ELAN: modELisation de l'Apparence des phénomènes Non-linéaires

Abstract Structures with artificially engineered mechanical properties, often called mechanical metamaterials, are interesting for their tunable functionality. Various types of mechanical metamaterials have been proposed in the literature, designed to harness light or magnetic interactions, structural instabilities in slender or hollow structures, and contact friction. However, most of the designs are ideally engineered without any imperfections, in order to perform deterministically as programmed. Here, we study the mechanical performance of randomly stacked cylindrical shells, which act as a disordered mechanical metamaterial. Combining experiments and simulations, we demonstrate that the stacked shells can absorb and store mechanical energy upon compression by exploiting large deformation and relocation of shells, snap-fits, and friction. Although shells are oriented randomly, the system exhibits statistically robust mechanical performance controlled by friction and geometry. Our results demonstrate that the rearrangement of flexible components could yield versatile and predictive mechanical responses.

The static-dynamic analogy discovered by Gustav Kirchhoff in 1859 shows that the statics of an elastic beam is equivalent to the dynamics of a spinning top. This analogy, where time and angular velocity are, for example, equivalent to arclength and curvatures, allows the use of Emmy Noether’s 1918 theorem on continuous symmetries to unravel a quantity that is invariant along elastic rods at equilibrium. A spinning top having a Lagrangian independent of time will have its mechanical energy constant in time. In the same manner, an elastic rod with uniform elastic properties will have the sum of its curvature energy and its tension force uniform along the structure. This arclength invariance property is known in simple cases, but the present approach generalises it to more complex scenarios where extensibility, shear, conservative loads (e.g. gravity), and contact are involved. Moreover, still using Noether’s theorem and bringing to light the continuous symmetries of the Lagrangian of the variational approach, we recover all known invariants for the statics and dynamics of rods and ribbons, including coordinate invariants. Furthermore, we show how the arclength invariant may be used to obtain pivotal information on some landmark elastic rod problems, including confinement buckling, sliding sleeves, or plectonemes. Finally, we extend the approach to vibrations. Overall, this paper is an attempt to explain, unify and extend all previous results on rod invariants thanks to the beautiful Noetherian formalism, and to show its practical use on a few relevant applications.

Measuring friction coefficients between cloth and an external body is a longstanding issue in mechanical engineering, never yet addressed with a pure vision-based system. The latter offers the prospect of simpler, less invasive friction measurement protocols compared to traditional ones, and can vastly benefit from recent deep learning advances. Such a novel measurement strategy however proves challenging, as no large labelled dataset for cloth contact exists, and creating one would require thousands of physics workbench measurements with broad coverage of cloth-material pairs. Using synthetic data instead is only possible assuming the availability of a soft-body mechanical simulator with true-to-life friction physics accuracy, yet to be verified. We propose a first vision-based measurement network for friction between cloth and a substrate, using a simple and repeatable video acquisition protocol. We train our network on purely synthetic data generated by a state-of-the-art frictional contact simulator, which we carefully calibrate and validate against real experiments under controlled conditions. We show promising results on a large set of contact pairs between real cloth samples and various kinds of substrates, with 93.6% of all measurements predicted within 0.1 range of standard physics bench measurements.

In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore flow in both two and three dimensions. These algorithms rely on alternating diffusions of the signed distance function to the interface and a redistanciation step, and with careful choice of the applied diffusions, end up moving the zero level-set of the distance function by some geometrical quantity without resorting to any explicit transport equation. The constraints are enforced between the diffusion and redistanciation steps via a simple rescaling method. The energy globally decreases at the end of each global step. The algorithms feature the computational efficiency of thresholding methods without requiring any adaptive remeshing thanks to the use of a signed distance function to describe the interface. This opens their application to dynamic fluid-structure simulations for large and realistic cases. The methodology is validated by computing the equilibrium shapes of two- and three-dimensional vesicles, as well as the Clifford torus.

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I. The toy model definition The fish is defined a rigid body with a ellipsoidal shape The rigid body is defined by a penalization in viscosity: The tail flapping is described by local forces directly applied in the Navier-Stokes Eq. Solved using FEEL++ [1], a finite element C++ library. Control parameters are: the torque T 0 , the force F 0 and the pulsation .

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