Pedro Miguel Reis MIT


Home Research Publications People Teaching News Archive Visit us

The wonders of thin structures Pedro Reis MIT
For an overview of our research interests, please watch the video [here].

Reversible patterning of spherical shells through constrained buckling
with: Joel Marthelot, Pierre-Thomas Brun, and Francisco López Jiménez,
Constrained buckling patterns Physical Review Materials Joel Marthelot Pierre-Thomas Brun Francisco López Jiménez, Pedro Reis MIT
Recent advances in active soft structures envision the large deformations resulting from mechanical instabilities as routes for functional shape-morphing. Numerous such examples exist for filamentary and plate systems. However, examples with double-curved shells are rarer, with progress hampered by challenges in fabrication and the complexities involved in analyzing their underlying geometrical nonlinearities. We show that on-demand patterning of hemispherical shells can be achieved through constrained buckling. Their post-buckling response is stabilized by an inner rigid mandrel. Through a combination of experiments, simulations and scaling analyses, our investigation focuses on the nucleation and evolution of the buckling patterns into a reticulated network of sharp ridges. The geometry of the system, namely the shell radius and the gap between the shell and the mandrel, is found to be the primary ingredient to set the surface morphology. This prominence of geometry suggests a robust, scalable, and tunable mechanism for reversible shape-morphing of elastic shells.

A video that summarizes this project can be found in the following links [Video1] [Video2].


Now I see you, now I don't: a tuneable optical switch
with: Francisco López Jiménez and Shanmugam Kumar 
Optical switch soft color composites Pedro Reis MIT EGS.Lab
We introduce a soft composite that is actuated mechanically to achieve switchable and tunable optical transmittance. Our design comprises a series of parallel opaque platelets embedded into an optically clear solicone-based elastomer matrix. Under an applied shear loading, the platelets rotate, thereby gradually increasing the transmittance of light through the device, in a controllable and reversible manner. Experiments on a prototype device are used to support finite element simulations that explore the parameter space of the system towards providing a set of design guidelines. Specifically, we study how the optical transmittance depends on the stiffness mismatch between the matrix and the platelets, as well as their initial orientation and aspect ratio. We also focus on the maximum attainable value of transmittance and the energetic requirements to achieve it.


Imperfection Sensitivity: Critical buckling pressure of precisely imperfect shells
with: Anna Lee, Francisco López Jiménez, Joel Marthelot, and John W. Hutchinson
knockdown factor critical buckling thin shells Pedro Reis MIT EGS.Lab
We study the effect of a dimplelike geometric imperfection on the critical buckling load of spherical elastic shells under pressure loading. This is a canonical problem in Structural Mechanics that has been longstanding for more than 50 years. Our investigation combines precision experiments, finite element modeling, and numerical solutions of a reduced shell theory, all of which are found to be in excellent quantitative agreement. In the experiments, the geometry and magnitude of the defect can be designed and precisely fabricated through a customizable rapid prototyping technique. Our primary focus is on predictively describing the imperfection sensitivity of the shell to provide a quantitative relation between its knockdown factor and the amplitude of the defect. In addition, we find that the buckling pressure becomes independent of the amplitude of the defect beyond a critical value. The level and onset of this plateau are quantified systematically and found to be affected by a single geometric parameter that depends on both the radius-to-thickness ratio of the shell and the angular width of the defect.

To the best of our knowledge, this is the first time that experimental results on the knockdown factors of imperfect spherical shells have been accurately predicted, through both finite element modeling and shell theory solutions.

A video that summarizes this project can be found in the following link [Video].

This project was done in collaboration with John Hutchinson (Harvard University).


Rapid fabrication of slender elastic shells
with: Anna Lee, Pierre-Thomas Brun, Joel Marthelot, Gioele Balestra and François Gallaire
Curved coating shells chocolate Pedro Reis MIT EGS.Lab
Various manufacturing techniques exist to produce double-curvature shells, including injection, rotational and blow molding, as well as dip coating. However, these industrial processes are typically geared for mass production and are not directly applicable to laboratory research settings, where adaptable, inexpensive and predictable prototyping tools are desirable.

