2023Activity reportProject-TeamELAN

3.1 Discrete modelling of slender elastic structures

For the last 15 years, we have investigated new discrete models for solving the Kirchhoff dynamic equations for thin elastic rods  19, 21, 24. All our models share a curvature-based spatial discretisation, allowing them to capture inextensibility of the rod intrinsically, without the need for adding any kinematic constraint. Moreover, elastic forces boil down to linear terms in the dynamic equations, making them well-suited for implicit integration. Interestingly, our discretisation methodology can be interpreted from two different points-of-views. From the finite-elements point-of-view, our strain-based discrete schemes can be seen as discontinuous Galerkin methods of zero and first orders. From the multibody system dynamics point of view, our discrete models can be interpreted as deformable Lagrangian systems in finite dimension, for which a dedicated community has started to grow recently  47. We note that adopting the multibody system dynamics point of view helped us formulate a linear-time integration scheme  20, which had only be investigated in the case of multibody rigid bodies dynamics so far.

3.2 Discrete and continuous modelling of frictional contact

Most popular approaches in Computer Graphics and Mechanical Engineering consist in assuming that the objects in contact are locally compliant, allowing them to slightly penetrate each other. This is the principle of penalty-based methods (or molecular dynamics), which consists in adding mutual repulsive forces of the form $kf\left(\delta \right)$, where $\delta$ is the penetration depth detected at current time step  26, 44. Though simple to implement and computationally efficient, the penalty-based method often fails to prevent excessive penetration of the contacting objects, which may prove fatal in the case of thin objects as those may just end up traversing each other. One solution might be to set the stiffness factor $k$ to a large enough value, however this causes the introduction of parasitical high frequencies and calls for very small integration steps  18. Penalty-based approaches are thus generally not satisfying for ensuring robust contact handling.

In the same vein, the friction law between solid objects, or within a yield-stress fluid (used to model foam, sand, or cement, which, unlike water, cannot flow beyond a certain threshold), is commonly modeled using a regularised friction law (sometimes even with simple viscous forces), for the sake of simplicity and numerical tractability (see e.g., 46, 37). Such a model cannot capture the threshold effect that characterises friction between contacting solids or within a yield-stress fluid. The nonsmooth transition between sticking and sliding is however responsible for significant visual features, such as the complex patterns resting on the outer surface of hair, the stable formation of sand piles, or typical stick-slip instabilities occurring during motion.

The search for a realistic, robust and stable frictional contact method encouraged us to depart from those, and instead to focus on rigid contact models coupled to the exact nonsmooth Coulomb law for friction (and respectively, to the exact nonsmooth Drucker-Prager law in the case of a fluid), which better integrate the effects of frictional contact at the macroscopic scale. This motivation was the sense of the hiring of F. Bertails-Descoubes in 2007 in the Inria/LJK Bipop team, specialised in nonsmooth mechanics and related convex optimisation methods. In the line of F. Bertails-Descoubes's work performed in the Bipop team, the Elan team keeps on including some active research on the finding of robust frictional contact algorithms specialised for slender deformable structures.

3.3 Inverse design of slender elastic structures [ERC Gem ]

With the considerable advance of automatic image-based capture in Computer Vision and Computer Graphics these latest years, it becomes now affordable to acquire quickly and precisely the full 3D geometry of many mechanical objects featuring intricate shapes. Yet, while more and more geometrical data get collected and shared among the communities, there is currently very little study about how to infer the underlying mechanical properties of the captured objects merely from their geometrical configurations.

An important challenge consists in developing a non-invasive method for inferring the mechanical properties of complex objects from a minimal set of geometrical poses, in order to predict their dynamics. In contrast to classical inverse reconstruction methods, our claim is that 1/ the mere geometrical shape of physical objects reveals a lot about their underlying mechanical properties and 2/ this property can be fully leveraged for a wide range of objects featuring rich geometrical configurations, such as slender structures subject to contact and friction (e.g., folded cloth or twined filaments).

