Category: Deformables

A Material Point Method for Viscoelastic Fluids, Foams, and Sponges

Daniel Ram, Theodore Gast, Chenfanfu Jiang, Craig Schroeder, Alexey Stomakhin, Joseph Teran, Pirouz Kavehpour

We present a new Material Point Method (MPM) for simulating viscoelastic fluids, foams and sponges. We design our discretization from the upper convected derivative terms in the evolution of the left Cauchy-Green elastic strain tensor. We combine this with an Oldroyd-B model for plastic flow in a complex viscoelastic fluid. While the Oldroyd-B model is traditionally used for viscoelastic fluids, we show that its interpretation as a plastic flow naturally allows us to simulate a wide range of complex material behaviors. In order to do this, we provide a modification to the traditional Oldroyd-B model that guarantees volume preserving plastic flows. Our plasticity model is remarkably simple (foregoing the need for the singular value decomposition (SVD) of stresses or strains). Lastly, we show that implicit time stepping can be achieved in a manner similar to [Stomakhin et al. 2013] and that this allows for high resolution simulations at practical simulation times.

A Material Point Method for Viscoelastic Fluids, Foams, and Sponges

Multifarious Hierarchies of Mechanical Models for Artist Assigned Levels-of-Detail

Richard Malgat, Benjamin Gilles, David I.W. Levin, Mathieu Nesme, Francois Faure

We present a new framework for artist driven level of detail in solid simulations. Simulated objects are simultaneously embedded in several, separately designed deformation models with their own independent degrees of freedom. The models are ordered to apply their deformations hierarchically, and we enforce the uniqueness of the dynamics solutions using a novel kinetic filtering operator designed to ensure that each child only adds detail motion to its parent without introducing redundancies. This new approach allows artists to easily add fine-scale details without introducing unnecessary degrees-of-freedom to the simulation or resorting to complex geometric operations like anisotropic volume meshing. We illustrate the utility of our approach with several detail enriched simulation examples.

Multifarious Hierarchies of Mechanical Models for Artist Assigned Levels-of-Detail

Nonlinear Material Design Using Principal Stretches

Hongyi Xu, Funshing Sin, Yufeng Zhu, Jernej Barbic

The Finite Element Method is widely used for solid deformable object simulation in film, computer games, virtual reality and medicine. Previous applications of nonlinear solid elasticity employed materials from a few standard families such as linear corotational, nonlinear St.Venant-Kirchhoff, Neo-Hookean, Ogden or Mooney-Rivlin materials. However, the spaces of all nonlinear isotropic and anisotropic materials are infinite-dimensional and much broader than these standard materials. In this paper, we demonstrate how to intuitively explore the space of isotropic and anisotropic nonlinear materials, for design of animations in computer graphics and related fields. In order to do so, we first formulate the internal elastic forces and tangent stiffness matrices in the space of the principal stretches of the material. We then demonstrate how to design new isotropic materials by editing a single stress-strain curve, using a spline interface. Similarly, anisotropic (orthotropic) materials can be designed by editing three curves, one for each material direction. We demonstrate that modifying these curves using our proposed interface has an intuitive, visual, effect on the simulation. Our materials accelerate simulation design and enable visual effects that are difficult or impossible to achieve with standard nonlinear materials.

Nonlinear Material Design Using Principal Stretches

Stable Constrained Dynamics

Maxime Tournier, Matthieu Nesme, Benjamin Gilles, Francois Faure

We present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers.

Stable Constrained Dynamics

High-Resolution Brittle Fracture Simulation with Boundary Elements

David Hahn, Chris Wojtan

We present a method for simulating brittle fracture under the assumptions of quasi-static linear elastic fracture mechanics (LEFM). Using the boundary element method (BEM) and Lagrangian crack-fronts, we produce highly detailed fracture surfaces. The computational cost of the BEM is alleviated by using a low-resolution mesh and interpolating the resulting stress intensity factors when propagating the high-resolution crack-front. Our system produces physics-based fracture surfaces with high spatial and temporal resolution, taking spatial variation of material toughness and/or strength into account. It also allows for crack initiation to be handled separately from crack propagation, which is not only more reasonable from a physics perspective, but can also be used to control the simulation. Separating the resolution of the crack-front from the resolution of the computational mesh increases the efficiency and therefore the amount of visual detail on the resulting fracture surfaces. The BEM also allows us to re-use previously computed blocks of the system matrix.

