Stable Orthotropic Materials

Yijing Li, Jernej Barbič

Isotropic Finite Element Method (FEM) deformable object simulations are widely used in computer graphics. Several applications (wood, plants, muscles) require modeling the directional dependence of the material elastic properties in three orthogonal directions. We investigate orthotropic materials, a special class of anisotropic materials where the shear stresses are decoupled from normal stresses. Orthotropic materials generalize transversely isotropic materials, by exhibiting different stiffnesses in three orthogonal directions. Orthotropic materials are, however, parameterized by nine values that are difficult to tune in practice, as poorly adjusted settings easily lead to simulation instabilities. We present a user-friendly approach to setting these parameters that is guaranteed to be stable. Our approach is intuitive as it extends the familiar intuition known from isotropic materials. We demonstrate our technique by augmenting linear corotational FEM implementations with orthotropic materials.

Stable Orthotropic Materials

Adaptive Tetrahedral Meshes for Brittle Fracture Simulation

Dan Koschier, Sebastian Lipponer, Jan Bender

We present a method for the adaptive simulation of brittle fracture of solid objects based on a novel reversible tetrahedral mesh refinement scheme. The refinement scheme preserves the quality of the input mesh to a large extent, it is solely based on topological operations, and does not alter the boundary, i.e. any geometric feature. Our fracture algorithm successively performs a stress analysis and increases the resolution of the input mesh in regions of high tensile stress. This results in an accurate location of crack origins without the need of a general high resolution mesh which would cause high computational costs throughout the whole simulation. A crack is initiated when the maximum tensile stress exceeds the material strength. The introduced algorithm then proceeds by iteratively recomputing the changed stress state and creating further cracks. Our approach can generate multiple cracks from a single impact but effectively avoids shattering artifacts. Once the tensile stress decreases, the mesh refinement is reversed to increase the performance of the simulation. We demonstrate that our adaptive method is robust, scalable and computes highly realistic fracture results.

Adaptive Tetrahedral Meshes for Brittle Fracture Simulation

SCA 2014

Physical simulation papers:

 

TVCG Papers appearing at SCA:

Ocean Waves Animation using Boundary Integral Equations and Explicit Mesh Tracking

Todd Keeler, Robert Bridson

We tackle deep water simulation in a scalable way, solving 3D irrotational flow using only variables stored in a mesh of the surface of the water, in time proportional to the rendered mesh. The heart of our method is a novel boundary integral equation formulation that is amenable to explicit mesh tracking with unstructured triangle meshes. Our method complements FFT style waves as it is able to handle solid boundaries. It is less memory intensive than volumetric methods and inherently handles the near-infinite depth of the deep ocean. We demonstrate acceleration techniques using the FMM and GPU computing. The natural Lagrangian motion of our model gives inherent adaptivity to our simulation without the need for direct mesh operations.

Ocean Waves Animation using Boundary Integral Equations and Explicit Mesh Tracking

View-Dependent Adaptive Cloth Simulation

Woojong Koh, Rahul Narain, James F. O’Brien

This paper describes a method for view-dependent cloth simulation using dynamically adaptive mesh refinement and coarsening. Given a prescribed camera motion, the method adjusts the criteria controlling refinement to account for visibility and apparent size in the camera’s view. Objectionable dynamic artifacts are avoided by anticipative refinement and smoothed coarsening. This approach preserves the appearance of detailed cloth throughout the animation while avoiding the wasted effort of simulating details that would not be discernible to the viewer. The computational savings realized by this method increase as scene complexity grows, producing a 2x speed-up for a single character and more than 4x for a small group.

