3.1 Discrete modeling 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  17, 19, 22. All our models share a curvature-based spatial discretization, 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 discretization 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  44. We note that adopting the multibody system dynamics point of view helped us formulate a linear-time integration scheme  18, which had only be investigated in the case of multibody rigid bodies dynamics so far.

3.2 Discrete and continuous modeling 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  24, 40. 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  16. 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 regularized friction law (sometimes even with simple viscous forces), for the sake of simplicity and numerical tractability (see e.g., 43, 35). Such a model cannot capture the threshold effect that characterizes 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, specialized in nonsmooth mechanics and related convex optimization 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 specialized 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 modeling 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 Sustained experimental work in Elan

From its beginning, Elan has integrated experimental work into its modelling pipeline. Experiments are particularly interesting for validating numerical models carefully, as well as for investigating new physical behaviours (collective effects in granular and fibrous media, for instance). This original coupling of experiments together with numerics will be sustained thanks to the hiring of Victor Romero in 2021 as a permanent researcher of the team. In particular, the ElanFab experimental platform (see Section 7.5.1), which made it possible to conduct important scientific studies within Elan and/or in collaboration with other Inria groups (Morphéo, Anima) and external partners (Sorbonne Université, IIT Delhi, Yale), will continue to be developed and maintained in the long run.

6.2 Fish In Silico with Hydrodynamics and Social Forces - FISHSIF

The FISHSIF project has received a three-year funding from the ANR (Agence Nationale pour la Recherche). The goal of this project is to introduce dynamical cognition models within full hydrodynamic simulations in order to understand the role played by social or flow interactions in the organisation and behaviour of schools of fish. The project will be led in a collaboration between the ELAN team, the Laboratoire Interdisciplianire de Physique (LIPhy, UGA/CNRS) and the Laboratoire de Psychologie et NeuroCognition (LPNC, UGA/CNRS).

6.3 Semi-plenary Talk at WCCM-ECCOMAS

In January 2021, F. Bertails-Descoubes was semi-plenary speaker at WCCM-ECCOMAS 2020, the 14th World Congress in Computational Mechanics.

7.1 Software development policy

Our research work involves a large number of software developments, as each new numerical model gives rise to the development of one or several home-made simulation softwares. On the one hand, our peculiar research activity has led to the design of effective and competitive softwares addressing some dedicated problems (such as specialised fiber or frictional contact models), some of which having been transfered to industry in the past. On the other hand, in the team we participate to the development and maintainance of some more generic platforms (such as Feel++), mostly for academic usage.

7.2 Software distribution policy

In the Elan team we chose to favor the free distribution of our source codes accompanying our major scientific publications, for replicability and dissemination purposes. To accomodate both free dissemination and industrial transfer, our current policy, publicly displayed here, is to find the right balance between free and proprietary licensing agreements, through dual licensing.

7.3 Experimental set-ups

In addition to software development, our recent activity includes the development of experimental set-ups, initially realised both in the Amiqual4Home “Atelier Numérique” in Montbonnot and in the experimental laboratory of Institut Jean le Rond d'Alembert in Paris, and now conducted in the new experimentation place of Inria GRA (formerly the "Halle Robotique"). The goal of our current platform ElanFab (see Section 7.5.1) is twofold: first, validate our simulators on some controlled experiments; second, discover some new physical phenomena worth investigating, with the help of the predictions brought by our simulators.

7.4 New software

7.5 New platforms

8.1 Estimation of friction coefficients in cloth

Participants: Haroon Rasheed, Victor Romero, Florence Bertails-Descoubes.

