Pedro Miguel Reis MIT



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Geometrically nonlinear configurations of thin elastic rods
with: Arnaud Lazarus and Jay Miller
Pedro Reis MIT Buckling induced encapsulation of structured elastic shells under pressure
We have developed a novel continuation method to calculate the equilibria of elastic rods under large geometrically nonlinear displacements and rotations. To describe the kinematics we exploit the synthetic power and computational efficiency of quaternions. The energetics of bending, stretching and torsion are all taken into account to derive the equilibrium equations which we solve using an asymptotic numerical continuation method. This provides access to the full set of analytical equilibrium branches (stable and unstable), a.k.a bifurcation diagrams. This is in contrast with the individual solution points attained by classical energy minimization or predictor-corrector techniques.

We challenge our numerics for the specific problem of an extremely twisted naturally curved rod and perform a detailed comparison against a precision desktop-scale experiments. The quantification of the underlying 3D buckling instabilities and the characterization of the resulting complex configurations are in excellent agreement between numerics and experiments.
Pedro Reis Elasticity of rods Writhing
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Mechanics of thin elastic shells: Geometry-Induced Rigidity and Localization
with: Arnaud Lazarus,  Bastiaan Florijn, Amin Ajdari and Ashkan Vaziri
Pedro Reis MIT Geometry-Induced rigidity of thin elastic shells







If one compresses an eggshell along its major axis, the shell is strikingly rigid and it is extremely challenging to break it with our bare hands. Conversely, if the eggshell is compressed along its equator, the resulting deflections are larger and, past a critical load one is typically able to fracture it. We have rationalized this difference in the rigidity of an eggshell depending on the shell-load orientation to be due to the local geometry near the points of indentation.

We have introduced a predictive framework for the rigidity of thin elastic shells which can also account for the situation when the shell is over-pressurized. Our concept of Geometry-Induced Rigidity can be used in reverse, as a precision non-destructive tool, to measure parameters of a shell (e.g. thickness) upon knowing the geometry of the underlying surface and the local mechanical response. The scale-invariance of Geometry-Induced Rigidity suggests that our framework should find uses across length scales: from the mechanical testing of viral capsids through Atomic Force Microscopy, to ocular tonometry procedures or in the design of architectural shells. All this work was inspired by the remarkable physics of an elegant eggshell!
Pedro Reis MIT Localization of deformation in thin shells under indentation Buckling Soft Matter
More recently, we have been studying the emergence and evolution of point and linear-like loci of localization on thin shells indented well into the nonlinear regime.  For large enough indentation, sharp points of localized curvature form, which we refer to as ‘s-cones’ (for shell-cones), in contrast with their developable cousins in plates, ‘d-cones’. Through experiments and FEM, e have found that the shape of the indenter has a significant effect on the mechanical response and that there is a qualitative different between sharp and blunt indenters. Given the importance of geometry and the scale-invariance of this problem, our results should find uses at the microscale, e.g. for AFM, where it is crucial to understand how the curvature of the tip, relative to the object being indented, affects the mechanical response.

Videos of S-cones of a thin shell under indentation: [Experiments, FEM Simulations]

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The Buckliball: buckling-induced encapsulation
with: Jongmin Shim, Elizabeth Chen, Claude Perdigou and Katia Bertoldi
Pedro Reis MIT Buckling induced encapsulation of structured elastic shells under pressure
We introduce a class of continuum shell structures, the Buckliball, which undergoes folding induced by buckling under pressure loading.  The geometry of the Buckliball consists of a spherical shell patterned with a regular array of circular voids. Topological constraints set that the possible number and arrangement of these voids are found to be restricted to five and only five specific configurations. Below a critical internal pressure, the narrow ligaments between the voids buckle, leading to a cooperative buckling cascade of the skeleton of the ball. This leads to closure of the voids and a reduction of the total volume of the shell by up to 54\%, while remaining spherical, thereby opening the possibility of encapsulation. Mechanical instabilities, which are often associated with failure in engineering, are here turned into an asset for functionality.

Video of the Buckliball in action:  [Movie]

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Fracture Toughness through Scratching
with: Ange-Therese Akono  and Franz Ulm
Scratching Butter fracture toughnessPedro Reis MIT
We present results of a hybrid experimental and theoretical investigation of the fracture scaling in scratch tests and show that scratching is a fracture dominated process. Validated for paraffin wax, cement paste, Jurassic limestone and steel, we derive a model that provides a quantitative means to relate quantities measured in scratch tests to fracture properties of materials at multiple scales. The scalability of scratching for different probes and depths opens new venues towards miniaturization of our technique, to extract fracture properties of materials at even smaller length scales.

