Finite Element Simulation of Dense Wire Packings

A finite element program is presented to simulate the process of packing and coiling elastic wires in two- and three-dimensional confining cavities. The wire is represented by third order beam elements and embedded into a corotational formulation to capture the geometric nonlinearity resulting from large rotations and deformations. The hyperbolic equations of motion are integrated in time using two different integration methods from the Newmark family: an implicit iterative Newton-Raphson line search solver, and an explicit predictor-corrector scheme, both with adaptive time stepping. These two approaches reveal fundamentally different suitability for the problem of strongly self-interacting bodies found in densely packed cavities. Generalizing the spherical confinement symmetry investigated in recent studies, the packing of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic limit. Evidence is given that packings in oblate spheroids and scalene ellipsoids are energetically preferred to spheres.Comment: 17 pages, 7 figures, 1 tabl

From measured physical parameters to the haptic feeling of fabric

Abstract real-time cloth simulation involves the solution of many computational challenges, particularly in the context of haptic applications, where high frame rates are necessary for obtaining a satisfactory tactile experience. In this paper, we present a real-time cloth simulation system that offers a compromise between a realistic physically-based simulation of fabrics and a haptic application with high requirements in terms of computation speed. We place emphasis on architecture and algorithmic choices for obtaining the best compromise in the context of haptic applications. A first implementation using a haptic device demonstrates the features of the proposed system and leads to the development of new approaches for haptic rendering using the proposed approac

Coupling, Conservation, and Performance in Numerical Simulations

This thesis considers three aspects of the numerical simulations, which arecoupling, conservation, and performance. We conduct a project and addressone challenge from each of these aspects.We propose a novel penalty force to enforce contacts with accurate Coulombfriction. The force is compatible with fully-implicit time integration and theuse of optimization-based integration. In addition to processing collisionsbetween deformable objects, the force can be used to couple rigid bodies todeformable objects or the material point method. The force naturally leads tostable stacking without drift over time, even when solvers are not run toconvergence. The force leads to an asymmetrical system, and we provide apractical solution for handling these.Next we present a new technique for transferring momentum and velocity betweenparticles and MAC grids based on the Affine-Particle-In-Cell (APIC) frameworkpreviously developed for co-locatedgrids. We extend the original APIC paper and show thatthe proposed transfers preserve linear and angular momentum and also satisfyall of the original APIC properties.Early indications in the original APIC paper suggested that APIC might besuitable for simulating high Reynolds fluids due to favorable retention ofvortices, but these properties were not studied further. We use twodimensional Fourier analysis to investigate dissipation in the limit \dt=0.We investigate dissipation and vortex retention numerically to quantify theeffectiveness of APIC compared with other transfer algorithms.Finally we present an efficient solver for problems typically seen inmicrofluidic applications.Microfluidic ``lab on a chip'' devices are small devices that operate on smalllength scales on small volumes of fluid. Designs for microfluidic chips aregenerally composed of standardized and often repeated components connected bylong, thin, straight fluid channels. We propose a novel discretizationalgorithm for simulating the Stokes equations on geometry with these features,which produces sparse linear systems with many repeated matrix blocks. Thediscretization is formally third order accurate for velocity and second orderaccurate for pressure in the $L^\infty$ norm. We also propose a novel linearsystem solver based on cyclic reduction, reordered sparse Gaussian elimination,and operation caching that is designed to efficiently solve systems withrepeated matrix blocks

Adaptive Physically Based Models in Computer Graphics

International audienceOne of the major challenges in physically-based modeling is making simulations efficient. Adaptive models provide an essential solution to these efficiency goals. These models are able to self-adapt in space and time, attempting to provide the best possible compromise between accuracy and speed. This survey reviews the adaptive solutions proposed so far in computer graphics. Models are classified according to the strategy they use for adaptation, from time-stepping and freezing techniques to geometric adaptivity in the form of structured grids, meshes, and particles. Applications range from fluids, through deformable bodies, to articulated solids

Locking-Proof Tetrahedra

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young\u27s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For , we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis

Reactive Flows in Deformable, Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is variable, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, or biological systems. Such models include various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. Having this as the background theme, this workshop focused on novel techniques and ideas in the analysis, the numerical discretization and the upscaling of such problems, as well as on applications of major societal relevance today

Real-Time Implementation of Time-Varying Surface Prediction and Projection

Spatial augmented reality makes use of projectors to transform an object into a display surface. However, for time-varying, non-rigid surfaces this can prove to be difficult, and often leads to image distortion. In order to avoid this highly accurate measurements of the surface are required. Traditional methods of measuring surface deformations are inadequate due to noise as well as potential sources of time delay, such as projector lag. To get more accurate results, a mass spring model can be used to simulate the dynamics of the time-varying surface. This model can be put into a nonlinear state space form to get a first order differential equation. Numerical integration techniques can then be used to solve the differential equation presented. In order to reduce uncertainty in the model generated a filtering algorithm can be used. Both, the extended Kalman filter (EKF) and the cubature Kalman filter (CKF) are evaluated as potential candidates. To be able to run these filters in real time a reduced order model is developed. This enables the use of fewer mass nodes in the model, allowing for faster compute times. Additionally, to reduce visual error, an optimal node placement algorithm is used. This ensures that the surface generated by the mass spring mesh closely matches the real, curved surface of the system, minimizing error. The EKF and CKF algorithms are implemented onto a hanging cloth system perturbed by an oscillating fan. A parameter identification technique is used to create a model that accurately represents this hanging cloth system. Additionally, noise parameters of the EKF and CKF are adjusted to compensate for modeling errors and sensor noise. Finally, The mean squared error of the EKF and CKF algorithms are compared to evaluate their effectiveness. Both algorithms provide satisfactory results for use in spatial augmented reality applications. However, in all cases tested the CKF is shown to have significantly lower error values. Although the CKF algorithm is shown to be more accurate than its EKF counterpart, its computation time is much larger. However, the computation time required is still within the threshold of being able to perform real-time estimation at up to 100Hz. Furthermore, due to the nature of the construction of the CKF, it can be applied as a multi-threaded workload to significantly reduce computation time. Therefore, the implementation of a CKF algorithm can be used to accurately estimate the positions of a measured surface for use in spatial augmented reality

Realistic Hair Simulation: Animation and Rendering

International audienceThe last five years have seen a profusion of innovative solutions to one of the most challenging tasks in character synthesis: hair simulation. This class covers both recent and novel research ideas in hair animation and rendering, and presents time tested industrial practices that resulted in spectacular imagery