Wrinkling of pressurized elastic shells

Host Material Viscoelasticity Determines Wrinkling of Fungal Films

Microbial organisms react to their environment and are able to change it through biological and physical processes. For example, fungi exhibit various growth morphologies depending on their host material. Here, we show how the rheological properties of the host material influence the fungal wrinkling morphology. Rheological data of the host material was set in relation to the growth morphology. On host material with high storage modulus, the fungal film was flat, whereas on host material with low storage modulus, the fungus showed a morphology made of folds and wrinkles. We combined our findings with mechanical instability theories and found that the formation of wrinkles and folds is dependent on the storage modulus of the host material. The connection between the wrinkling morphology and the storage modulus of the host material is shown with simple scaling theories. The amplitude, number of wrinkles, and wrinkle length follow geometrical laws, and the mechanical properties of the fungal film are expected to increase with increasing host material elasticity. The obtained results show the connection between living biological films, how they react to their surroundings, and the underlying physical mechanisms. They can provide a framework to further design fungal materials with specific surface morphologies.

Impact of a pressurized membrane: Coefficient of restitution

Pressurized membranes are usually used for low cost structures (e.g., inflatable beds), impact protections (e.g., airbags), or sport balls. The last two examples deal with impacts on the human body. Underinflated protective membranes are not effective whereas overinflated objects can cause injury at impact. The coefficient of restitution represents the ability of a membrane to dissipate energy during an impact. Its dependence on membrane properties and inflation pressure is investigated on a model experiment using a spherical membrane. The coefficient of restitution increases with inflation pressure but decreases with impact speed. For a spherical membrane, it is shown that kinetic energy is lost by transfer to vibration modes. A physical modeling of a spherical membrane impact is built considering a quasistatic impact with small indentation. Finally, the dependency of the coefficient of restitution with mechanical parameters, pressurization, and impact characteristics is given.

Axisymmetric ridges and circumferential buckling of indented shells of revolution

When poking a thin shell-like structure, like a plastic water bottle, experience shows that an initial axisymmetric dimple forms around the indentation point. The ridge of this dimple, with increasing indentation, eventually buckles into a polygonal shape. The polygon order generally continues to increase with further indentation. In the case of spherical shells, both the underlying axisymmetric deformation and the buckling evolution have been studied in detail. However, little is known about the behavior of general geometries. In this work we describe the geometrical and mechanical features of the axisymmetric ridge that forms in indented general shells of revolution with non-negative Gaussian curvature and the conditions for circumferential buckling of this ridge. We show that under the assumption of "mirror buckling," a single unified description of this ridge can be written if the problem is nondimensionalized using the local slope of the undeformed shell midprofile at the ridge radial location. However, in dimensional form the ridge properties evolve in quite different ways for different midprofiles. Focusing on the indentation of shallow shells of revolution with constant Gaussian curvature, we use our theoretical framework to study the properties of the ridge at the circumferential buckling threshold and evaluate the validity of the mirror buckling assumption against a linear stability analysis on the shallow shell equations, showing very good agreement. Our results highlight that circumferential buckling in indented thin shells is controlled by a complex interplay between the geometry and the stress state in the ridge. The results of our study will provide greater insight into the mechanics of thin shells. This could enable indentation to be used as a means to measure the mechanical properties of a wide range of shell geometries or used to design shells with specific mechanical behaviors.

Shape instabilities of islands in smectic films under lateral compression

Smectic liquid crystals are fluids, and in most rheological situations they behave as such. Nevertheless, when thin freely floating films of smectic A or smectic C materials are compressed quickly in-plane, they resist such stress by buckling similar to solid membranes under lateral stress. We report experimental observations of wrinkling and bulging of finite domains within the films, so-called islands, and give a qualitative explanation of different observed patterns. Depending on the external stress and their dimensions, the islands can expel a specifically shaped bulge in their center, form radial wrinkles or develop target-like wrinkle structures. When the external stress is relaxed, these patterns disappear reversibly.

