relation. We validate the efficacy of our method by comparing the estimations to the measurements from a rheometer (for materials without large-scale inclusions) and show applications to materials with large-scale inclusions, including various salad or pasta sauces, and congee.

Non-Newtonian ViRheometry via Similarity Analysis

Subspace Mixed Finite Elements for Real-Time Heterogeneous Elastodynamics

Otman Benchekroun, Ty Trusty, Eitan Grinspun, Danny M. Kaufman, David I.W. Levin

Real-time elastodynamic solvers are well-suited for the rapid simulation of homogeneous elastic materials, with high-rates generally enabled by aggressive early termination of timestep solves. Unfortunately, the introduction of strong domain heterogeneities can make these solvers slow to converge. Stopping the solve short creates visible damping artifacts and rotational errors. To address these challenges we develop a reduced mixed finite element solver that pre serves rich rotational motion, even at low-iteration regimes. Specifically, this solver augments time-step solve optimizations with auxiliary stretch degrees of freedom at mesh elements, and maintains consistency with the primary positional degrees of freedoms at mesh nodes via explicit constraints. We make use of a Skinning Eigenmode subspace for our positional degrees of freedom. We accelerate integration of non-linear elastic energies with a cubature approximation, placing stretch degrees of freedom at cubature points. Across a wide range of examples we demonstrate that this subspace is particularly well suited for heterogeneous material simulation. Our resulting method is a subspace mixed finite element method completely decoupled from the resolution of the mesh that is well-suited for real-time simulation of heterogeneous domains.

Subspace Mixed Finite Elements for Real-Time Heterogeneous Elastodynamics

ViCMA: Visual Control of Multibody Animations

Doug L. James, David I.W. Levin

Motion control of large-scale, multibody physics animations with contact is difficult. Existing approaches, such as those based on optimization, are computationally daunting, and, as the number of interacting objects increases, can fail to find satisfactory solutions. We present a new, complementary method for the visual control of multibody animations that exploits object motion and visibility, and has overall cost comparable to a single simulation. Our method is highly practical, and is demonstrated on numerous large-scale, contact-rich examples involving both rigid and deformable bodies.

ViCMA: Visual Control of Multibody Animations

Real-Time Reconstruction of Fluid Flow under Unknown Disturbance

Kinfung Chu, Jiawei Huang, Hidemasa Takan, Yoshifumi Kitamura

We present a framework that captures sparse Lagrangian flow information from a volume of real liquid and reconstructs its detailed kinematic information in real time. Our framework can perform flow reconstruction even when the liquid is disturbed by an object of unknown movement and shape. Through a large dataset of liquid moving under external disturbance, an agent is trained using reinforcement learning to reproduce the target flow kinematics with only the captured sparse information as inputs while remaining oblivious to the movement and the shape of the disturbance sources. To ensure that the underlying simulation model faithfully obeys physical reality, we also optimize the viscosity parameters in Smoothed Particle Hydrodynamics (SPH) using classical fluid dynamics knowledge and gradient-based optimization. By quantitatively comparing the reconstruction results against real-world and simulated ground truth, we verified that our reconstruction method is resilient to different agitation patterns.

Real-Time Reconstruction of Fluid Flow under Unknown Disturbance

Progressive Shell Quasistatics for Unstructured Meshes

Jiayi Eris Zhang, Jérémie Dumas, Yun (Raymond) Fei, Alec Jacobson, Doug L. James, Danny M. Kaufman

Thin shell structures exhibit complex behaviors critical for modeling and design across wide-ranging applications. Capturing their mechanical response requires finely detailed, high-resolution meshes. Corresponding simulations for predicting equilibria with these meshes are expensive, whereas coarse-mesh simulations can be fast but generate unacceptable artifacts and inaccuracies. The recently proposed progressive simulation framework [Zhang et al. 2022] offers a promising avenue to address these limitations with consistent and progressively improving simulation over a hierarchy of increasingly higher-resolution models. Unfortunately, it is currently severely limited in application to meshes and shapes generated via Loop subdivision. We propose Progressive Shells Quasistatics to extend progressive simulation to the high-fidelity modeling and design of all input shell (and plate) geometries with unstructured (as well as structured) triangle meshes. To do so, we construct a fine-to-coarse hierarchy with a novel nonlinear prolongation operator custom-suited for curved-surface simulation that is rest-shape preserving, supports complex curved boundaries, and enables the reconstruction of detailed geometries from coarse-level meshes. Then, to enable convergent, high-quality solutions with robust contact handling, we propose a new, safe, and efficient shape-preserving upsampling method that ensures non-intersection and strain limits during refinement. With these core contributions, Progressive Shell Quasistatics enables, for the first time, wide generality for progressive simulation, including support for arbitrary curved-shell geometries, progressive collision objects, curved boundaries, and unstructured triangle meshes – all while ensuring that preview and final solutions remain free of intersections. We demonstrate these features across a wide range of stress tests where progressive simulation captures the wrinkling, folding, twisting, and buckling behaviors of frictionally contacting thin shells with orders-of-magnitude speed-up in examples over direct fine-resolution simulation.