In this project we have studied the rapid fabrication of hemispherical elastic shells by coating a curved surface with a polymer solution that yields a nearly uniform shell, upon polymerization of the resulting thin film. We experimentally characterize how the curing of the polymer affects its drainage dynamics and eventually selects the shell thickness. The coating process is then rationalized through a theoretical analysis that predicts the final thickness, in quantitative agreement with experiments and numerical simulations of the lubrication flow field. This robust fabrication framework should be invaluable for future studies on the mechanics of thin elastic shells and their intrinsic geometric nonlinearities.

A video that summarizes this project can be found in the following link [Video].

This project was done in collaboration with the group of François Gallaire at EPFL (Switerzland).


Press Coverage:

Curvature-Controlled Defect Localization in Elastic Surface Crystals
with: Francisco López Jiménez, Norbert Stoop, Denis Terwagne, Miha Brojan, Romain Lagrance and Jörn Dunkel
surface elastic crystals curved crystallography wrinkling Pedro Reis MIT EGS.Lab
Curved crystals cannot comprise hexagons alone; additional defects are required by both topology and energetics that depend on the system size. These constraints are present in systems as diverse as virus capsules, soccer balls, and geodesic domes. We have study the structure of defects of the crystalline dimpled patterns that self-organize through curved wrinkling on a thin elastic shell bound to a compliant substrate. The dimples are treated as point-like packing units, even if the shell is a continuum. Our results provide quantitative evidence that our macroscopic wrinkling system can be mapped into and described within the framework of curved crystallography, albeit with some important differences attributed to the far- from-equilibrium nature of our patterns.

Moreover, we have investigated the influence of curvature and topology on crystalline dimpled patterns on the surface of generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal, and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elastic materials, thus promising improved control over hierarchical bending, buckling, or folding processes.

Generally, our work suggests that bilayer systems provide an inexpensive yet valuable experimental test bed for exploring the effects of geometrically induced forces on assemblies of topological charges.

This project was done in collaboration with the group of Jörn Dunkel (MIT Math).


Soft color composites with tunable optical transmittance
with: Francisco López Jiménez and Shanmugam Kumar
Soft Color composites tunable optical transmittance Pedro Reis MIT EGS.Lab
A class of soft color composites whose light transmittance can be actively tuned and controlled through mechanical actuation is studied. The design comprises thin sheets of polydimethylsiloxane, an optically clear silicone- based rubber, that is mixed with a colloidal suspension of black micrometer- sized dye particles to provide tunable opacity to the specimens. The thickness of the samples can be reduced by mechanical loading (e.g., pneumatically), which modulates the thickness and, in turn, the transmittance by as much as 40%. The mechanism is independent of the specific method of actuation chosen for loading. Scaling analysis and finite element modeling are combined to predictively describe and rationalize the evolution of the transmittance of our samples as a function of the applied mechanical loading and validate the predictions against biaxial tensile experiments. Compared to existing solutions, the main advantages of this mechanism are that it is remarkably simple and robust, as well as fast and fully reversible. Making use of this framework, pneumatic bulging is then chosen as a representative loading strategy, for which a series of design guidelines is presented, which may be implemented in practical applications, such as smart windows and other visually active materials.


Press Coverage:

Instabilities of a flexible helical rod rotating in a viscous fluid
with: Khalid Jawed
Flagella Buckling Bacteria Locomotion Pedro Reis MIT EGS.Lab
We combine experiments with simulations to investigate the fluid-structure interaction of a flexible helical rod rotating in a viscous fluid, under low Reynolds number conditions. Our analysis takes into account the coupling between the geometrically nonlinear behavior of the elastic rod with a nonlocal hydrodynamic model for the fluid loading. We quantify the resulting propulsive force, as well as the buckling instability of the originally helical filament that occurs above a critical rotation velocity. A scaling analysis is performed to rationalize the onset of this instability. A universal phase diagram is constructed to map out the region of successful propulsion and the corresponding boundary of stability is established. Comparing our results with data for flagellated bacteria suggests that this instability may be exploited in nature for physiological purposes.

We also consider the case when the helical filament is simultaneously subjected to an axial flow. Under axial flow, and in the absence of rotation, the initially helical rod is extended. Above a critical flow speed its configuration comprises a straight portion connected to a localized helix near the free end. When the rod is also rotated about its helical axis, propulsion is only possible in a finite range of angular velocity, with an upper bound that is limited by buckling of the soft helix arising due to viscous stresses. A systematic exploration of the parameter space allows us to quantify regimes for successful propulsion for a number of specific bacteria.