View-Dependent Adaptive Cloth Simulation

From Capture to Simulation – Connecting Forward and Inverse Problems in Fluids

James Gregson, Ivo Irkhe, Nils Thuerey, Wolfgang Heidrich

We explore the connection between fluid capture, simulation and proximal methods, a class of algorithms commonly used for inverse problems in image processing and computer vision. Our key finding is that the proximal operator constraining fluid velocities to be divergence-free is directly equivalent to the pressure-projection methods commonly used in incompressible flow solvers. This observation lets us treat the inverse problem of fluid tracking as a constrained flow problem all while working in an efficient, modular framework. In addition it lets us tightly couple fluid simulation into flow tracking, providing a global prior that significantly increases tracking accuracy and temporal coherence as compared to previous techniques. We demonstrate how we can use these improved results for a variety of applications, such as re-simulation, detail enhancement, and domain modification. We furthermore give an outlook of the applications beyond fluid tracking that our proximal operator framework could enable by exploring the connection of deblurring and fluid guiding.

From Capture to Simulation – Connecting Forward and Inverse Problems in Fluids

Multiple-Fluid SPH Simulation Using a Mixture Model

Bo Reng, Chenfeng Li, Xiao Yan, Ming C. Lin, Javier Bonet, Shi-Min Hu

This paper presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or components is modeled using the volume fraction representation, the dynamics of multiple-fluid flows is captured by using an improved mixture model, and a stable and accurate SPH formulation is rigorously derived to resolve the complex transport and transformation processes encountered in multiple-fluid flows. The new approach can capture a wide range of realworld multiple-fluid phenomena, including mixing/unmixing of miscible and immiscible fluids, diffusion effect and chemical reaction etc. Moreover, the new multiple-fluid SPH scheme can be readily integrated into existing state-of-the-art SPH simulators, and the multiple-fluid simulation is easy to set up. Various examples are presented to demonstrate the effectiveness of our approach.

Multiple-Fluid SPH Simulation Using a Mixture Model

Projective Dynamics: Fusing Constraint Projections for Fast Simulation

Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, Mark Pauly

We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuum-based
potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based  simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation.

Projective Dynamics: Fusing Constraint Projections for Fast Simulation

Strain-Based Dynamics

Matthias Mueller, Nuttapong Chentanez, Tae-Yong Kim, Miles Macklin

We propose a new set of constraints within the Position Based Dynamics (PBD) framework that allow the control of strain in directions that are independent of the edge directions of the simulation mesh. Instead of constraining distances between points, we constrain the entries of the Green – St Venant strain tensor. Varying the stiffness values corresponding to the individual strain coefficients lets us simulate anisotropic behavior. By working with Green’s rotation-independent, non-linear strain tensor directly we do not have to perform a polar decomposition of the deformation gradient as in most strain limiting approaches. In addition, we propose a modification of the constraints corresponding to the diagonal entries of the strain tensor such that they can be solved in a single step and a modification of the constraints corresponding to the off-diagonal entries to decouple stretch from shear resistance. By formulating the constraints within the PBD framework, they can be used not only for strain limiting but to perform the actual simulation of the deformable object whereas traditional strain limiting methods have to be paired with a separate simulation method.

Strain-Based Dynamics

A Reduced Model for Interactive Hairs

Menglei Chai, Changxi Zheng, Kun Zhou

Realistic hair animation is a crucial component in depicting virtual characters in interactive applications. While much progress has been made in high-quality hair simulation, the overwhelming computation cost hinders similar fidelity in realtime simulations. To bridge this gap, we propose a data-driven solution. Building upon precomputed simulation data, our approach constructs a reduced model to optimally represent hair motion characteristics with a small number of guide hairs and the corresponding interpolation relationships. At runtime, utilizing such a reduced model, we only simulate guide hairs that capture the general hair motion and interpolate all rest strands. We further propose a hair correction method that corrects the resulting hair motion with a position-based model to resolve hair collisions and thus captures motion details. Our hair simulation method enables a simulation of a full head of hairs with over 150K strands in realtime. We demonstrate the efficacy and robustness of our method with various hairstyles and driven motions (e.g., head movement and wind force), and compared against full simulation results that does not appear in the training data.

A Reduced Model for Interactive Hairs