Progressive Shell Quasistatics for Unstructured Meshes

3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing

Payam Khanteimouri, Marcel Campen

We present a method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space).

3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing

Implicit Surface Tension for SPH Fluid Simulation

Stefan Rhys Jeske, Lukas Westhofen, Fabian Löschner, José Antonio Fernández-Fernández, Jan Bender

The numerical simulation of surface tension is an active area of research in many different fields of application and has been attempted using a wide range of methods. Our contribution is the derivation and implementation of an implicit cohesion force based approach for the simulation of surface tension effects using the Smoothed Particle Hydrodynamics (SPH) method. We define a continuous formulation inspired by the properties of surface tension at the molecular scale which is spatially discretized using SPH. An adapted variant of the linearized backward Euler method is used for time discretization, which we also strongly couple with an implicit viscosity model. Finally, we extend our formulation with adhesion forces for interfaces with rigid objects. Existing SPH approaches for surface tension in computer graphics are mostly based on explicit time integration, thereby lacking in stability for challenging settings. We compare our implicit surface tension method to these approaches and further evaluate our model on a wider variety of complex scenarios, showcasing its efficacy and versatility. Among others, these include but are not limited to simulations of a water crown, a dripping faucet and a droplet-toy.

Implicit Surface Tension for SPH Fluid Simulation

Authoring and Simulating Meandering Rivers

Axel Paris, Eric Guérin, Pauline Collon, Eric Galin

We present a method for interactively authoring and simulating meandering river networks. Starting from a terrain with an initial low-resolution network encoded as a directed graph, we simulate the evolution of the path of the different river channels using a physically-based migration equation augmented with control terms. The curvature-based terms in the equation allow us to reproduce phenomena identified in geomorphology, such as downstream migration of bends. Control terms account for the influence of the landscape topography and user-defined river trajectory constraints. Our model implements abrupt events that shape meandering networks, such as cutoffs forming oxbow lakes and avulsions. We visually show the effectiveness of our method and compare the generated networks quantitatively to river data by analyzing sinuosity and wavelength metrics. Our vector-based model runs at interactive rates, allowing for efficient authoring of large-scale meandering networks.

Authoring and Simulating Meandering Rivers

An Implicitly Stable Mixture Model for Dynamic Multi-fluid Simulations

Y. Xu, X. Wang, J. Wang, C. Song, T. Wang, Y. Zhang, J. Chang, J. Zhang, J. Kosinka, A. Telea, X. Ban

Particle-based simulations have become increasingly popular in real-time applications due to their efficiency and adaptability, especially for generating highly dynamic fluid effects. However, the swift and stable simulation of interactions among distinct fluids continues to pose challenges for current mixture model techniques. When using a single-mixture flow field to represent all fluid phases, numerical discontinuities in phase fields can result in significant losses of dynamic effects and unstable conservation of mass and momentum. To tackle these issues, we present an advanced implicit mixture model for smoothed particle hydrodynamics. Instead of relying on an explicit mixture field for all dynamic computations and phase transfers between particles, our approach calculates phase momentum sources from the mixture model to derive explicit and continuous velocity phase fields. We then implicitly obtain the mixture field using a phase-mixture momentum-mapping mechanism that ensures conservation of incompressibility, mass, and momentum. In addition, we propose a mixture viscosity model and establish viscous effects between the mixture and individual fluid phases to avoid instability under extreme inertia conditions. Through a series of experiments, we show that, compared to existing mixture models, our method effectively improves dynamic effects while reducing critical instability factors. This makes our approach especially well-suited for long-duration, efficiency-oriented virtual reality scenarios

An Implicitly Stable Mixture Model for Dynamic Multi-fluid Simulations

Neural Metamaterial Networks for Nonlinear Material Design

Yue Li, Stelian Coros, Bernhard Thomaszewski

Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to ideal approximation of high-level performance goals is a challenging task. In this work, we propose Neural Metamaterial Networks (NMN) — smooth neural representations that encode the nonlinear mechanics of entire metamaterial families. Given structure parameters as input, NMN return continuously differentiable strain energy density functions, thus guaranteeing conservative forces by construction. Though trained on simulation data, NMN do not inherit the discontinuities resulting from topological changes in finite element meshes. They instead provide a smooth map from parameter to performance space that is fully differentiable and thus well-suited for gradient-based optimization. On this basis, we formulate inverse material design as a nonlinear programming problem that leverages neural networks for both objective functions and constraints. We use this approach to automatically design materials with desired strain-stress curves, prescribed directional stiffness and Poisson ratio profiles. We furthermore conduct ablation studies on network nonlinearities and show the advantages of our approach compared to native-scale optimization.

Neural Metamaterial Networks for Nonlinear Material Design