Lateral indentation of a thin elastic film

Indentation is a standard, widely used technique in mechanical assays and theoretical analysis. It unveils the fundamental modes of deformation and predicts the response of the material under more complex loads. Here we present an experimental setup for testing thin-film materials by studying the lateral indentation of a narrow opening cut into a film, triggering a cascade of buckling events. The force response F is dominated by bending and stretching effects for small displacements and slowly varies with indenter displacement F ∼ d^2/5, to finally reach a wrinkled state that results in a robust nonlinear asymptotic relation, F ∼ d⁴. Experiments with films of various thicknesses and material properties, and numerical simulations confirm our analysis and help to define an order parameter that accounts for the different response regimes observed in experiments and simulations.

Motion of Particles in a Monolayer Induced by Coalescing of a Bubble with a Planar Air-Water Interface

The motion of particles in a monolayer induced by the coalescing of a bare bubble with a planar air-water interface was investigated in a modified Langmuir trough. Experiments were performed to understand the effect of particle hydrophobicity, subphase pH, packing density, the presence of a weak surfactant, and particle size distribution on the behavior of particle movement in the monolayer during the coalescence process. Video tracking software was used to track the particles and extract data based on the video footage. Visual inspection indicated that the coalescence of the bubble with the monolayer was a chaotic process which led the interface to oscillate to an extent that the particles underwent complete rearrangement. A simple analysis was carried out on the main forces involved in particle motion and rearrangement at the oscillating air-water interface. The motion characteristic of particles was evaluated by speed and mean-square displacement (MSD). The results showed that the butanol-treated particles had higher speed and MSD than the particles with a stronger affinity to the air-water interface. Similar results were also found at high subphase pH and low packing factor.

A new wrinkle on liquid sheets: Turning the mechanism of viscous bubble collapse upside down

Viscous bubbles are prevalent in both natural and industrial settings. Their rupture and collapse may be accompanied by features typically associated with elastic sheets, including the development of radial wrinkles. Previous investigators concluded that the film weight is responsible for both the film collapse and wrinkling instability. Conversely, we show here experimentally that gravity plays a negligible role: The same collapse and wrinkling arise independently of the bubble's orientation. We found that surface tension drives the collapse and initiates a dynamic buckling instability. Because the film weight is irrelevant, our results suggest that wrinkling may likewise accompany the breakup of relatively small-scale, curved viscous and viscoelastic films, including those in the respiratory tract responsible for aerosol production from exhalation events.

Bioinspired Multiscale Wrinkling Patterns on Curved Substrates: An Overview

The surface wrinkling of biological tissues is ubiquitous in nature. Accumulating evidence suggests that the mechanical force plays a significant role in shaping the biological morphologies. Controlled wrinkling has been demonstrated to be able to spontaneously form rich multiscale patterns, on either planar or curved surfaces. The surface wrinkling on planar substrates has been investigated thoroughly during the past decades. However, most wrinkling morphologies in nature are based on the curved biological surfaces and the research of controllable patterning on curved substrates still remains weak. The study of wrinkling on curved substrates is critical for understanding the biological growth, developing three-dimensional (3D) or four-dimensional (4D) fabrication techniques, and creating novel topographic patterns. In this review, fundamental wrinkling mechanics and recent advances in both fabrications and applications of the wrinkling patterns on curved substrates are summarized. The mechanics behind the wrinkles is compared between the planar and the curved cases. Beyond the film thickness, modulus ratio, and mismatch strain, the substrate curvature is one more significant parameter controlling the surface wrinkling. Curved substrates can be both solid and hollow with various 3D geometries across multiple length scales. Up to date, the wrinkling morphologies on solid/hollow core-shell spheres and cylinders have been simulated and selectively produced. Emerging applications of the curved topographic patterns have been found in smart wetting surfaces, cell culture interfaces, healthcare materials, and actuators, which may accelerate the development of artificial organs, stimuli-responsive devices, and micro/nano fabrications with higher dimensions.