The interplay between the mechanics and topology of elastic knots
with: Khalid Jawed, Peter Dieleman and Basile Audoly
Mechanics Topology of Knots Pedro Reis MIT EGS.Lab

We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to quantify the dependence of the mechanical response of the knot as a function of the geometry of the self-contacting region, and for different topologies as measured by their crossing number. An analytical model based on the nonlinear theory of thin elastic rods is then developed to describe how the physical and topological parameters of the knot set the tensile force required for equilibrium. Excellent agreement is found between theory and experiments for overhand knots over a wide range of crossing numbers.


Press Coverage:

Buckling of a rod inside a cylindrical constraint: Applications to coiled tubing operations
with: Jay Miller, Jahir Prabon and Nathan Wicks
Coiled Tubing Pedro Reis MIT EGS.Lab
We present results of an experimental investigation of a new mechanism for extending the reach of an elastic rod injected into a horizontal cylindrical constraint, prior to the onset of helical buckling. This is accomplished through distributed, vertical vibration of the constraint during injection. A model system is developed that allows us to quantify the critical loads and resulting length scales of the buckling configurations, while providing direct access to the buckling process through digital imaging. In the static case (no vibration), we vary the radial size of the cylindrical constraint and find that our experimental results are in good agreement with existing predictions on the critical injection force and length of injected rod for helical buckling. When vertical vibration is introduced, reach can be extended by up to a factor of four, when compared to the static case. The injection speed (below a critical value that we uncover), as well as the amplitude and frequency of vibration, are studied systematically and found to have an effect on the extent of improvement attained.

Image courtesy of Schlumberger-Doll Research.


Press Coverage:

Coiling 'spaghetti' onto rigid substrates
with: Eitan Grinspun
Coiling of thin elastic rods Pedro Reis MIT EGS.Lab
The deployment of a rodlike structure onto a moving substrate is commonly found in a variety engineering applications, from the fabrication of nanotube serpentines to the laying of submarine cables and pipelines. Predictively understanding the resulting coiling patterns is challenging given the nonlinear geometry of deposition.

In this study, we combine precision model experiments with computer simulations tools and explore the mechanics of coiling. In particular, the natural curvature of the rod is found to dramatically affect the coiling process. We have introduced a computational framework that is widely used in computer animation into engineering, as a predictive tool for the mechanics of filamentary structures.

This work was done in close collaboration with Eitan Grinspun's Computer Graphics Group (Columbia University).

We have also performed a systematic numerical study of the various coiling patterns obtained in the above system. The Discrete Elastic Rods (DER) method is employed to explore the parameter space, construct phase diagrams, identify their phase boundaries and characterize the pattern morphology. The curvature near the contact point, together with the dimensionless speed mismatch between deployment and the belt, dictate the characteristics of the patterns. The phase boundaries are found to be independent of both the gravito-bending length and the deployment height, as long as the latter is above a threshold value. We  evaluate the relative importance of twist and curvature strains, which confirms that bending has a dominant role.

[Introductory video about this study]
[Video showing a detailed comparison between Experiments and Simulations]

An historical example of this deployment process is the then highly classified Operation PLUTO (Pipe-Lines Under the Ocean), which provided fuel supplies across the English Channel at the end of World War II. [See video here]

Press Coverage:

Wrinkling on curved surfaces &
: Smart Morphable Surface for Aerodynamic Drag Reduction

with: Denis Terwagne, Miha Brojan, Romain Lagrange, Norbert Stoop, Jorn Dunkel

Smorphs Smart Morphable Surfaces Drag reduction aerodynamics Pedro Reis MIT EGS.LabShell theory wrinkling pedro reis egs.lab mitShell theory wrinkling pedro reis egs.lab mit
We have devised a new class of Smart Morphable Surfaces, which we refer to as Smorphs, that make use of a wrinkling instability on curved surfaces to generate custom, switchable and tunable topography. Our experiments show that surface curvature qualitatively affects the wrinkled pattern, when compared to flat film-substrate systems. Inspired by the resemblance of our dimpled patterns and those of golf balls, we have characterized their aerodynamic performance and found that the drag coefficient can be reduced, on demand, by up to a factor of two. 