Video of the scratching experiments on paraffin:  [Movie]

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Wrinklons as Building-blocks in Wrinkling Cascades:
From Curtains to Graphene Sheets
wrinkling curtains graphene wrinklons Pedro Reis MIT
We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons (the  transition zones in the merging of two wrinkles) as building-blocks of the global pattern. Contrary to the case of crumpled paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work by B. Davidovich et al. This formalism is validated  through experiments from hundreds of nm for graphene sheets to meters for ordinary curtains, which shows the universality of our description.  We finally describe the effect of an external tension to the distribution of the wrinkles.

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How Cats Lap: Water uptake by Felis catus
with: Sunny Jung, Jeff Aristoff and Roman Stocker
How Cats Lap Reis Jung Aristoff Stocker
Have you ever wondered how a cat drinks? Various animals have developed a range of drinking strategies depending on physiological and environmental constraints. Vertebrates with incomplete cheeks use their tongue to drink; the most common example is the lapping of cats and dogs. We have shown that the domestic cat (Felis catus) laps by a subtle mechanism based on water adhesion to the dorsal side of the tongue. A combined experimental and theoretical analysis reveals that Felis catus exploits fluid inertia to defeat gravity and pull liquid into the mouth. This competition between inertia and gravity sets the lapping frequency and yields a prediction for the dependence of frequency on animal mass. Measurements of lapping frequency across the family Felidae support this prediction, which suggests that the lapping mechanism is conserved among felines.

How does a cat drink? (slowed down 12x)  [Movie]
And now even slower? (slowed down 67x)? [Movie]
The physical experiments. [Movie]


How Cats Lap Science Cover
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Grabbing Water
with: Jérémy Hure, Sunny Jung, John Bush and Christophe Clanet
Grabbing Water Pedro Reis MIT
We introduce a novel technique for grabbing water with a flexible solid. This new passive pipetting mechanism was inspired by floating flowers and relies purely on the coupling of the elasticity of thin plates and the hydrodynamic forces at the liquid interface. Developing a theoretical model has enabled us to design petal-shaped objects with maximum grabbing capacity.

How to grab a bubble of air?  [Movie]
How to grab a drop of water? [Movie]


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The Clapping Book
with: Peter Buchack, Christophe Eloy
Clapping Book Pedro Reis MIT
We present a hybrid experimental and theoretical study on the oscillatory behavior exhibited by multiple thin sheets under aerodynamic loading. Our clapping book consists of a stack of paper, clamped at the downstream end, placed in a wind tunnel with steady flow. As pages lift off, they accumulate onto a bent stack held up by the wind. The book collapses shut once the elasticity and weight of the pages overcome the aerodynamic force; this process repeats periodically. We develop a theoretical model that predictively describes this periodic clapping process.

A movie of this Clapping process can be found [here].

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Rolling of Flexible Ribbons
with: Pascal Raux, John Bush and Christophe Clanet
Rolling Ribbons Pedro Reis MIT
Galileo’s study of rigid spheres rolling down an inclined ramp is often considered as the starting point of modern physics, since it involves both theory and experiment.  In this study we consider a variant of Galileo’s problem in which the ramp is rigid but the rolling body, an elastic cylindrical shell, is thin, flexible and therefore deformable. Particular attention is given to characterizing the steady shapes that arise in static and dynamic rolling configurations. In both cases, above a critical value of the forcing (either gravitational or centrifugal), the ribbon assumes a two-lobed peanut shape. Our theoretical model allows us to rationalize the observed shapes through consideration of the ribbon’s bending and stretching in response to the applied forcing. This dynamical elastic problem presents some common features with the rolling of a liquid drop on a hydrophobic surface or a lubricated ramp.

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Tearing of Graphene Sheets
with: Dipanjan Sen, Kostya Novoselov and Markus Buehler
Graphene Tears Pedro Reis MIT
Graphene is a truly two-dimensional atomic crystal with exceptional electronic and mechanical properties. Whereas conventional bulk and thin-film materials have been studied extensively, the key mechanical properties of graphene, such as tearing and cracking, remain unknown, partly due to its two-dimensional nature and ultimate single-atom-layer thickness, which result in the breakdown of conventional material models. By combining first-principles ReaxFF molecular dynamics and experimental studies, a bottom-up investigation of the tearing of graphene sheets from adhesive substrates is reported, including the discovery of the formation of tapered graphene nanoribbons. Through a careful analysis of the underlying molecular rupture mechanisms, it is shown that the resulting nanoribbon geometry is controlled by both the graphene-substrate adhesion energy and by the number of torn graphene layers. By considering graphene as a model material for a broader class of two-dimensional atomic crystals, these results provide fundamental insights into the tearing and cracking mechanisms of highly confined nanomaterials.

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 Negative Poisson's ratio materials
with: Katia Berdoldi and Tom Mullin
Negative Poisson Ratio Pedro Reis MIT



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 Pedro Reis MIT

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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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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