Visualizing Morphogenesis through Instability Formation in 4-D Printing

Heterogeneous growth in a myriad of biological systems can lead to the formation of distinct morphologies during the maturation processes of different species. We demonstrate that the distinct circumferential buckling observed in pumpkins can be reproduced by a core-shell barrel structure using four-dimensional (4D) printing, taking advantage of digital light processing (DLP)-based three-dimensional (3D) printing and stimulus-responsive hydrogels. The mechanical mismatch between the stiff core and compliant shell results in buckling instability on the surface. The initiation and development of the buckling are governed by the ratio of core/shell radius, the ratio of core/shell swelling ratios, and the mismatch between the core and shell in stiffness. Furthermore, the rigid core not only acts as a source of circumferential confinement but also sets a boundary at the poles of the entire structure. The heterogeneous structures with controllable buckling geometrically and structurally behave much like plants' fruits. This replicates the biological morphologic change and elucidates the general mechanism and dynamics of the complex instability formation of heterogeneous 3D objects.

Curvature Regularization near Contacts with Stretched Elastic Tubes

Inserting a rigid object into a soft elastic tube produces conformal contact between the two, resulting in contact lines. The curvature of the tube walls near these contact lines is often large and is typically regularized by the finite bending rigidity of the tube. Here, it is demonstrated using experiments and a Föppl-von Kármán-like theory that a second, independent, mechanism of curvature regularization occurs when the tube is axially stretched. In contrast with the effects of finite bending rigidity, the radius of curvature obtained increases with the applied stretching force and decreases with sheet thickness. The dependence of the curvature on a suitably rescaled stretching force is found to be universal, independent of the shape of the intruder, and results from an interplay between the longitudinal stresses due to the applied stretch and hoop stresses characteristic of curved geometry. These results suggest that curvature measurements can be used to infer the mechanical properties of stretched tubular structures.

Tunable wrinkling of thin nematic liquid crystal elastomer sheets

Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rodlike molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to compression of a thin sheet of nematic liquid crystal elastomer atop an elastic or fluid substrate. We find the scaling of the wrinkle wavelength in terms of material parameters and the applied compression. The wavelength of the wrinkles is found to be nonmonotonic in the compressive strain due to the presence of the nematic. Finally, due to soft modes, the critical stress for the appearance of wrinkles can be much higher than in an isotropic elastomer and depends nontrivially on the manner in which the elastomer was prepared.

Let's deflate that beach ball

We investigate the relationship between pre-buckling and post-buckling states as a function of shell properties, within the deflation process of shells of an isotropic material. With an original and low-cost set-up that allows to measure simultaneously volume and pressure, elastic shells whose relative thicknesses span on a broad range are deflated until they buckle. We characterize the post-buckling state in the pressure-volume diagram, but also the relaxation toward this state. The main result is that before as well as after the buckling, the shells behave in a way compatible with predictions generated through thin shell assumption, and that this consistency persists for shells where the thickness reaches up to 0.3 the shell's midsurface radius.

Controlled reversible buckling of polydopamine spherical microcapsules: revealing the hidden rich phenomena of post-buckling of spherical polymeric shells

Under external pressure compression, various kinds of artificial microcapsules can undergo buckling induced deformation and catastrophic rupturing failure, which needs to be understood for their diverse practical applications. For this, many theories and numerical simulations have recently emerged, leading to some intriguing but often debatable predictions and scaling laws. However, experimental testing of these predictions is very limited, due to challenges in realizing prescribed buckling pathways and in situ monitoring of the buckling procedure. Herein, we report the buckling behaviors of well-defined spherical polydopamine (PDA) capsules with tunable sizes and homogeneous nanoscale shells. Simple but controlled solvent evaporation was implemented inside a home-made optical chamber to induce buckling of PDA capsules by following a prescribed pathway toward targeted shapes that are only dictated by the inherent material properties of the capsules. In addition, the buckling speed was slowed down to the timescale of minutes, which can prevent buckling from being trapped at some metastable intermediate states as well as facilitating in situ optical monitoring of the whole buckling procedure in slow motion. In this way, several classic buckling behaviors were clearly observed, including the sudden appearance of spinodal-like dimples above critical pressures, transition of the indentation rim from the axisymmetric to polygonal shape, and evolution of multi-indented buckling into single indented buckling following Ostwald ripening. These observations are qualitatively comparable with recent predictions from numerical results. Furthermore, some novel buckling phenomena have been reported for the first time, which might stimulate further theories and numerical simulations.

