# Research

## Activity Reports

### Overall objectives

Elan is a young research team of Inria and Laboratoire Jean Kuntzmann (UMR 5224), with an original positioning across Computer Graphics and Computational Mechanics. The team is focussed on the design of predictive, robust, efficient, and controllable numerical models for capturing the shape and motion of visually rich mechanical phenomena, such as the buckling of an elastic ribbon, the flowing of sand, or the entangling of large fiber assemblies. Target applications encompass the digital entertainment industry (e.g., feature film animation, special effects), as well as virtual prototyping for the mechanical engineering industry (e.g., aircraft manufacturing, cosmetology); though very different, these two application fields require predictive and scalable models for capturing complex mechanical phenomena at the macroscopic scale. An orthogonal objective is the improvement of our understanding of natural physical and biological processes involving slender structures and frictional contact, through active collaborations with soft matter physicists. To achieve its goals, the team strives to master as finely as possible the entire modeling pipeline, involving a pluridisciplinary combination of scientific skills across Mechanics and Physics, Applied Mathematics, and Computer Science.

### Raweb (until 2020)

#### Estimation of friction coefficients in cloth

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.

#### Willmore flow simulation with diffusion-redistanciation numerical schemes

In collaboration with Arnaud Sengers (Université Claude Bernard, Emmanuel Maitre (Laboratoire Jean Kuntzmann, Grenoble INP) and Mourad Ismail (Laboratoire Interdisciplinaire de Physique, UGA), we have proposed original diffusion-redistanciation numerical schemes to compute the static shapes of elastic membranes with bending stiffness under constant area and volume constraints. This numerical method relies on an implicit representation of the surface which is used as an initial condition for diffusion-like equations. This allows to circumvent the usual difficulties pertaining to the high geometrical order and non-linearities of the bending energy and to benefit from the robustness of discretised diffusion operators. The resulting numerical schemes provide very a good stability behaviour thanks to their inherent diffusive nature and demonstrate a convergence order close to the optimal one, which is a nice achievement in regards of the low-order geometrical discretisation used. We have implemented the schemes within the finite-element library Feel++ and provided efficient and parallel solvers for the resolution of the diffusion equation and the redistanciation of the implicit surface representation. We have validated our method using comparative benchmarks computed with standard approaches. This work has led to a recent publication in Computational Physics

8

and has been presented at the Numerical Analysis Seminar from Laboratoire J.A. Dieudonné and Inria Cote d’Azur.

#### Validation of simulators for slender elastic structures and frictional contact

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 .

#### Validation of granular flow simulations against experimental column collapses

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.

#### Lateral Indentation of a Thin Elastic Film.

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.

## Collaborations

The ELAN team is involved, since 2015, in the ERC Starting Grant GEM. Within this project, several national and international collaborations have been set up, among which:

• Inria teams MORPHEO and IMAGINE
• Institut Jean le Rond d’Alembert (Paris)
• OLM Digital (Japan)

The team is also involved in a long-term partnership with the University of Minnesota (USA) and IIT Delhi (India), and in several industrial collaborations in the fields of mechanical engineering and the feature film industry.