High-Resolution Brittle Fracture Simulation with Boundary Elements

Continuum Foam: A Material Point Method for Shear-Dependent Flows

Yonghao Yue, Breannan Smith, Christopher Batty, Changxi Zheng, Eitan Grinspun

We consider the simulation of dense foams composed of microscopic bubbles, such as shaving cream and whipped cream. We represent foam not as a collection of discrete bubbles, but instead as a continuum. We employ the Material Point Method (MPM) to discretize a hyperelastic constitutive relation augmented with the Herschel-Bulkley model of non-Newtonian plastic flow, which is known to closely approximate foam behavior. Since large shearing flows in foam can produce poor distributions of material points, a typical MPM implementation can produce non-physical internal holes in the continuum. To address these artifacts, we introduce a particle resampling method for MPM. In addition, we introduce an explicit tearing model to prevent regions from shearing into artificially-thin, honey-like threads. We evaluate our method’s efficacy by simulating a number of dense foams, and we validate our method by comparing to real-world footage of foam.

Continuum Foam: A Material Point Method for Shear-Dependent Flows

The Affine Particle-In-Cell Method

Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, Alexey Stomakhin

Hybrid Lagrangian/Eulerian simulation is commonplace in computer graphics for fluids and other materials undergoing large deformation. In these methods, particles are used to resolve transport and topological change, while a background Eulerian grid is used for computing mechanical forces and collision responses. Particle- in-Cell (PIC) techniques, particularly the Fluid Implicit Particle (FLIP) variants have become the norm in computer graphics calculations. While these approaches have proven very powerful, they do suffer from some well known limitations. The original PIC is stable, but highly dissipative, while FLIP, designed to remove this dissipation, is more noisy and at times, unstable. We present a novel technique designed to retain the stability of the original PIC, with- out suffering from the noise and instability of FLIP. Our primary observation is that the dissipation in the original PIC results from a loss of information when transferring between grid and particle representations. We prevent this loss of information by augmenting each particle with a locally affine, rather than locally constant, description of the velocity. We show that this not only stably removes the dissipation of PIC, but that it also allows for exact conservation of angular momentum across the transfers between particles and grid.

The Affine Particle-In-Cell Method

Deformation Capture and Modeling of Soft Objects

Bin Wang, Longhua Wu, Kangkang Yin, Uri Ascher, Libin Liu, Hui Huang

We present a data-driven method for the deformation capture and physics-based modeling of soft deformable objects. Our framework enables both realistic motion reconstruction and synthesis of virtual soft object models in response to user stimulation. Low cost depth sensors are used for the deformation capture, and we do not insist on any force-displacement measurements which are commonly required by previous work, thus making the capturing a cheap and convenient process. A physics-based probabilistic tracking method is employed to increase the tracking robustness to noise, occlusions, fast movements and large deformations. The deformation estimation task that includes the reference shape, material elasticity parameters and damping coefficient is then formulated and solved as a spacetime optimization problem, aiming at matching the simulated trajectories with the tracked ones. The optimized deformation parameters are used in turn to make the physics-based tracking results more accurate, consequently improving the deformation estimation itself. Numerical experiments demonstrate that our physics-based deformation tracking and deformation parameter optimization can be unified and made complementary to each other. The obtained optimal deformation parameters can yield high quality animations for various soft models.

Deformation Capture and Modeling of Soft Objects

Air Meshes for Robust Collision Handling

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

We propose a new method for both collision detection and collision response geared towards handling complex deformable objects in close contact. Our method does not miss collision events between time steps and solves the challenging problem of untangling automatically and robustly. It is conceptually simple and straight forward to parallelize due to the regularity of the algorithm. The main idea is to tessellate the air between objects once before the simulation and by considering one unilateral constraint per element that prevents its inversion during the simulation. If large relative rotations and translations are present in the simulation, an additional dynamic mesh optimization step is needed to prevent mesh locking. This step is fast in 2D and allows the simulation of arbitrary scenes. Because mesh optimization is expensive in 3D, however, the method is best suited for the subclass of 3D scenarios in which relative motions are limited. This subclass contains two important problems, namely the simulation of multi-layered clothing and tissue on animated characters.

Air Meshes for Robust Collision Handling

Subspace Condensation: Full Space Adaptivity for Subspace Deformations

Yun Teng, Mark Meyer, Tony DeRose, Theodore Kim

Subspace deformable body simulations can be very fast, but can behave unrealistically when behaviors outside the prescribed subspace, such as novel external collisions, are encountered. We address this limitation by presenting a fast, flexible new method that allows full space computation to be activated in the neighborhood of novel events while the rest of the body still computes in a subspace. We achieve this using a method we call subspace condensation, a variant on the classic static condensation precomputation. However, instead of a precomputation, we use the speed of subspace methods to perform the condensation at every frame. This approach allows the full space regions to be specified arbitrarily at runtime, and forms a natural two-way coupling with the subspace regions. While condensation is usually only applicable to linear materials, the speed of our technique enables its application to non-linear materials as well. We show the effectiveness of our approach by applying it to a variety of articulated character scenarios.

Subspace Condensation: Full Space Adaptivity for Subspace Deformations