Mechanical Properties of Particle Films on Curved Interfaces Probed through Electric Field-Induced Wrinkling of Particle Shells

Similar to the human skin, a monolayer of packed particles capillary bound to a liquid interface wrinkles when subjected to compressive stress. The induced wrinkles absorb the applied stress and do not disappear unless the stress is removed. Experimental and theoretical investigations of wrinkle formation typically concern flat particle monolayers subjected to uniaxial stress. In this work, we extend the results on wrinkling of particle-covered interfaces to the investigation of mechanical properties of particle films on a curved interface, that is, we study particle shells formed on droplets and subjected to hoop stress. Opposed to flat particle layers where liquid buoyancy alone acts as the effective stiffness, the mechanical properties of particle layers on small droplets are also affected by the surface curvature. We show here that this leads to formation of wrinkles with different characteristic wavelengths compared to those found at flat interfaces. Our experimental results also reveal that the wrinkle wavelength of particle shells is proportional to the square root of particle size and the size of the droplets on which the shells are formed. Wrinkling of particle layers composed of microparticles with diameters ranging from around 1-100 μm was induced using a novel approach combining electrodeformation and electrohydrodynamic flows. We demonstrate that our contactless approach for studying the mechanical properties of particle shells enables estimation of elasticity, particle film thickness, and bending stiffness of particle shells. The proposed approach is insensitive to both particle coverage and electric field strength. In addition, it enables manipulation of particle packing that is intimately linked with formation of wrinkling patterns. With a wide range of applications depending on accurate mechanical properties (e.g., drug-delivery capsules to self-healing materials), this work provides a valuable method to characterize the mechanical properties of shells and tailor their surface properties (i.e., permeability and roughness).

Arcuate wrinkling on stiff film/compliant substrate induced by thrust force with a controllable micro-probe

Wrinkling patterns are widely observed in nature and can be used in many high-tech applications such as microfluidic channel, self-assembly ordered microstructures and improved adhesives. In order to use the wrinkling patterns for these applications, it is necessary to precisely control the formation and geometry of the wrinkles. In this paper, we investigate the localized wrinkling of a stiff film/compliant substrate system subjected to a thrust force with a controllable micro-probe. A thin Au film is deposited onto a thick PDMS substrate attached to a glass to form the stiff film/compliant substrate system. And a micro-probe is controlled by a piezoelectric microrobotic system to exert a point force onto the stiff film/compliant substrate to demonstrate the evolution of the localized wrinkles. The experiments show that the film will wrinkle into orthoradial morphology spontaneously when it is deformed in the vertical direction, and then it will wrinkle into arcuate morphology with deformation in the horizontal direction. Since the compressive stress and tensile stress of the film are generated simultaneously, the evolution of the arcuate wrinkles is always accompanied by some radial cracks. The morphological characteristic, formation mechanism and dynamic evolution of the arcuate wrinkles are demonstrated and discussed in detail.

Shell buckling: from morphogenesis of soft matter to prospective applications

Being one of the commonest deformation modes for soft matter, shell buckling is the primary reason for the growth and nastic movement of many plants, as well as the formation of complex natural morphology. On-demand regulation of buckling-induced deformation associated with wrinkling, ruffling, folding, creasing and delaminating has profound implications for diverse scopes, which can be seen in its broad applications in microfabrication, 4D printing, actuator and drug delivery. This paper reviews the recent remarkable developments in the shell buckling of soft matter to explain the most representative natural morphogenesis from the perspectives of theoretical analysis in continuum mechanics, finite element analysis, and experimental validations. Imitation of buckling-induced shape transformation and its applications are also discussed for the innovations of sophisticated materials and devices in future.

Regimes of wrinkling in an indented floating elastic sheet

A thin, elastic sheet floating on the surface of a liquid bath wrinkles when poked at its center. We study the onset of wrinkling as well as the evolution of the pattern as indentation progresses far beyond the wrinkling threshold. We use tension field theory to describe the macroscopic properties of the deformed film and show that the system passes through a host of different regimes, even while the deflections and strains remain small. We show that the effect of the finite size of the sheet ultimately plays a key role in determining the location of the wrinkle pattern, and obtain scaling relations that characterize the number of wrinkles at threshold and its variation as the indentation progresses.

