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
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
Nathan Mitchell, Court Cutting, Eftychios Sifakis
We present an interactive simulation framework for authoring surgical procedures of soft tissue manipulation using physics-based simulation to animate the flesh. This interactive authoring tool can be used by clinical educators to craft three-dimensional illustrations of the intricate maneuvers involved in craniofacial repairs, in contrast to two-dimensional sketches and still photographs which are the medium used to describe these procedures in the traditional surgical curriculum. Our virtual environment also allows surgeons-intraining to develop cognitive skills for craniofacial surgery by experimenting with different approaches to reconstructive challenges, adapting stock techniques to flesh regions with nonstandard shape, and reach preliminary predictions about the feasibility of a given repair plan. We use a Cartesian grid-based embedded discretization of nonlinear elasticity to maximize regularity, and expose opportunities for aggressive multithreading and SIMD accelerations. Using a grid-based approach facilitates performance and scalability, but constrains our ability to capture the topology of thin surgical incisions. We circumvent this restriction by hybridizing the grid-based discretization with an explicit hexahedral mesh representation in regions where the embedding mesh necessitates overlap or nonmanifold connectivity. Finally, we detail how the front-end of our system can run on lightweight clients, while the core simulation capability can be hosted on a dedicated server and delivered as a network service.
GRIDiron: An interactive authoring and cognitive training foundation for reconstructive plastic surgery procedures
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
Yufeng Zhu, Robert Bridson, Chen Greif
We present a new brittle fracture simulation method based on a boundary integral formulation of elasticity and recent explicit surface mesh evolution algorithms. Unlike prior physically-based simulations in graphics, this avoids the need for volumetric sampling and calculations, which aren’t reflected in the rendered output. We represent each quasi-rigid body by a closed triangle mesh of its boundary, on which we solve quasi-static linear elasticity via boundary integrals in response to boundary conditions and loads such as impact forces and gravity. A fracture condition based on maximum tensile stress is subsequently evaluated at mesh vertices, while crack initiation and propagation are formulated as an interface tracking procedure in material space. Existing explicit mesh tracking methods are modified to support evolving cracks directly in the triangle mesh representation, giving highly detailed fractures with sharp features, independent of any volumetric sampling (unlike tetrahedral mesh or level set approaches); the triangle mesh representation also allows simple integration into rigid body engines. We also give details on our well-conditioned integral equation treatment solved with a kernel-independent Fast Multipole Method for linear time summation. Various brittle fracture scenarios demonstrate the efficacy and robustness of our new method.
Simulating Rigid Body Fracture with Surface Meshes
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
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
Bo Zhu, Minjae Lee, Ed Quigley, Ronald Fedkiw
We present a novel method to simulate codimensional nonNewtonian fluids on simplicial complexes. Our method extends previous work for codimensional incompressible flow to various types of non-Newtonian fluids including both shear thinning and thickening, Bingham plastics, and elastoplastics. We propose a novel time integration scheme for semi-implicitly treating elasticity, which when combined with a semi-implicit method for variable viscosity alleviates the need for small time steps. Furthermore, we propose an improved treatment of viscosity on the rims of thin fluid sheets that allows us to capture their elusive, visually appealing twisting motion. In order to simulate complex phenomena such as the mixing of colored paint, we adopt a multiple level set framework and propose a discretization on simplicial complexes that facilitates the tracking of material interfaces across codimensions. We demonstrate the efficacy of our approach by simulating a wide variety of non-Newtonian fluid phenomena exhibiting various codimensional features.
Co-Dimensional Non-Newtonian Fluids
Nuttapong Chentanez, Matthias Mueller, Miles Macklin, Tae-Yong Kim
We present a novel explicit surface tracking method. Its main advantage over existing approaches is the fact that it is both completely grid-free and fast which makes it ideal for the use in large unbounded domains. A further advantage is that its running time is less sensitive to temporal variations of the input mesh than existing approaches. In terms of performance, the method provides a good trade-off point between speed and quality. The main idea behind our approach to handle topological changes is to delete all overlapping triangles and to fill or join the resulting holes in a robust and efficient way while guaranteeing that the output mesh is both manifold and without boundary. We demonstrate the flexibility, speed and quality of our method in various applications such as Eulerian and Lagrangian liquid simulations and the simulation of solids under large plastic deformations.
Fast Grid-Free Surface Tracking
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