Pedro Miguel Reis Physics ParisResearch


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 Negative Poisson's ratio materials
with: Katia Berdoldi and Tom Mullin
Anti Cracks Photo



We have uncovered negative Poisson's ratio (auxetic) behavior in cellular solids that comprise a solid matrix with a square array of circular voids. The simplicity of the fabrication implies robust behavior, which is relevant over a range of scales. The behavior results from an elastic instability, which induces a pattern transformation and excellent quantitative agreement is found between experiment and numerical simulations.





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Anticracks in solid foams
with: Benoit Roman, Francis Corson, Arezki Boudadoud
Anti Cracks Photo

We report a combined experimental and theoretical study of the compression of a solid foam coated
with a thin elastic film. Past a critical compression threshold, a pattern of localized folds emerges with a characteristic size that is imposed by an instability of the thin surface film. We perform optical surface measurements of the statistical properties of these localization zones and find that they are characterized by robust exponential tails in the strain distributions. Following a hybrid continuum and statistical approach, we develop a theory that accurately describes the nucleation and length scale of these structures and predicts the characteristic strains associated with the localized regions.




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Delamination of thin films from an elastic substrate
             with: Dominic Vella, Benoit Roman, José Bico and Arezki Boudaoud

Delamination blistersThe wrinkling and delamination of stiff thin films adhered to a polymer substrate  have important applications in `flexible electronics'. The resulting periodic structures, when used for circuitry, have remarkable mechanical properties since stretching or twisting of the substrate is mostly accommodated through  bending of the film, which minimizes fatigue or fracture. To date,  applications in this
context have used  substrate patterning to create an anisotropic substrate-film adhesion energy, thereby producing a controlled array of delamination `blisters'. However, even in the absence of such patterning, blisters appear spontaneously, with a characteristic size. Here, we perform well-controlled experiments at macroscopic scales to study what sets the dimensions of these blisters in terms of the material properties and explain our results using a combination of scaling and analytical methods. As well as pointing to a novel method for determining the interfacial toughness our analysis suggests a number of  design guidelines for the thin films used in flexible electronic applications. Crucially, we show that to avoid the possibility  that delamination may cause fatigue damage, the thin film thickness must be greater than a critical value, which we determine. [Video here]

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Tearing of thin adhesive sheets
with: Benoit Roman, Enrique Cerda, and Eugenio Hamm
Leaf network
Thin adhesive films have become increasingly important in applications involving packaging, coating or for advertising. Once a film is adhered to a substrate, flaps can be detached by tearing and peeling, but they narrow and collapse in pointy shapes. Similar geometries  are observed when peeling ultrathin films grown or deposited on a solid substrate, or skinning the natural protective cover of a ripe fruit. In this work, we have shown that the detached flaps have perfect triangular shapes with a well-defined vertex angle; this is a signature of the conversion of bending energy into surface energy of fracture and adhesion.In particular, this triangular shape of the tear encodes the mechanical parameters related to these three forms of energy and could form the basis of a quantitative assay for the mechanical  characterization of thin adhesive films, nanofilms deposited on substrates or fruit skin.



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Mechanics of growth in plant tissue
with: Benoit Roman, Mokthar Adda-Bedia, Arezki Boudaoud and Francis Corson
Leaf network
Wether mechanical forces have a role, or not, in the differentiation and growth of plant tissue is still far from established. Two scenarios in which this may be possible in the development of organs at the meristem and of the venation network in leaves. It is, of course, possible that such structures are purely geneticaly driven. However, within a leaf, for example, it is known that differential growth between the various layers of cells induces compressive stresses. Whether these play any role in development is not known. Yves Couder et. al. have recently put forward the idea that the striking similarities between venation networks in leaves and the network of cracks in drying gels suggests that a tensorial quantity, such as a stress, is at play. Within the MechPlant European team, we are currently collaborating with three plant biology groups (Bern, Jerusalem and Oxford) to develop experimental settings in which to test these ideas.



Oscillatory Fracture in Thin Sheets
with: Benoit Roman, Basile Audoly, Anil Kumar, Mark Shattuck and Simon de Villiers
Oscillatory cracks photo
Opening the plastic packaging film of biscuit packs or CD cases has never been easy, specially if one lacks a pen-knife in our pocket. One way out is to use a key or a pen. If we use such a blunter object to tear open the plastic, rather than observing a straight cut, the crack follows a well defined and highly reproducible oscillatory path. We have developed a well controlled experiment in which to study this phenomena. Moreover, we have developed a geometrical 2D model that takes into account bending and stretching of the thing plastic film. This simplemodel yields results in excellent agreement with the experiments.


For more info and videos of the experiment please visit the following webpage.



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Uniformly Heated Granular Fluids: How far from equilibrium?
with: Mark Shattuck and Rohit Ingale
hori2Dgran
We have developed an experimental system to study Non-equilibrium steady states in a quasi-2D granular fluid in which energy is injected uniformly across the cell. Using a number of classic measures commonly used in statistical mechanics (Lindemann criterion, radial distribution function, bond-order orientation parameter, shape factor, intermediate scattering function, etc) we have shown that our system assumes equilibrium-like structural configurations. Moreover, we observe a fluid-to-crystal transition, as the filling fraction of the granular layer is increased, exactly at the point at which it occurs for equilibrium hard disks. Prior to crystallization, there is an intermediate region in which caging of particles is dominant with a relaxation timescale that follows a Vogel-Fulcher law, typical of many glassy systems. Despite this strong equilibrium-like behaviour, non-equilibrium features are observed, as expected, in the dynamics of the system as measured by deviations from Maxwellians of the probability distribution functions of velocities.


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Segregation in granular binary mixtures
with: Tom  Mullin, George Ehrhardt and Andrew Stephenson
Segregation pic
An interesting and counter-intuitive issue in the collective behavior granular materials is the segregation of binary assemblies, where an initially uniform mixture of particles can spontaneously de-mix under flow. During my Ph.D. I developed an experimental physical model system in which to study segregation of binary mixtures of particles. I constructed an approximately two-dimensional precision apparatus consisting of a monolayer driven by the frictional forces with the surface of an oscillatory tray. Systematically starting from homogeneously mixed initial conditions, I uncovered the existence and self-organisation of three phases of segregation, as a function of the total filling fraction of the layer. The foremost result was the discovery a critical phenomena in granular segregation. This implies the existence of a transition point in below which the layer remains mixed and above which segregation occurs. This behaviour had characteristics of continuous phase transitions, usually observed in well understood equilibrium statistical mechanical systems.

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