A particularly novel aspect of our Smorphs is that complex topography can be rapidly activated with a single pressure signal and their actuation speed is only limited by how fast the depressurization can be set. The fast elastic response of our mechanism opens the possibility of on demand and dynamic drag control. We envision that our Smorphs could find applications in a variety of aerodynamic structures. Strategically reducing the overall drag on the outer-body shell of automobiles or aircraft could potentially lead to enhanced fuel efficiency; a timely priority for these industries.

A video of one of our Smorphs in action can be found here:  [Movie]

Press Coverage:

The Mechanics of Curly Hair
with: Jay Miller, Arnaud Lazarus and Basile Audoly

We tackle the deceivingly simple problem of a suspended naturally curved rod, which we consider as an analogue for curly hair, to predict its resulting shapes. The role of natural curvature in the mechanics of rods, as a control parameter, has been largely overlooked in the literature.
Mechanics of Curly Hair Physical Review Letters Wigs Pedro Reis EGS.Lab MIT
Mechanics of Curly Hair Pedro Reis EGS.Lab MITIn this study we seek to understand how natural curvature affects the configuration of a thin elastic rod suspended under its own weight. We combine precision desktop experiments, numerics, and theoretical analysis to explore the equilibrium shapes set by the coupled effects of elasticity, natural curvature, nonlinear geometry, and gravity. A phase diagram is constructed in terms of the control parameters of the system, namely the dimensionless curvature and weight, where we identify three distinct regions: planar curls, localized helices, and global helices. We analyze the stability of planar configurations, and describe the localization of helical patterns for long rods, near their free end. The observed shapes and their associated phase boundaries are then rationalized based on the underlying physical ingredients. Our framework is applicable to a variety of natural and engineered rodlike structures, over many length scales.

Press Coverage:

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

Fiber Matrix EGS.Lab Pedro Reis MIT
We have also studied the buckling of a slender rod embedded in a soft elastomeric matrix. In our experiments, depending on the control parameters, both planar wavy (2D) or non-planar coiled (3D) configurations are observed in the post-buckling regime. Our analytical and numerical results indicate that the rod buckles into 2D configurations when the compression forces associated to the two lowest critical modes are well separated. In contrast, 3D coiled configurations occur when the two buckling modes are triggered at onset, nearly simultaneously. We show that the separation between these two lowest critical forces can be controlled by tuning the ratio between the stiffness of the matrix and the bending stiffness of the rod, thereby allowing for specific buckling configurations to be target by design.


Mechanics of thin elastic shells: Geometry-Induced Rigidity and Localization
with: Arnaud Lazarus,  Bastiaan Florijn, Amin Ajdari and Ashkan Vaziri

Geometry Induced Rigidity  Eggshell egg Pedro Reis MIT
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]

Publications: Press Coverage:

The Buckliball and Buckligami: buckling-induced encapsulation and soft Actuation
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]

Soft Actuation of Structured Cylinders through Auxetic Behavior Pedro Reis MIT
In a separate study, we have introduced a new class of soft actuators based on the auxetic behavior of patterned cylindrical shells containing a layout of voids that can be designed to reversibly achieve flexural or twisting motion. Depressurizing our samples allows for tunable and controllable motion. Given that the deformation is primarily governed by the geometry of the design, coupled to the buckling of the thin ligaments of the pattern, the resulting modes of actuation should be readily scalable. 

Press Coverage:

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]

Publications: Press Coverage:
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.

Publications: Press Coverage:
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
Publications: Press Coverage:
Cats Boston Globe ARLO & JANIS Jimmy Johnson
ARLO & JANIS, by Jimmy Johnson, Boston Globe (27 May 2014)

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]

Publications: Press Coverage:
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].


Press Coverage:

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.

Publications: Press Coverage:

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.

Press Coverage:

 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.

Press Coverage:

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.


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]

Press Coverage:
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.

Press Coverage:
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.

Press Coverage:

Uniformly Heated Granular Fluids: How far from equilibrium?
with: Mark Shattuck and Rohit Ingale
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.

Press Coverage:

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.

Press Coverage: