Frederic Lechenault

Mechanical response of a creased sheet.

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 structures 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.

Local origins of volume fraction fluctuations in dense granular materials

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and interparticle friction μ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Voronoï tessellation, we find the variance of the local volume fraction Φ monotonically decreases as the system becomes more dense, independent of boundary condition and μ. We examine the universality and origins of this trend using experiments and the recent granocentric model [M. Clusel, E. I. Corwin, A. O. N. Siemens, and J. Brujić, Nature (London) 460, 611 (2009); E. I. Corwin, M. Clusel, A. O. N. Siemens, and J. Brujić, Soft Matter 6, 2949 (2010)], modified to draw particle locations from an arbitrary distribution P(s) of neighbor distances s. The mean and variance of the observed P(s) are described by a single length scale controlled by ̅Φ. Through the granocentric model, we observe that diverse functional forms of P(s) all produce the trend of decreasing fluctuations, but only the experimentally observed P(s) provides quantitative agreement with the measured Φ fluctuations. Thus, we find that both P(s) and P(Φ) encode similar information about the ensemble of observed packings and are connected to each other by the local granocentric model.

Evidence of Deep Water Penetration in Silica during Stress Corrosion Fracture

We measure the thickness of the heavy water layer trapped under the stress corrosion fracture surface of silica using neutron reflectivity experiments. We show that the penetration depth is 65-85   Å, suggesting the presence of a damaged zone of ∼100   Å extending ahead of the crack tip during its propagation. This estimate of the size of the damaged zone is compatible with other recent results.

Effects of Finite Probe Size on Self-Affine Roughness Measurements

The roughness of fracture surfaces exhibits self-affinity for a wide variety of materials and loading conditions. The universality and the range of scales over which this regime extends are still debated. The topography of these surfaces is however often investigated with a finite contact probe. In this case, we show that the correlation function of the roughness can only be measured down to a length scale Deltax{c} which depends on the probe size R, the Hurst exponent zeta of the surface and its topothesy l, and exhibits spurious behavior at smaller scales. First, we derive the dependence of Deltax{c} on these parameters from a simple scaling argument. Then, we verify this dependence numerically. Finally, we establish the relevance of this analysis from AFM measurements on an experimental glass fracture surface and provide a metrological procedure for roughness measurements.

Elastic theory of origami-based metamaterials.

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.

Equilibration of granular subsystems

We experimentally investigate the steady states of two granular assemblies differing in their material properties and allowed to exchange volume with each other under external agitation in the vicinity of their jamming transition. We extract the statistics of various static and dynamic quantities, and uncover a materials-independent relationship between the average packing fraction and its fluctuations. This relationship defines an intensive parameter which decouples from the volume statistics, and remarkably takes the same value in both subsystems. We also observe that an effective diffusion coefficient also takes the same value in each subsystem, even as the structural relaxation time increases over several orders of magnitude. These observations provide strong constraints on the eventual establishment of a granular equation of state.

Trajectory entanglement in dense granular materials

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 Sbraid, which has previously been used to quantify mixing efficiency in fluid systems. Here, we investigate the utility of Sbraid in characterizing the dynamics of a dense, driven granular material at packing densities near the static jamming point J. From particle trajectories measured within a two-dimensional granular material, we typically observe that Sbraid is well defined and extensive. However, for systems where , we find that Sbraid (like D) is not well defined, signifying that these systems are not ergodic on the experimental timescale. Both Sbraid 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.

Geometry and design of origami bellows with tunable response

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.

Generating ensembles and measuring mixing in a model granular system

A major open question in the field of granular materials is the identification of relevant state variables which can predict macroscopic behavior. We experimentally investigate the mixing properties of an idealized granular liquid in the vicinity of its jamming transition, through the generation of ensembles of configurations under various boundary conditions. Our apparatus consists of a two‐dimensional aggregate of particles which rearrange under agitation from the outer boundaries. As expected, the system acts like a slow liquid at low pressure or low packing fraction, and jams at higher pressure or high packing fraction. We characterize mixing in the system by computing the topological entropy of the braids formed by the trajectories of the grains. This entropy is shown to be well‐defined and very sensitive to the approach to jamming, reflecting the dynamical arrest of the assembly.

Roughness of oxide glass subcritical fracture surfaces

An original setup combining a very stable loading stage, an atomic force microscope and an environmental chamber, allows to obtain very stable sub-critical fracture propagation in oxide glasses under controlled environment, and subsequently to finely characterize the nanometric roughness properties of the crack surfaces. The analysis of the surface roughness is conducted both in terms of the classical root mean square roughness to compare with the literature, and in terms of more physically adequate indicators related to the self-affine nature of the fracture surfaces. Due to the comparable nanometric scale of the surface roughness, the AFM tip size and the instrumental noise, a special care is devoted to the statistical evaluation of the metrologic properties. The 2 roughness amplitude of several oxide glasses was shown to decrease as a function of the stress intensity factor, to be quite insensitive to the relative humidity and to increase with the degree of heterogeneity of the glass. The results are discussed in terms of several modeling arguments concerning the coupling between crack propagation, materials heterogeneity, crack tip plastic deformation and water diffusion at the crack tip. A synthetic new model is presented combining the predictions of a model by Wiederhorn et al. [1] on the effect of the materials heterogeneity on the crack tip stresses with the self-affine nature of the fracture surfaces.