Super Space Clothoids

Special Issue: SIGGRAPH 2013 ConferenceInternational audienceThin elastic filaments in real world such as vine tendrils, hair ringlets or curled ribbons often depict a very smooth, curved shape that low-order rod models -- e.g., segment-based rods -- fail to reproduce accurately and compactly. In this paper, we push forward the investigation of high-order models for thin, inextensible elastic rods by building the dynamics of a G2-continuous piecewise 3D clothoid: a smooth space curve with piecewise affine curvature. With the aim of precisely integrating the rod kinematic problem, for which no closed-form solution exists, we introduce a dedicated integration scheme based on power series expansions. It turns out that our algorithm reaches machine precision orders of magnitude faster compared to classical numerical integrators. This property, nicely preserved under simple algebraic and differential operations, allows us to compute all spatial terms of the rod kinematics and dynamics in both an efficient and accurate way. Combined with a semi-implicit time-stepping scheme, our method leads to the efficient and robust simulation of arbitrary curly filaments that exhibit rich, visually pleasing configurations and motion. Our approach was successfully applied to generate various scenarios such as the unwinding of a curled ribbon as well as the aesthetic animation of spiral-like hair or the fascinating growth of twining plants

The Contact Problem in Lagrangian Systems subject to Bilateral and Unilateral constraints with sliding Coulomb's Friction

International audienceThis work concerns the existence and uniqueness of the acceleration and Lagrange multipliers for Lagrangian systems subject to sliding Coulomb's friction with bilateral and unilateral constraints. Focus is put on providing sufficient conditions for singularities like Painlevé paradoxes to be avoided. Explicit criteria, in the form of upper bounds on the friction coefficients, are given so as to preserve the well posedness of the frictional problem

Approcher des courbes par des hélices

National audienceLa forme élancée des structures fibreuses - telles que les cheveux, les brins d'ADN ou encore les tiges de plantes - peut se représenter à l'aide de courbes de l'espace. En particulier, les courbes en hélices par morceaux offrent une représentation intéressante pour modéliser numériquement de telles données, car elle s'avère très compacte : 2 nombres (une courbure et une torsion) suffisent à caractériser un morceau d'hélice circulaire. Dans cet article, nous présentons une méthode à la fois précise et rapide pour approcher une courbe quelconque de l'espace par une courbe lisse en hélices par morceaux

Fast Cloth Simulation with Implicit Contact and Exact Coulomb Friction

International audienceCloth dynamics plays an important role in the visual appearance of moving characters. Properly accounting for frictional contact is of utmost importance to avoid cloth-body penetration and to capture folding behavior due to dry friction. We present here the first method able to account for contact with exact Coulomb friction between a cloth and the underlying character. Our key contribution is to formulate and solve the frictional contact problem merely on velocity variables, by leveraging some tools of convex analysis. Our method is both fast and robust, allowing us to simulate full-size garments with more realistic body-cloth interactions compared to former methods, while maintaining similar computational timings

Approcher des courbes par des hélices

National audienceLa forme élancée des structures fibreuses - telles que les cheveux, les brins d'ADN ou encore les tiges de plantes - peut se représenter à l'aide de courbes de l'espace. En particulier, les courbes en hélices par morceaux offrent une représentation intéressante pour modéliser numériquement de telles données, car elle s'avère très compacte : 2 nombres (une courbure et une torsion) suffisent à caractériser un morceau d'hélice circulaire. Dans cet article, nous présentons une méthode à la fois précise et rapide pour approcher une courbe quelconque de l'espace par une courbe lisse en hélices par morceaux

Dynamics of a developable shell with uniform curvatures

International audienceMany surface-like objects around us such as leaves, garments, or boat sails, may easily bend but hardly stretch. One is thus faced with the need for numerical models able to handle inextensibility constraints properly. In the present work we restrict ourselves to the modeling of elastic developable surfaces, i.e., surfaces which always remain isometric to a planar configuration. Our surfaces of interest may however take a non-planar rest configuration, hence we shall model them as developable thin elastic shells. Our goal is to design a both robust and efficient discrete model for simulating the motion of such objects. This work presents a first step towards this direction, by introducing a perfectly inextensible patch for a developable thin elastic shell

Simulation of Drucker–Prager granular flows inside Newtonian fluids

Granular-fluid interactions appear in a variety of real-life scenarios ranging from immersed avalanches to ash clouds. We present a continuum-based numerical method for the simulation of such phenomena. Our approach avoids the heavy computational cost inherent to a fluid-solid coupling at the grain scale, while still being able to capture the distinctive regimes governing the collapse of an immersed granular column. To the best of our knowledge, the method presented here is the first to combine fully-coupled two-phase equations for immersed granular flows with an implicit nonsmooth treatment of the Drucker–Prager rheology

Simulation par éléments discrets de fibres flexibles avec frottement de Coulomb

National audienceOn présente ici une méthode pour la simulation d'ensembles de fibres basée sur une discrétisation du modèle de Kirchhoff ( modèle des Super-Hélices ). Le contact avec frottement de Coulomb exact entre les fibres est résolu grâce à un algorithme itératif de type Gauss-Seidel faisant intervenir un solveur local hybride. La méthode est appliquée à l'informatique graphique, et en particulier à la simulation réaliste de chevelures

Revisiting the role of friction coefficients in granular collapses: confrontation of 3-D non-smooth simulations with experiments

In this paper, transient granular flows are examined both numerically and experimentally. Simulations are performed using the continuous 3D granular model introduced in Daviet & Bertails-Descoubes (2016), which represents the granular medium as an inelastic and dilatable continuum subject to the Drucker-Prager yield criterion in the dense regime. One notable feature of this numerical model is to resolve such a non-smooth rheology without any regularisation. We show that this non-smooth model, which relies on a constant friction coefficient, is able to reproduce with high fidelity various experimental granular collapses over inclined erodible beds, provided the friction coefficient is set to the avalanche angle - and not to the stop angle, as generally done. In order to better characterise the range of validity of the fully plastic rheology in the context of transient frictional flows, we further revisit scaling laws relating the shape of the final collapse deposit to the initial column aspect ratio, and accurately recover established power-law dependences up to aspect ratios in the order of 10. The influence of sidewall friction is then examined through experimental and simulated collapses with varying channel widths. The effective flow thickness is estimated in relation to the channel width, thereby challenging previously held assumptions on its estimation. Finally, we discuss the potential extension of the constant coefficient model with a hysteretic model to refine predictions of early-stage collapse dynamics, illustrating the impact of such phenomenology on transient flows and paving the way to more elaborate analysis.Comment: 25 figures and 6 movie

Dynamics of a developable shell with uniform curvatures

International audienceMany surface-like objects around us such as leaves, garments, or boat sails, may easily bend but hardly stretch. One is thus faced with the need for numerical models able to handle inextensibility constraints properly. In the present work we restrict ourselves to the modeling of elastic developable surfaces, i.e., surfaces which always remain isometric to a planar configuration. Our surfaces of interest may however take a non-planar rest configuration, hence we shall model them as developable thin elastic shells. Our goal is to design a both robust and efficient discrete model for simulating the motion of such objects. This work presents a first step towards this direction, by introducing a perfectly inextensible patch for a developable thin elastic shell