In addition to significant advances in fast image-based measurement of diverse mechanical materials stemming from physics, biology, or manufacturing, this research is expected in the long run to ease considerably the design of physically realistic virtual worlds, as well as to boost the creation of dynamic human doubles.

To achieve this goal, we shall develop an original inverse modelling strategy based upon the following research topics:

4.1 Mechanical Engineering

Many physicists and mathematicians have strived for centuries to understand the principles governing those complex mechanical phenomena, providing a number of continuous models for slender structures, granular matter, and frictional contact. In the XX${}^{\mathrm{th}}$ century, industrial applications such as process automatization and new ways of transportation have boosted the fields of Mechanical Engineering and Computer-Aided Design, where material strength, reliability of mechanisms, and safety, standed for the main priorities. Instead, large displacements of structures, buckling, tearing, or entanglement, and even dynamics, were long considered as undesirable behaviors, thus restraining the search for corresponding numerical models.

Only recently, the engineering industry has shown some new and growing interest into the modeling of dynamic phenomena prone to large displacements, contact and friction. For instance, the cosmetology industry is more and more interested in understanding the nonlinear deformation of hair and skin, with the help of simulation. Likewise, auto and aircraft manufacturers are facing new challenges involving buckling or entanglement of thin structures such as carbon or optical fibers; they clearly lack predictive, robust and efficient numerical tools for simulating and optimizing their new manufacturing process, which share many common features with the large-scale simulation scenarii traditionally studied in Computer Graphics applications.

4.2 Computer Graphics

In contrast, Computer Graphics, which has emerged in the 60's with the advent of modern computers, was from the very beginning eager to capture such peculiar phenomena, with the sole aim to produce spectacular images and create astonishing stories. At the origin, Computer Graphics thus drastically departed from other scientific fields. Everyday-life phenomena such as cloth buckling, paper tearing, or hair fluttering in the wind, mostly ignored by other scientists at that time, became actual topics of interest, involving a large set of new research directions to be explored, both in terms of modelling and simulation. Nowadays, although the image production still remains the core activity of the Computer Graphics community, more and more research studies are directed through the virtual and real prototyping of mechanical systems, notably driven by a myriad of new applications in the virtual try on industry (e.g., hairstyling and garment fitting). Furthermore, the advent of additive fabrication is currently boosting research in the free design of new mechanisms or systems for various applications, from architecture design and fabrication of metamaterials to the creation of new locomotion modes in robotics. Some obvious common interests and approaches are thus emerging between Computer Graphics and Mechanical Engineering, yet the two communities remain desperately compartmentalized.

4.3 Soft Matter Physics

From the physics-based viewpoint, since a few decades a new generation of physicists became interested again in the understanding of such visually fascinating phenomena, and started investigating the tight links between geometry and elasticity 2. Common objects such as folded or torn paper, twined plants, coiled honey threads, or human hair have thus regained some popularity among the community in Nonlinear Physics 3. In consequence, phenomena of interest have become remarkably close to those of Computer Graphics, since scientists in both places share the common goal to model complex and integrated mechanical phenomena at the macroscopic scale. Of course, the goals and employed methodologies differ substantially from one community to the other, but showcase some evident complementarity: while computer scientists are eager to learn and understand new physical models, physicists get more and more interested in the numerical tools, in which they perceive not only a means to confirm predictions afterwards, but also a support for testing new hypothesis and exploring scenarios that would be too cumbersome or even impossible to investigate experimentally. Besides, numerical exploration starts becoming a valuable tool for getting insights into the search for analytic solutions, thus fully participating to the modeling stage and physical understanding. However, physicists may be limited to a blind usage of numerical black boxes, which may furthermore not be dedicated to their specific needs. According to us, promoting a science of modeling in numerical physics would thus be a promising and rich avenue for the two research fields. Unfortunately, very scarce cooperation currently exists between the two communities, and large networks of collaboration still need to be set up.

5.1 Footprint of research activities

The Elan team is environment-sensitive. Since its creation in 2017, 100% of its research staff moves daily from home to the lab using soft transportation means (biking, public transportation). Intercontinental missions are limited while train is the preferred mode of transportation in Europe.

