Corentin Coulais

Programmable mechanical metamaterials

We create mechanical metamaterials whose response to uniaxial compression can be programmed by lateral confinement, allowing monotonic, nonmonotonic, and hysteretic behavior. These functionalities arise from a broken rotational symmetry which causes highly nonlinear coupling of deformations along the two primary axes of these metamaterials. We introduce a soft mechanism model which captures the programmable mechanics, and outline a general design strategy for confined mechanical metamaterials. Finally, we show how inhomogeneous confinement can be explored to create multistability and giant hysteresis.

Combinatorial design of textured mechanical metamaterials

The structural complexity of metamaterials is limitless, but, in practice, most designs comprise periodic architectures that lead to materials with spatially homogeneous features. More advanced applications in soft robotics, prosthetics and wearable technology involve spatially textured mechanical functionality, which requires aperiodic architectures. However, a naive implementation of such structural complexity invariably leads to geometrical frustration (whereby local constraints cannot be satisfied everywhere), which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic, yet frustration-free, mechanical metamaterials that exhibit spatially textured functionalities. We implement this strategy using cubic building blocks—voxels—that deform anisotropically, a local stacking rule that allows cooperative shape changes by guaranteeing that deformed building blocks fit together as in a three-dimensional jigsaw puzzle, and three-dimensional printing. These aperiodic metamaterials exhibit long-range holographic order, whereby the two-dimensional pixelated surface texture dictates the three-dimensional interior voxel arrangement. They also act as programmable shape-shifters, morphing into spatially complex, but predictable and designable, shapes when uniaxially compressed. Finally, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens up a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.

Static non-reciprocity in mechanical metamaterials

Reciprocity is a general, fundamental principle governing various physical systems, which ensures that the transfer function—the transmission of a physical quantity, say light intensity—between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity (and therefore show non-reciprocity) have been mostly considered in dynamic systems involving electromagnetic, acoustic and mechanical wave propagation associated with fields varying in space and time. Here we show that it is possible to break reciprocity in static systems, realizing mechanical metamaterials that exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. This is achieved by combining large nonlinearities with suitable geometrical asymmetries and/or topological features. In addition to extending non-reciprocity and isolation to statics, our work sheds light on energy propagation in nonlinear materials with asymmetric crystalline structures and topological properties. We anticipate that breaking reciprocity will open avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.

Discontinuous buckling of wide beams and metabeams

We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams-beams made from a mechanical metamaterial-exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally.

Shear Modulus and Dilatancy Softening in Granular Packings above Jamming

We investigate experimentally the mechanical response to shear of a monolayer of bidisperse frictional grains across the jamming transition. We inflate an intruder inside the packing and use photoelasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 10(-3) and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in: both the shear modulus and the dilatancy shear soften at small strain until a critical strain is reached where effective linearity is recovered. The scaling of the critical strain and the associated critical stresses on the distance to jamming are extracted. We check that the constitutive laws, together with mechanical equilibrium, correctly predict to the observed stress and strain profiles. These profiles exhibit a spatial crossover between an effective linear regime close to the inflater and the truly nonlinear regime away from it. The crossover length diverges at the jamming transition.

Surface Wind-Speed Statistics Modelling: Alternatives to the Weibull Distribution and Performance Evaluation

Wind-speed statistics are generally modelled using the Weibull distribution. However, the Weibull distribution is based on empirical rather than physical justification and might display strong limitations for its applications. Here, we derive wind-speed distributions analytically with different assumptions on the wind components to model wind anisotropy, wind extremes and multiple wind regimes. We quantitatively confront these distributions with an extensive set of meteorological data (89 stations covering various sub-climatic regions in France) to identify distributions that perform best and the reasons for this, and we analyze the sensitivity of the proposed distributions to the diurnal to seasonal variability. We find that local topography, unsteady wind fluctuations as well as persistent wind regimes are determinants for the performances of these distributions, as they induce anisotropy or non-Gaussian fluctuations of the wind components. A Rayleigh–Rice distribution is proposed to model the combination of weak isotropic wind and persistent wind regimes. It outperforms all other tested distributions (Weibull, elliptical and non-Gaussian) and is the only proposed distribution able to catch accurately the diurnal and seasonal variability.

Local rheological measurements in the granular flow around an intruder.

The rheological properties of granular matter within a two-dimensional flow around a moving disk is investigated experimentally. Using a combination of photoelastic and standard tessellation techniques, the strain and stress tensors are estimated at the grain scale in the time-averaged flow field around a large disk pulled at constant velocity in an assembly of smaller disks. On the one hand, one observes inhomogeneous shear rate and strongly localized shear stress and pressure fields. On the other hand, a significant dilation rate, which has the same magnitude as the shear strain rate, is reported. Significant deviations are observed with local rheology that justify the need of searching for a nonlocal rheology.

Programmable mechanical metamaterials: the role of geometry.

We experimentally and numerically study the role of geometry for the mechanics of biholar metamaterials, which are quasi-2D slabs of rubber patterned by circular holes of two alternating sizes. We recently showed how the response to uniaxial compression of these metamaterials can be programmed by lateral confinement. In particular, there is a range of confining strains εx for which the resistance to compression becomes non-trivial-non-monotonic or hysteretic-in a range of compressive strains εy. Here we show how the dimensionless geometrical parameters t and χ, which characterize the wall thickness and size ratio of the holes that pattern these metamaterials, can significantly tune these ranges over a wide range. We study the behavior for the limiting cases where the wall thickness t and the size ratio χ become large, and discuss the new physics that arises there. Away from these extreme limits, the variation of the strain ranges of interest is smooth with porosity, but the variation with size ratio evidences a cross-over at low χ from biholar to monoholar (equal sized holes) behavior, related to the elastic instabilities in purely monoholar metamaterials. Our study provides precise guidelines for the rational design of programmable biholar metamaterials, tailored to specific applications, and indicates that the widest range of programmability arises for moderate values of both t and χ.

A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials

Mechanism-based metamaterials leverage geometric design to control deformations — a strategy that works well on small scales. But the discovery of a characteristic length scale suggests that the underlying mechanism is distorted for larger systems.

Coupling the Leidenfrost effect and elastic deformations to power sustained bouncing

Water droplets skid across hot surfaces, hovering imperceptibly as they undergo rapid vaporization. Elastic solids are now shown to exhibit a variant of this behaviour, engaging in sustained bouncing by coupling vapour release to elastic deformation. The Leidenfrost effect occurs when an object near a hot surface vaporizes rapidly enough to lift itself up and hover1,2. Although well understood for liquids1,2,3,4,5,6,7,8,9,10,11,12,13,14 and stiff sublimable solids15,16,17,18, nothing is known about the effect with materials whose stiffness lies between these extremes. Here we introduce a new phenomenon that occurs with vaporizable soft solids—the elastic Leidenfrost effect. By dropping hydrogel spheres onto hot surfaces we find that, rather than hovering, they energetically bounce several times their diameter for minutes at a time. With high-speed video during a single impact, we uncover high-frequency microscopic gap dynamics at the sphere/substrate interface. We show how these otherwise-hidden agitations constitute work cycles that harvest mechanical energy from the vapour and sustain the bouncing. Our findings suggest a new strategy for injecting mechanical energy into a widely used class of soft materials, with potential relevance to fields such as active matter, soft robotics and microfluidics.