Static bistability of spherical caps

Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two 'self-equilibrated' states, one natural and the other inside out (or 'everted'). Though this is familiar from everyday life-an umbrella is remarkably stable, yet a contact lens can be easily turned inside out-the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite-element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more 'robust' to snap-through. Our work sheds new light on the robustness of the 'mirror buckling' symmetry of spherical shell caps.

Evolution of local wrinkles near defects on stiff film/compliant substrate

Disordered wrinkles are widely observed in stiff film deposited onto a thermally expanded polymer when compressive stress exceeds the critical wrinkling stress of the film. Highly ordered wrinkles can be fabricated by introducing regularly arranged patterns on the polymer before deposition. However, the study on the morphological evolution of localized wrinkling patterns near defects on the stiff film/compliant substrate is neglected. In this paper, we show two morphological transitions of the local wrinkles induced by defects on an Au film/PDMS substrate. The observation shows that the straight wrinkles form perpendicularly to the line defects and the radial wrinkles form near spot-like defects. We observe that the extended radial wrinkles tend to split and evolve into branching patterns, this limits the deviation of the local wrinkle wavelength from the equilibrium wrinkle wavelength and causes the wrinkle wavelength to be always maintained in a narrow interval. Because the herringbone patterns have the minimum energy state, the straight and radial wrinkles evolve into herringbone wrinkles spontaneously. The morphological characteristic and evolution mechanism of the local wrinkles are described in detail. The observation may provide some clues to the formation and evolution of some localized wrinkling patterns in nature and multilayer materials.

Wrinkling patterns in soft shells

Curvature plays an important role in the morphological evolution of soft shells under stretch. Here, through a combination of experiment, theory and simulation, we investigate the behavior of a hemispherical soft shell subject to an increasing outward point force at its pole. In contrast to an inward point force inducing a polygonal pattern of buckling in the shell, we observe a four-stage morphological transition and symmetry breaking under an increasing outward point force. The shell undergoes axisymmetric deformation around its pole and then buckles into a non-axisymmetric shape with a number of shallow wrinkles emanating from the pole, followed by the emergence of crater-like deep crumples and ultimately a transformation into a wrinkled pseudocone. Our theoretical analysis and numerical simulations yield the critical conditions for the morphological transitions at each stage of deformation and reveal the underlying interplays between elastic bending and stretching energies and the curvature of the shell.

Form finding in elastic gridshells

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We study elastic gridshells with a focus on the rational design of the final shapes. Our precision desktop experiments exhibit complex geometries, even from seemingly simple initial configurations and actuation processes. The numerical simulations capture this nonintuitive behavior with excellent quantitative agreement, allowing for an exploration of parameter space that reveals multistable states. We then turn to the theory of smooth Chebyshev nets to address the inverse design of hemispherical elastic gridshells. The results suggest that rod inextensibility, not elastic response, dictates the zeroth-order shape of an actuated elastic gridshell. As it turns out, this is the shape of a common household strainer. Therefore, the geometry of Chebyshev nets can be further used to understand elastic gridshells. In particular, we introduce a way to quantify the intrinsic shape of the empty, but enclosed regions, which we then use to rationalize the nonlocal deformation of elastic gridshells to point loading. This justifies the observed difficulty in form finding. Nevertheless, we close with an exploration of concatenating multiple elastic gridshell building blocks.

Regimes of wrinkling in pressurized elastic shells

We consider the point indentation of a pressurized elastic shell. It has previously been shown that such a shell is subject to a wrinkling instability as the indentation depth is quasi-statically increased. Here we present detailed analysis of this wrinkling instability using a combination of analytical techniques and finite-element simulations. In particular, we study how the number of wrinkles observed at the onset of instability grows with increasing pressurization. We also study how, for fixed pressurization, the number of wrinkles changes both spatially and with increasing indentation depth beyond onset. This 'Far from threshold' analysis exploits the largeness of the wrinkle wavenumber that is observed at high pressurization and leads to quantitative differences with the standard 'Near threshold' stability analysis.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Flow-induced buckling of flexible shells with non-zero Gaussian curvatures and thin spots

We study the influence of one or multiple thin spots on the flow-induced instabilities of flexible shells of revolution with non-zero Gaussian curvatures. The shell's equation of motion is described by a thin doubly-curved shell theory and is coupled with perturbed flow pressure, calculated based on an inviscid flow model. We show that for shells with positive Gaussian curvatures conveying fluid, the existence of a thin spot results in a localized flow-induced buckling response of the shell in the neighborhood of the thin spot, and significantly reduces the critical flow velocity for buckling instability. For shells with negative Gaussian curvatures, the buckling response is extended along the shell's characteristic lines and the critical flow velocity is only slightly reduced. We also show that the length scale of the localized deformation generated by a thin spot is proportional to the shell's global thickness when the stiffness of the thin spot is negligible compared with the stiffness of the rest of the shell. When two thin spots exist at a distance, their influences are independent from each other for shells with positive Gaussian curvatures, but large-scale deformations can be created due to multiple thin spots on shells with negative curvatures, depending on the thin spots' relative position.

The pressure sensitivity of wrinkled B-doped nanocrystalline diamond membranes

Nanocrystalline diamond (NCD) membranes are promising candidates for use as sensitive pressure sensors. NCD membranes are able to withstand harsh conditions and are easily fabricated on glass. In this study the sensitivity of heavily boron doped NCD (B:NCD) pressure sensors is evaluated with respect to different types of supporting glass substrates, doping levels and membrane sizes. Higher pressure sensing sensitivities are obtained for membranes on Corning Eagle 2000 glass, which have a better match in thermal expansion coefficient with diamond compared to those on Schott AF45 glass. In addition, it is shown that larger and more heavily doped membranes are more sensitive. After fabrication of the membranes, the stress in the B:NCD films is released by the emergence of wrinkles. A better match between the thermal expansion coefficient of the NCD layer and the underlying substrate results in less stress and a smaller amount of wrinkles as confirmed by Raman spectroscopy and 3D surface imaging.

Elasticity and glocality: initiation of embryonic inversion in Volvox

Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are glocal, set by a complicated balance between local properties and global geometric constraints. Here, we explore this interplay during the inversion process of the green alga Volvox, whose embryos must turn themselves inside out to complete their development. This process has recently been shown to be well described by the deformations of an elastic shell under local variations of its intrinsic curvatures and stretches, although the detailed mechanics of the process have remained unclear. Through a combination of asymptotic analysis and numerical studies of the bifurcation behaviour, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.

Retinal and Choroidal Folds in Papilledema

PURPOSE

To determine the frequency, patterns, associations, and biomechanical implications of retinal and choroidal folds in papilledema due to idiopathic intracranial hypertension (IIH).

METHODS

Retinal and choroidal folds were studied in patients enrolled in the IIH Treatment Trial using fundus photography (n = 165 study eyes) and spectral-domain optical coherence tomography (SD-OCT; n = 125). We examined the association between folds and peripapillary shape, retinal nerve fiber layer (RNFL) thickness, disc volume, Frisén grade, acuity, perimetric mean deviation, intraocular pressure, intracranial pressure, and refractive error.

RESULTS

We identified three types of folds in IIH patients with papilledema: peripapillary wrinkles (PPW), retinal folds (RF), and choroidal folds (CF). Frequency, with photos, was 26%, 19%, and 1%, respectively; SD-OCT frequency was 46%, 47%, and 10%. At least one type of fold was present in 41% of patients with photos and 73% with SD-OCT. Spectral-domain OCT was more sensitive. Structural parameters related to the severity of papilledema were associated with PPW and RF, whereas anterior deformation of the peripapillary RPE/basement membrane layer was associated with CF and RF. Folds were not associated with vision loss at baseline.

CONCLUSIONS

Folds in papilledema are biomechanical signs of stress/strain on the optic nerve head and load-bearing structures induced by intracranial hypertension. Folds are best imaged with SD-OCT. The patterns of retinal and choroidal folds are the products of a complex interplay between the degree of papilledema and anterior deformation of the load-bearing structures (sclera and possibly the lamina cribrosa), both modulated by structural geometry and material properties of the optic nerve head. (ClinicalTrials.gov number, NCT01003639.).

Ultrafast desorption of colloidal particles from fluid interfaces

The self-assembly of solid particles at fluid-fluid interfaces is widely exploited to stabilize emulsions and foams, and in materials synthesis. The self-assembly mechanism is very robust owing to the large capillary energy associated with particle adsorption, of the order of millions of times the thermal energy for micrometer-sized colloids. The microstructure of the interfacial colloid monolayer can also favor stability, for instance in the case of particle-stabilized bubbles, which can be indefinitely stable against dissolution due to jamming of the colloid monolayer. As a result, significant challenges arise when destabilization and particle removal are a requirement. Here we demonstrate ultrafast desorption of colloid monolayers from the interface of particle-stabilized bubbles. We drive the bubbles into periodic compression-expansion using ultrasound waves, causing significant deformation and microstructural changes in the particle monolayer. Using high-speed microscopy we uncover different particle expulsion scenarios depending on the mode of bubble deformation, including highly directional patterns of particle release during shape oscillations. Complete removal of colloid monolayers from bubbles is achieved in under a millisecond. Our method should find a broad range of applications, from nanoparticle recycling in sustainable processes to programmable particle delivery in lab-on-a-chip applications.

The secondary buckling transition: wrinkling of buckled spherical shells

We theoretically explain the complete sequence of shapes of deflated spherical shells. Decreasing the volume, the shell remains spherical initially, then undergoes the classical buckling instability, where an axisymmetric dimple appears, and, finally, loses its axisymmetry by wrinkles developing in the vicinity of the dimple edge in a secondary buckling transition. We describe the first axisymmetric buckling transition by numerical integration of the complete set of shape equations and an approximate analytic model due to Pogorelov. In the buckled shape, both approaches exhibit a locally compressive hoop stress in a region where experiments and simulations show the development of polygonal wrinkles, along the dimple edge. In a simplified model based on the stability equations of shallow shells, a critical value for the compressive hoop stress is derived, for which the compressed circumferential fibres will buckle out of their circular shape in order to release the compression. By applying this wrinkling criterion to the solutions of the axisymmetric models, we can calculate the critical volume for the secondary buckling transition. Using the Pogorelov approach, we also obtain an analytical expression for the critical volume at the secondary buckling transition: The critical volume difference scales linearly with the bending stiffness, whereas the critical volume reduction at the classical axisymmetric buckling transition scales with the square root of the bending stiffness. These results are confirmed by another stability analysis in the framework of Donnel, Mushtari and Vlasov (DMV) shell theory, and by numerical simulations available in the literature.

Microcapsule mechanics: from stability to function

Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties for functional aspects. At first, assembly strategies are presented that allow control over the decisive geometrical parameters, diameter and wall thickness, which both influence the capsule's mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified. Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences.

Anisotropic blistering instability of highly ellipsoidal shells

The formation of localized periodic structures in the deformation of elastic shells is well documented and is a familiar first stage in the crushing of a spherical shell such as a ping-pong ball. While spherical shells manifest such periodic structures as polygons, we present a new instability that is observed in the indentation of a highly ellipsoidal shell by a horizontal plate. Above a critical indentation depth, the plate loses contact with the shell in a series of well-defined "blisters" along the long axis of the ellipsoid. We characterize the onset of this instability and explain it using scaling arguments, numerical simulations, and experiments. We also characterize the properties of the blistering pattern by showing how the number of blisters and their size depend on both the geometrical properties of the shell and the indentation but not on the shell's elastic modulus. This blistering instability may be used to determine the thickness of highly ellipsoidal shells simply by squashing them between two plates.

Morphing metal-polymer janus particles

The direct deformation and shape recovery of micron-sized polystyrene particles via nanoimprint lithography is reported. The recovery of the programmed PS particles can be utilized to create a range of smart Janus particles with contrasting properties in conductivity and topography, by use of metal-layer constrained recovery.

Elastometry of deflated capsules: elastic moduli from shape and wrinkle analysis

Elastic capsules, prepared from droplets or bubbles attached to a capillary (as in a pendant drop tensiometer), can be deflated by suction through the capillary. We study this deflation and show that a combined analysis of the shape and wrinkling characteristics enables us to determine the elastic properties in situ. Shape contours are analyzed and fitted using shape equations derived from nonlinear membrane-shell theory to give the elastic modulus, Poisson ratio and stress distribution of the membrane. We include wrinkles, which generically form upon deflation, within the shape analysis. Measuring the wavelength of wrinkles and using the calculated stress distribution gives the bending stiffness of the membrane. We compare this method with previous approaches using the Laplace-Young equation and illustrate the method on two very different capsule materials: polymerized octadecyltrichlorosilane (OTS) capsules and hydrophobin (HFBII) coated bubbles. Our results are in agreement with the available rheological data. For hydrophobin coated bubbles, the method reveals an interesting nonlinear behavior consistent with the hydrophobin molecules having a rigid core surrounded by a softer shell.

Wrinkling in the deflation of elastic bubbles

The protein hydrophobin HFBII self-assembles into very elastic films at the surface of water; these films wrinkle readily upon compression. We demonstrate and study this wrinkling instability in the context of non-planar interfaces by forming HFBII layers at the surface of bubbles whose interfaces are then compressed by deflation of the bubble. By varying the initial concentration of the hydrophobin solutions, we are able to show that buckling occurs at a critical packing fraction of protein molecules on the surface. Independent experiments show that at this packing fraction the interface has a finite positive surface tension, and not zero surface tension as is usually assumed at buckling. We attribute this non-zero wrinkling tension to the finite elasticity of these interfaces. We develop a simple geometrical model for the evolution of the wrinkle length with further deflation and show that wrinkles grow rapidly near the needle (used for deflation) towards the mid-plane of the bubble. This geometrical model yields predictions for the length of wrinkles in good agreement with experiments independently of the rheological properties of the adsorbed layer.

Indentation of ellipsoidal and cylindrical elastic shells

Thin shells are found in nature at scales ranging from viruses to hens' eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus et al. [following paper, Phys. Rev. Lett. 109, 144301 (2012)] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells.

Delayed buckling and guided folding of inhomogeneous capsules

Colloidal capsules can sustain an external osmotic pressure; however, for a sufficiently large pressure, they will ultimately buckle. This process can be strongly influenced by structural inhomogeneities in the capsule shells. We explore how the time delay before the onset of buckling decreases as the shells are made more inhomogeneous; this behavior can be quantitatively understood by coupling shell theory with Darcy's law. In addition, we show that the shell inhomogeneity can dramatically change the folding pathway taken by a capsule after it buckles.

Tunable wrinkling pattern in annular graphene under circular shearing at inner edge

This work is concerned with the wrinkling phenomenon observed in an annular graphene sheet under circular shearing at its inner edge. By performing molecular mechanics simulations on the aforementioned loaded annular graphene sheet, it is observed that the unusual wrinkles formed are confined to within an annulus that hugs the perimeter of the inner radius. This confined wrinkling pattern is in contrast to the wrinkling patterns that spread throughout rectangular graphene sheets under tension or shear. The present wrinkling pattern is characterized by a wave number and wrinkle profile. The wave number at the bifurcation wrinkle is found to depend only on the inner radius of the annular graphene and it increases almost linearly with increasing inner radius. The orientation of these developed waves is found to be at a constant angle and independent from the radii ratio of annular graphene. The wrinkle profile in terms of wave amplitude and wavelength depends on the magnitude of the circular shearing. The predictable formation of wrinkles in annular graphene can be exploited for applications in nano-force sensors, tunable magnetic or electronic devices, as well as patterned stretchable electronics.

Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such a surface may model a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry through folding along portions of meridians. For the thinnest shells, a direct transition from the spherical conformation to the folded one can be observed. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of Poisson's ratio. In the folded conformation, the number of folds and inner pressure are investigated, allowing us to infer shell features from mere observation and/or knowledge of external constraints.