5.2 Impact of research results

A large part of the research conducted in the team is of fundamental level. Direct applications lie in numerical arts, cloth design, sports, and environmental studies, all of these being of limited negative impact for the environment. Collaborations with industry leading specially harmful activities to the environment are avoided.

6.1 Awards

Our 2011 paper entitled "A hybrid iterative solver for robustly capturing Coulomb friction in hair dynamics"  28 has been awarded a Test of Time Award at Siggraph Asia 2023 in Sydney.

This paper introduced the first nonsmooth algorithm able to capture dry friction in flexible fibre assemblies in a fast and robust manner. The method was inspired by the French Moreau school on nonsmooth mechanics pioneered in the 80’s, which was essentially applied to granular materials and rigid bodies at that time. The frictional contact algorithm was implemented in the free so-bogus library and was used in several FX movies (including The Hobbit: An unexpected journey and Superman: Man of steel) for simulating hair and fur realistically.

7.1 New software

7.2 New platforms

8.1 Nonsmooth simulations of 3D Drucker-Prager granular flows and validation against experimental column collapses

Participants: Thibaut Métivet, Florence Bertails-Descoubes.

In collaboration with Gauthier Rousseau (TU Wien, formerly post-doc in the team), Hugo Rousseau (INRAE) and Gilles Daviet (NVIDIA, formerly Ph.D. student in the team), we have performed thorough comparisons between the predictions of our numerical solver Sand6 for granular flows 7.1.2, and collapse experiments conducted in a narrow channel (in collaboration with EPFL). We have shown that our nonsmooth simulator, which relies on a constant friction coefficient corresponding to the yield angle of a granular heap, is able to reproduce with high fidelity various experimental granular collapses over inclined erodible beds. Our results, obtained for two different granular materials and for various bed inclinations, suggest that a simple constant friction rheology choice remains reasonable for capturing a large variety of unsteady granular flows at low inertial number. Using the versatility of our numerical approach, we have further analysed the possible biases pertaining to laboratory-scale experiments, and shown that, in the case of granular collapses, accurate predictions could be performed as long as care was taken in measuring yield angle of the granular material appropriately. This study has been published in the Journal of Fluid Mechanics 8, and all the research data provided for reproducibility at doi.org/10.5281/zenodo.7288829.

8.2 Randomly stacked open-cylindrical shells as a functional mechanical device

Participants: Émile Hohnadel, Thibaut Métivet, Florence Bertails-Descoubes.

In collaboration with Tomohiko Sano (Keio University), we have studied the mechanical behaviour of open cylindrical shells, randomly stacked in 2D configurations. Using both numerical simulations (relying on our validated curvature-based fibre model with non-smooth frictional contact 7) and experiments, we have shown that despite the randomness of the configurations, the stacked shells exhibit robust macroscopic dissipative properties, involving complex interplay between elasticity and friction, which control the occurrence of snap-fit events at the micro-scale. Our results demonstrate that the rearrangement of flexible components could yield versatile but predictive mechanical responses, paving the way to new kinds of metamaterials. These results have been presented at the HFSS 2023 international conference 12 and published in Nature Communications Materials 9.

8.3 Hydrodynamic model for fish locomotion

Participants: Thibaut Métivet.

In collaboration with Bruno Ventéjou (co-supervised post-doc) and Philippe Peyla (LIPhy, UGA), we study the respective roles of hydrodynamic and social interactions within schools of fish, in the context of the FISHSIF ANR project. As a first step toward the simulation of large assemblies of swimming fish, we have developed a simplified hydrodynamic model, able to account for individual fish swimming and stigmergy, in particular regarding the generation of vortices wakes, without the need to introduce deformation of the body of the fish. The scaling analysis of our model falls accurately within universal swimming laws observed among many aquatic species  38, and further extends the laws of swimming efficiency to the low-inertial regime. Our model has been presented at the 2023 APS Division of Fluid Dynamics international conference 14, and a publication is in preparation.

8.4 Mixed elements for a curvature-based ribbon model

Participants: Florence Bertails-Descoubes.

In collaboration with Sébastien Neukirch (Institut D'Alembert, Sorbonne Université) and our former Ph.D. student Raphaël Charrondière, we have improved our initial curvature-based numerical model for thin elastic ribbons  2 by developing a mixed strategy, where each ribbon element is treated independently, and glued to each other only at the final solving stage through well-chosen bilateral constraints.

Thanks to this mixed variational strategy, which yields a banded Hessian, our algorithm recovers the linear complexity of low-order models while preserving the quadratic convergence of curvature-based models. As a result, our approach is scalable to a large number of elements, and suitable for various boundary conditions and unilateral contact constraints, making it possible to handle challenging scenarios such as confined buckling experiments or Möbius bands with contact. Additionally, our numerical model can incorporate various ribbon energies, including the recent 16 model for quasi-developable ribbons recently introduced in Physics, which allows to transition smoothly between a rectangular Kirchhoff rod and a (developable) Sadowsky ribbon. Our numerical scheme is carefully validated against demanding experiments of the Physics literature, which demonstrates its accuracy, efficiency, robustness, and versatility.

This work is currently under review for a journal publication.

8.5 High-order contact detection between fibres

Participants: Octave Crespel, Émile Hohnadel, Thibaut Métivet, Florence Bertails-Descoubes.

In this work we analyse the contact forces yielded by fibre models coupled to a segment-based contact detection algorithm. We note the occurrence of spurious jumps which, to the best of our knowledge, were never reported before. We demonstrate that these artifacts are actually directly linked to the low-order contact detection being used between the fibre and the obstacles, and that they worsen as curvature at contact increases. Low-order detection, based on segment proxys, is classically used due to its simplicity of treatment, even for fibre models possessing a higher-order geometry like super-helices. We show that spurious artifacts occur whatever the fibre model and contact response solver used, as soon as a segment-segment detection scheme is employed. To remove such numerical artifacts in the force profile, which can accumulate to yield large force errors, we introduce an efficient high-order detection algorithm, relying on an efficient adaptive pruning strategy.

This work, available as a preprint 15, is currently under review for a journal publication.

8.6 Numerical modeling of a feather's vane, a highly anisotropic membrane

Participants: Jouve Jean, Romero Victor, Florence Bertails-Descoubes.

In the context of Jean Jouve's doctoral thesis, in collaboration with Rahul Narain (Indian Institute of Technology Delhi, India) and Theodore Kim (Yale University, United States), we have developed a macroscopic shell simulator capable of dealing with highly anisotropic materials, such as feathers.

Feathers have a multi-scale structure with very interesting properties. From a central stiff rod (the rachis) hundreds of small fibers (barbs) come out to form a membrane-like structure, which is held together by yet another set of smaller fibers (barbules). This intricate structure drives the elastic response of the membrane and gives feathers the capability of reversible rupture. Our interest is to produce a simulator capable of realistically portray the deformation of a feather. This simulation is challenging because the membrane has two main directions with elastic coefficients differing by 4 orders of magnitude. We have compared and validated our results with experimental data, and an article has been submitted for publication.

8.7 Untangling the physics of self-locking in tight knots

Participants: Alexandre Teixeira Da Silva, Thibaut Métivet, Victor Romero, Florence Bertails-Descoubes.

In the context of the Ph.D. of Alexandre Teixeira Da Silva, co-supervised by Florence Bertails-Descoubes, Thibaut Métivet, Victor Romero, and Mélina Skouras (Anima, Inria GRA), we study the mechanical behaviour of tight knots, with a particular focus on the respective roles of elasticity and friction in the self-locking events – knot configurations where the knot remains tight even in the absence of external charge. We investigate such behaviour using both numerical simulations, performed with the PolyFEM software, and experiments, conducted within our 7.1.4 platform. Preliminary results have been presented for the overhand knot configuration at the HFSS international conference 13, along with an important validation study of the PolyFEM numerical methods in the context of large-strains mechanics.

8.8 Frictional three-point bending test: disentangling the role of friction through real and numerical experiments

Participants: Émile Hohnadel, Thibaut Métivet, Florence Bertails-Descoubes.

In collaboration with Joël Marthelot, Ignacio Andrade-Silva and Olivier Pouliquen (IUSTI, Aix Marseille Université), we have investigated the role of friction in the well-known three-point bending test, traditionally used to measure the bending modulus of slender structures. By performing experiments and numerical simulations, both compared to our new theoretical model, we have devised an efficient protocol to disentangle the respective roles of elasticity and friction in the force response of an indented rod lying on frictional supports, thereby allowing accurate and independent measurements of both the bending modulus and the friction coefficient of the considered material. This work has been presented at the ESMC 2022 international conference  41, and an article is in preparation.

9.1 International research visitors

9.2 European initiatives

9.3 National initiatives

10.1 Promoting scientific activities

10.2 Teaching - Supervision - Juries

10.3 Popularization

In October 2023, Octave Crespel participated in La Fête de la Science organised at Inria Grenoble.

11.1 Major publications

• 1 articleF.Florence Bertails-Descoubes, A.Alexandre Derouet-Jourdan, V.Victor Romero and A.Arnaud Lazarus. Inverse design of an isotropic suspended Kirchhoff rod: theoretical and numerical results on the uniqueness of the natural shape.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences4742212April 2018, 1-26HALDOIback to text
• 2 articleR.Raphaël Charrondière, F.Florence Bertails-Descoubes, S.Sébastien Neukirch and V.Victor Romero. Numerical modeling of inextensible elastic ribbons with curvature-based elements.Computer Methods in Applied Mechanics and Engineering364June 2020, 1-32HALDOIback to textback to textback to text
• 3 articleJ.Jie Li, G.Gilles Daviet, R.Rahul Narain, F.Florence Bertails-Descoubes, M.Matthew Overby, G.George Brown and L.Laurence Boissieux. An Implicit Frictional Contact Solver for Adaptive Cloth Simulation.ACM Transactions on Graphics374August 2018, 1-15HALDOI
• 4 articleM.Mickaël Ly, R.Romain Casati, F.Florence Bertails-Descoubes, M.Mélina Skouras and L.Laurence Boissieux. Inverse Elastic Shell Design with Contact and Friction.ACM Transactions on Graphics376November 2018, 1-16HALDOIback to text
• 5 articleT.Thibaut Metivet, A.Arnaud Sengers, M.Mourad Ismail and E.Emmanuel Maitre. Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles.Journal of Computational Physics4362021, 110288HALDOI
• 6 articleA.-H.Abdullah-Haroon Rasheed, V.Victor Romero, F.Florence Bertails-Descoubes, S.Stefanie Wuhrer, J.-S.Jean-Sébastien Franco and A.Arnaud Lazarus. A Visual Approach to Measure Cloth-Body and Cloth-Cloth Friction.IEEE Transactions on Pattern Analysis and Machine IntelligenceJuly 2021HALDOIback to text
• 7 articleV.Victor Romero, M.Mickaël Ly, A.-H.Abdullah-Haroon Rasheed, R.Raphaël Charrondière, A.Arnaud Lazarus, S.Sébastien Neukirch and F.Florence Bertails-Descoubes. Physical validation of simulators in Computer Graphics: A new framework dedicated to slender elastic structures and frictional contact.ACM Transactions on Graphics404August 2021, Article 66: 1-19HALDOIback to textback to text