Our objective was to estimate friction coefficients in fabric, for which no reliable experimental process exists yet. Our idea was to leverage our accurate simulator for cloth frictional contact  39, possibly complemented by deep learning techniques, in order to considerably alleviate this task and build non-invasive measurement protocols. The PhD thesis of Abdullah-Haroon Rasheed (2017 - 2021), co-advised by F. Bertails-Descoubes and Stefanie Wuhrer and Jean-Sébastien Franco from the Morpheo team (Computer Vision), made several important advances on this topic. Thanks to a pluridisciplinary collaboration encompassing Physical Modelling, Computer Vision, Machine Learning, and Experimental Physics (in collaboration with Victor Romero and Arnaud Lazarus, Sorbonne Université), we have built a new non-invasive protocol for estimating material properties of cloth and friction during dynamic interaction, including cloth-solid and cloth-cloth interaction. The method relies on a neural network trained only on simulated data (yielded by our cloth simulator Argus), after a careful validation of the simulator. From this trained network, we were able to predict on a real experiment both the material class of the cloth sample as well as the friction coefficient between the cloth sample and the substrate (either smooth or cloth-like), with a good level of prediction. This work was published in a major conference venue in Computer Vision  42 (selected for an oral presentation) and the cloth-to-cloth extension was published in the journal IEEE PAMI 9. The latter paper, where we have evidenced the influence of the predictibility of the simulator on the accuracy of the network, also marked a turning point in our research interests, as now we consider the physical validation of numerical models as a major research axis in the Elan team.

8.2 Willmore flow simulation with diffusion-redistanciation numerical schemes

Participant: Thibaut Metivet.

8.3 Validation of simulators for slender elastic structures and frictional contact

Participants: Victor Romero, Mickaël Ly, Haroon Rasheed, Raphaël Charrondière, Florence Bertails-Descoubes.

In collaboration with Arnaud Lazarus and Sébastien Neukirch (Sorbonne Université, Institut Jean le Rond d'Alembert), we have set up a new framework for validating simulators of slender elastic structures (rods and plates) and frictional contact. To this aim we leverage and enrich a set of protocols from the Soft Matter Physics community, initially devised for measuring elasticity and frictional properties of slender elastic structures. These retained tests, that we experimentally validate, are characterized by scaling laws which only depend on a few dimensionless parameters, making them ideal for benchmarking robustly a large diversity of codes across different physical regimes, without having to worry about scales or dimensions. We have passed a number of popular codes of Computer Graphics through our benchmarks by defining a rigorous, consistent, and as fair as possible methodology. Our results show that while some popular simulators for plates/shells and frictional contact fail even on the simplest scenarios, more recent ones, as well as well-known codes for rods, generally perform well and sometimes even better than some reference commercial tools of Mechanical Engineering. This long-term study led to an original publication at ACM Siggraph 2021 10 and multiple invited talks in both Computer Science events (Colloque Sciences & Games 2021) and Physics events (Rencontres du Non-Linéaire 2021), see Section 10.1.2 .

8.4 Validation of granular flow simulations against experimental column collapses

Participants: Thibaut Métivet, Florence Bertails-Descoubes.

In collaboration with Gauthier Rousseau, formerly post-doc in the team (and PhD student at EPFL), and with Hugo Rousseau (INRAE) and Gilles Daviet (formerly PhD student in the team), we have performed some thorough comparisons between the predictions of our numerical solver Sand6 for granular flows 7.4.3, 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. We will submit this original study for publication in Mechanics in 2022.

8.5 Lateral Indentation of a Thin Elastic Film.

Participant: Victor Romero.

In collaboration with Enrique Cerda, Eugenio Hamm, from Universidad de Santiago de Chile, and Miguel Trejo from Universidad de Buenos Aires, we published a paper 11 where we present an experimental setup for testing thin-film materials by studying the lateral indentation of a narrow opening cut into a film, triggering a cascade of buckling events. We showed that the force response F is dominated by bending and stretching effects for small displacements and slowly varies with indenter displacement $F\sim d^{2/5}$, to finally reach a wrinkled state that results in a robust nonlinear asymptotic relation, $F\sim d^4$ . We present experiments with films of various thicknesses and material properties, and numerical simulations to confirm our analysis defining an order parameter that accounts for the different response regimes observed in experiments and simulations.

9.1 International Collaborations

• Long-term collaboration with Rahul Narain (IIT Delhi, India).
• Long-term collaboration with Enrique Cerda (Universidad de Santiago, Chile).
• Long-term collaboration with Eugenio Hamm (Universidad de Santiago, Chile).
• Long-term collaboration with Miguel Trejo (Universidad de Buenos Aires, Argentina).
• Starting collaboration with Theodore Kim (Yale, USA).
• Starting collaboration with Tomohiko Sano (Dept of Mechanical Engineering, Keio University, Sigma Lab (Japan)).

