laboratoire de physique statistique
laboratoire de physique statistique


Geometry and design of origami bellows with tunable response - Reid, Austin and Lechenault, Frederic and Rica, Sergio and Adda-Bedia, Mokhtar

Abstract : Origami folded cylinders (origami bellows) have found increasingly sophisticated applications in space flight and medicine. In spite of this interest, a general understanding of the mechanics of an origami folded cylinder has been elusive. With a newly developed set of geometrical tools, we have found an analytic solution for all possible cylindrical rigid-face states of both Miura-ori and triangular tessellations. Although an idealized bellows in both of these families may have two allowed rigid-face configurations over a well-defined region, the corresponding physical device, limited by nonzero material thickness and forced to balance hinge and plate-bending energy, often cannot stably maintain a stowed configuration. We have identified the parameters that control this emergent bistability, and we have demonstrated the ability to design and fabricate bellows with tunable deployability.
Elastic theory of origami-based metamaterials - Brunck, V. and Lechenault, F. and Reid, A. and Adda-Bedia, M.

Abstract : Origami offers the possibility for new metamaterials whose overall mechanical properties can be programed by acting locally on each crease. Starting from a thin plate and having knowledge about the properties of the material and the folding procedure, one would like to determine the shape taken by the structure at rest and its mechanical response. In this article, we introduce a vector deformation field acting on the imprinted network of creases that allows us to express the geometrical constraints of rigid origami structures in a simple and systematic way. This formalism is then used to write a general covariant expression of the elastic energy of n-creases meeting at a single vertex. Computations of the equilibrium states are then carried out explicitly in two special cases: the generalized waterbomb base and the Miura-Ori. For the waterbomb, we show a generic bistability for any number of creases. For the Miura folding, however, we uncover a phase transition from monostable to bistable states that explains the efficient deployability of this structure for a given range of geometrical and mechanical parameters. Moreover, the analysis shows that geometric frustration induces residual stresses in origami structures that should be taken into account in determining their mechanical response. This formalism can be extended to a general crease network, ordered or otherwise, and so opens new perspectives for the mechanics and the physics of origami-based metamaterials.
Inverse Leidenfrost Effect: Levitating Drops on Liquid Nitrogen - Adda-Bedia, M. and Kumar, S. and Lechenault, F. and Moulinet, S. and Schillaci, M. and Vella, D.
LANGMUIR 324179-4188 (2016) 

Abstract : We explore the interaction between a liquid drop (initially at room temperature) and a bath of liquid nitrogen. In this scenario, heat transfer occurs through film-boiling: a nitrogen vapor layer develops that may cause the drop to levitate at the bath surface. We report the phenomenology of this inverse Leidenfrost effect, investigating the effect of the drop size and density by using an aqueous solution of a tungsten salt to vary the drop density. We find that (depending on its size and density) a drop either levitates or instantaneously sinks into the bulk nitrogen. We begin by measuring the duration of the levitation as a function of the radius R and density rho(d) of the liquid drop. We find that the levitation time increases roughly linearly with drop radius but depends weakly on the drop density. However, for sufficiently large drops, R >= R-c(rho(d)), the drop sinks instantaneously; levitation does not occur. This sinking of a (relatively) hot droplet induces film-boiling, releasing a stream of vapor bubbles for a well-defined length of time. We study the duration of this immersed-drop bubbling finding similar scalings (but with different prefactors) to the levitating drop case. With these observations, we study the physical factors limiting the levitation and immersed-film-boiling times, proposing a simple model that explains the scalings observed for the duration of these phenomena, as well as the boundary of (R,rho(d)) parameter space that separates them.
Generic Bistability in Creased Conical Surfaces - Lechenault, F. and Adda-Bedia, M.

Abstract : The emerging field of mechanical metamaterials has sought inspiration in the ancient art of origami as archetypal deployable structures that carry geometric rigidity, exhibit exotic material properties, and are potentially scalable. A promising venue to introduce functionality consists in coupling the elasticity of the sheet and the kinematics of the folds. In this spirit, we introduce a scale-free, analytical description of a very general class of snap-through, bistable patterns of creases naturally occurring at the vertices of real origami that can be used as building blocks to program and actuate the overall shape of the decorated sheet. These switches appear at the simplest possible level of creasing and admit straightforward experimental realizations.
Mechanical Response of a Creased Sheet - Lechenault, F. and Thiria, B. and Adda-Bedia, M.

Abstract : We investigate the mechanics of thin sheets decorated by noninteracting creases. The system considered here consists of parallel folds connected by elastic panels. We show that the mechanical response of the creased structure is twofold, depending both on the bending deformation of the panels and the hingelike intrinsic response of the crease. We show that a characteristic length scale, defined by the ratio of bending to hinge energies, governs whether the structure's response consists in angle opening or panel bending when a small load is applied. The existence of this length scale is a building block for future works on origami mechanics.
Trajectory entanglement in dense granular materials - Puckett, James G. and Lechenault, Frederic and Daniels, Karen E. and Thiffeault, Jean-Luc

Abstract : The particle-scale dynamics of granular materials have commonly been characterized by the self-diffusion coefficient D. However, this measure discards the collective and topological information known to be an important characteristic of particle trajectories in dense systems. Direct measurement of the entanglement of particle space-time trajectories can be obtained via the topological braid entropy S-braid, which has previously been used to quantify mixing efficiency in fluid systems. Here, we investigate the utility of S-braid in characterizing the dynamics of a dense, driven granular material at packing densities near the static jamming point phi(J). From particle trajectories measured within a two-dimensional granular material, we typically observe that S-braid is well defined and extensive. However, for systems where phi greater than or similar to 0.79, we find that S-braid (like D) is not well defined, signifying that these systems are not ergodic on the experimental timescale. Both S-braid and D decrease with either increasing packing density or confining pressure, independent of the applied boundary condition. The related braiding factor provides a means to identify multi-particle phenomena such as collective rearrangements. We discuss possible uses for this measure in characterizing granular systems.
Super-diffusion around the rigidity transition: Levy and the Lilliputians - Lechenault, F. and Candelier, R. and Dauchot, O. and Bouchaud, J. -P. and Biroli, G.
SOFT MATTER 63059-3064 (2010) 

Abstract : By analyzing the displacement statistics of an assembly of horizontally vibrated bi-disperse frictional grains in the vicinity of the jamming transition experimentally studied before (F. Lechenault, O. Dauchot, G. Biroli and J.-P. Bouchard, Europhys. Lett., 2008, 83, 46003), we establish that their superdiffusive motion is a genuine Levy flight, but with a `jump' size that is very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.