11.2 Publications of the year

11.3 Cited publications

• 16 articleB.Basile Audoly and S.Sébastien Neukirch. A one-dimensional model for elastic ribbons: A little stretching makes a big difference.Journal of the Mechanics and Physics of Solids1532021, 104457DOIback to text
• 17 articleB.B. Audoly and S.S. Neukirch. Fragmentation of Rods by Cascading Cracks: Why Spaghetti Does Not Break in Half.Physical Review Letters9592005, 095505back to text
• 18 inproceedingsD.D. Baraff. Analytical methods for dynamic simulation of non-penetrating rigid bodies.Computer Graphics Proceedings (Proc. ACM SIGGRAPH'89 )New York, NY, USAACM1989, 223--232back to text
• 19 inproceedingsF.F. Bertails, B.B. Audoly, M.-P.M.-P. Cani, B.B. Querleux, F.F. Leroy and J.-L.J.-L. Lévêque. Modélisation de coiffures naturelles à partir des propriétés physiques du cheveu.Journées Francophones d'Informatique Graphique (AFIG)AFIG / EG-FranceStrasbourg, Francenov 2005back to text
• 20 articleF.F. Bertails. Linear Time Super-Helices.Computer Graphics Forum (Proc. Eurographics'09)282apr 2009, URL: http://www-ljk.imag.fr/Publications/Basilic/com.lmc.publi.PUBLI_Article@1203901df78_1d3cdaa/back to text
• 21 articleF.F. Bertails-Descoubes. Super-Clothoids.Computer Graphics Forum (Proc. Eurographics'12)312pt22012, 509--518URL: http://www.inrialpes.fr/bipop/people/bertails/Papiers/superClothoids.htmlDOIback to text
• 22 inproceedingsA.Alejandro Blumentals, F.Florence Bertails-Descoubes and R.Romain Casati. Dynamics of a developable shell with uniform curvatures.The 4th Joint International Conference on Multibody System DynamicsMontréal, CanadaMay 2016HALback to textback to text
• 23 phdthesisA.Alejandro Blumentals. Numerical modelling of thin elastic solids in contact.Université de Grenoble AlpesJuly 2017back to text
• 24 articleR.R. Casati and F.F. Bertails-Descoubes. Super Space Clothoids.ACM Transactions on Graphics (Proc. ACM SIGGRAPH'13)324July 2013, 48:1--48:12URL: http://doi.acm.org/10.1145/2461912.2461962DOIback to text
• 25 bookD.Dominique Chapelle and K.K.J. Bathe. The Finite Element Analysis of Shells - Fundamentals - Second Edition.Computational Fluid and Solid MechanicsSpringer2011, 410HALDOIback to text
• 26 inproceedingsP.P. Cundall. A computer model for simulating progressive large scale movements of blocky rock systems. In Proceedings of the Symposium of the International Society of Rock Mechanics.Proceedings of the Symposium of the International Society of Rock Mechanics11971, 132--150back to text
• 27 articleG.Gilles Daviet and F.Florence Bertails-Descoubes. A semi-implicit material point method for the continuum simulation of granular materials.ACM Transactions on Graphics354July 2016, 13HALDOIback to text
• 28 articleG.G. Daviet, F.F. Bertails-Descoubes and L.L. Boissieux. A hybrid iterative solver for robustly capturing Coulomb friction in hair dynamics.ACM Transactions on Graphics (Proc. ACM SIGGRAPH Asia'11)3062011, 139:1--139:12URL: http://www.inrialpes.fr/bipop/people/bertails/Papiers/hybridIterativeSolverHairDynamicsSiggraphAsia2011.htmlback to textback to text
• 29 articleG.Gilles Daviet and F.Florence Bertails-Descoubes. Nonsmooth simulation of dense granular flows with pressure-dependent yield stress.Journal of Non-Newtonian Fluid Mechanics234April 2016, 15-35HALDOIback to text
• 30 unpublishedG.Gilles Daviet and F.Florence Bertails-Descoubes. Simulation of Drucker--Prager granular flows inside Newtonian fluids.February 2017, working paper or preprintHALback to text
• 31 phdthesisG.G. Daviet. Modèles et algorithmes pour la simulation du contact frottant dans les matériaux complexes : application aux milieux fibreux et granulaires.Grenoble Alpes UniversitésDecember 2016back to text