9.2 European initiatives

9.3 National Collaborations

• Long-term collaboration with Arnaud Lazarus and Sébastien Neukirch (Institut Jean le Rond d'Alembert, Sorbonne Université), within the GEM project.
• Long-term collaboration with Christophe Prud'homme and Vincent Chabannes (Université de Strasbourg and Centre de modélisation et de simulation de Strasbourg).
• Collaboration with Olivier Pouliquen and Joël Marthelot (IUSTI, Aix-Marseille University).

9.4 Regional collaborations

• Collaboration with Philippe Peyla, Aurélie Dupont (LIPhy, UGA/CNRS) and Christian Graff (LPNC, UGA/CNRS) within the FISHSIF project.
• Collaboration with Mélina Skouras (Inria/LJK - Anima team) within the GEM project.
• Collaboration with Stefanie Wuhrer and Jean-Sébastien Franco (Inria/LJK - Morphéo team) within the GEM project.

10.1 Promoting scientific activities

10.2 Teaching - Supervision - Juries

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, 1-26
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• 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, 1-32
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• 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, 1-15
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• 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, 1-16
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• 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, 110288
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• 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 2021
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• 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: 1-19
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11.2 Publications of the year

11.3 Cited publications

• 15 articleB.B. Audoly and S.S. Neukirch. Fragmentation of Rods by Cascading Cracks: Why Spaghetti Does Not Break in Half.Physical Review Letters9592005, 095505
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• 16 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--232
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• 17 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 2005
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• 18 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/
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• 19 articleF.F. Bertails-Descoubes. Super-Clothoids.Computer Graphics Forum (Proc. Eurographics'12)312pt22012, 509--518URL: http://www.inrialpes.fr/bipop/people/bertails/Papiers/superClothoids.html
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• 20 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 2016
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• 21 phdthesisA.Alejandro Blumentals. Numerical modelling of thin elastic solids in contact.Université de Grenoble AlpesJuly 2017
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• 22 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/10.1145/2461912.2461962
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• 23 bookD.Dominique Chapelle and K.K.J. Bathe. The Finite Element Analysis of Shells - Fundamentals - Second Edition.Computational Fluid and Solid MechanicsSpringer2011, 410
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• 24 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--150
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• 25 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, 13
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• 26 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.html
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• 27 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, 15-35
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• 28 unpublishedG.Gilles Daviet and F.Florence Bertails-Descoubes. Simulation of Drucker--Prager granular flows inside Newtonian fluids.February 2017, working paper or preprint
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• 29 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 2016
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• 30 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/10.1145/2508363.2508398
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• 31 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/10.1145/1882261.1866159
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• 32 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/s10659-014-9487-0
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• 33 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 2006
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• 34 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-pomeau
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• 35 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--26
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• 36 bookA. L.A. L. Gol'Denveizer. Theory of Elastic Thin Shells.Pergamon Press1961
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• 37 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.108.078101
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• 38 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, 235-257
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• 39 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, 1-15
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• 40 inproceedingsM.M. Moore and J.J. Wilhelms. Collision detection and response for computer animation.Computer Graphics Proceedings (Proc. ACM SIGGRAPH'88 )1988, 289--298
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• 41 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/S0022509617310104
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• 42 inproceedingsA.-H.Abdullah-Haroon Rasheed, V.Victor Romero, F.Florence Bertails-Descoubes, S.Stefanie Wuhrer, J.-S.Jean-Sébastien Franco and A.Arnaud Lazarus. Learning to Measure the Static Friction Coefficient in Cloth Contact.CVPR 2020 - IEEE Conference on Computer Vision and Pattern RecognitionSeattle, United StatesIEEEJune 2020, 9909-9918
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• 43 articleJ.J. Spillmann and M.M. Teschner. An Adaptive Contact Model for the Robust Simulation of Knots.Computer Graphics Forum272Proc. Eurographics'082008
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• 44 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 2013
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