• 32 articleA.A. Derouet-Jourdan, F.F. Bertails-Descoubes, G.G. Daviet and J.J. Thollot. Inverse Dynamic Hair Modeling with Frictional Contact.ACM Trans. Graph.326November 2013, 159:1--159:10URL: http://doi.acm.org/10.1145/2508363.2508398DOIback to text
• 33 articleA.A. Derouet-Jourdan, F.F. Bertails-Descoubes and J.J. Thollot. Stable Inverse Dynamic Curves.ACM Transactions on Graphics (Proc. ACM SIGGRAPH Asia'10 )296December 2010, 137:1--137:10URL: http://doi.acm.org/10.1145/1882261.1866159DOIback to text
• 34 articleM. A.Marcelo A. Dias and B.Basile Audoly. ``Wunderlich, Meet Kirchhoff'': A General and Unified Description of Elastic Ribbons and Thin Rods.Journal of Elasticity1191Apr 2015, 49--66URL: https://doi.org/10.1007/s10659-014-9487-0DOIback to text
• 35 manualE. J.E. J. Doedel, R. C.R. C. Pfaffenroth, A. R.A. R. Chambodut, T. F.T. F. Fairgrieve, Y. A.Y. A. Kuznetsov, B. E.B. E. Oldeman, B.B. Sandstede and X.X. Wang. AUTO 2000: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont).March 2006back to text
• 36 miscESPCI. Rencontre en l'honneur de Yves Pomeau, octobre 2016.https://www.sfpnet.fr/rencontre-celebrant-la-medaille-boltzmann-d-yves-pomeauESPCI2016, URL: https://www.sfpnet.fr/rencontre-celebrant-la-medaille-boltzmann-d-yves-pomeauback to text
• 37 articleI.I.A. Frigaard and C.C. Nouar. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation.Journal of Non-Newtonian Fluid Mechanics1271April 2005, 1--26DOIback to text
• 38 articleM.Mattia Gazzola, M.Médéric Argentina and L.Lakshminarayanan Mahadevan. Scaling macroscopic aquatic locomotion.Nature Physics10102014, 758--761back to text
• 39 bookA. L.A. L. Gol'Denveizer. Theory of Elastic Thin Shells.Pergamon Press1961back to text
• 40 articleR. E.Raymond E. Goldstein, P. B.Patrick B. Warren and R. C.Robin C. Ball. Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles.Phys. Rev. Lett.1087Feb 2012, 078101URL: https://link.aps.org/doi/10.1103/PhysRevLett.108.078101DOIback to text
• 41 inproceedingsÉ.Émile Hohnadel, J.Joel Marthelot, I.Ignacio Andrade-Silva, T.Thibaut Métivet, O.Olivier Pouliquen and F.Florence Bertails-Descoubes. Frictional three-point bending test: disentangling the role of friction through real and numerical experiments.European Solid Mechanics Conference ESMC 2022Galway, IrelandJuly 2022HALback to text
• 42 articleM.M. Jean. The Non Smooth Contact Dynamics Method.Computer Methods in Applied Mechanics and Engineering177Special issue on computational modeling of contact and friction, J.A.C. Martins and A. Klarbring, editors1999, 235-257back to text
• 43 articleJ.Jie Li, G.Gilles Daviet, R.Rahul Narain, F.Florence Bertails-Descoubes, M.Matthew Overby, G.George Brown and L.Laurence Boissieux. An Implicit Frictional Contact Solver for Adaptive Cloth Simulation.ACM Transactions on Graphics374August 2018, 1-15HALDOIback to text
• 44 inproceedingsM.M. Moore and J.J. Wilhelms. Collision detection and response for computer animation.Computer Graphics Proceedings (Proc. ACM SIGGRAPH'88 )1988, 289--298back to text
• 45 articleD.D. Moulton, P.P. Grandgeorge and S.S. Neukirch. Stable elastic knots with no self-contact.Journal of the Mechanics and Physics of Solids1162018, 33--53URL: http://www.sciencedirect.com/science/article/pii/S0022509617310104DOIback to text
• 46 articleJ.J. Spillmann and M.M. Teschner. An Adaptive Contact Model for the Robust Simulation of Knots.Computer Graphics Forum272Proc. Eurographics'082008back to text
• 47 articleH.H. Sugiyama, J.J. Gertsmayr and A.A. Mikkola. Flexible Multibody Dynamics — Essential for Accurate Modeling in Multibody System Dynamics.Journal of Computational Nonlinear Dynamics91Novembler 2013back to text