Wrinkling of pressurized elastic shells

We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping-pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We study wrinkling in depth, presenting scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells.     

Glassy conformations in wrinkled membranes

Partially polymerized membranes display a striking mechanical transition at low temperature known as the wrinkling transition. Fluorescence and scanning electron microscopy as well as profile measurements using an atomic force microscope revealed the existence of three degrees of wrinkling depending on the degree of the membrane polymerization. At low polymerization the membrane undergoes a cascade of wrinkling to form a folded phase with a characteristic exponent eta equal to 3, at intermediate polymerization, the membrane is in an intermediate-wrinkled phase (similar to the crumpling of an elastic sheet) with eta approximately 2.5, while at high polymerization the membrane undergoes an abrupt "compaction" to the wrinkled-rough phase with eta approximately 2.     

Modelling drying pathways of an evaporating soft matter droplet

Micro-droplets of soft matter solutions have different morphologies upon drying, and can become wrinkled, buckled or cavitated particles. We investigate the morphology evolution of a drying soft matter droplet in this work: at the early stage of drying, wrinkling or cavitation instability can occur in the droplet, depending on the comparison between the critical wrinkling and cavitation pressure; at a later stage of drying, no wrinkles will appear if cavitation happens first, while cavitation can still occur if wrinkling happens first. A three-dimensional phase diagram in the space of elastic length, gel layer thickness and weight loss is provided to illustrate the drying pathways of a soft matter droplet. This diagram can help guide future fabrications of micro-particles with desired morphologies.     

Contact instability in adhesion and debonding of thin elastic films

Based on experiments and 3D simulations, we show that a soft elastic film during adhesion and debonding from a rigid flat surface undergoes morphological transitions to pillars, labyrinths, and cavities, all of which have the same lateral pattern length scale, lambda close to lambda/H approximately 3 for thick films, H > 1 microm . The linear stability analysis and experiments show a new thin film regime where lambda/H approximately equal to 3 + 2pi(lambda/3 muH)1/4 (gamma is surface tension, mu is shear modulus) because of a significant surface energy penalty (for example, lambda/H approximately equal to 6 for H = 200 nm; mu = 1 MPa).     

Floating carpets and the delamination of elastic sheets

We investigate the deformation of a thin elastic sheet floating on a liquid surface and subject to a uniaxial compression. We show that at a critical compression the sheet delaminates from the liquid over a finite region forming a delamination "blister." This blistering regime adds to the wrinkling and localized folding regimes that have been studied previously. The transition from wrinkled to blistered states occurs when delamination becomes energetically favorable compared with wrinkling. We determine the initial blister size and the evolution of blister size with continuing compression before verifying our theoretical results with experiments at a macroscopic scale.     

Effect of the configuration of a wrinklon on the distributions of the energy and elastic strain in a graphene nanoribbon

The formation of wrinkles in thin membranes is a widespread phenomenon. In particular, wrinkles can appear in graphene, which is the thinnest natural membrane, and affect its properties. A region where wrinkles with different wavelengths are linked is called wrinklon. Conditions of the fixing of an elastically deformed graphene sheet dictate a certain wavelength of wrinkles near the fixed edge. Wrinkles with a longer wavelength become more energetically favorable with an increase in the distance from the edge. As a result, wrinklons appear and reduce the potential energy of the system by uniting wrinkles into larger wrinkles with an increase in the distance from the edge. The possibility of implementing various equilibrium configurations of wrinklons at given plane strains in graphene has been demonstrated by the molecular quasistatic method. The distributions of the energy and elastic strain components in wrinklons with various configurations for nanoribbons with different widths have been calculated.     

Breakdown of dynamic scaling in surface growth under shadowing

Using Monte Carlo simulations and experimental results, we show that for common thin film deposition techniques, such as sputter deposition and chemical vapor deposition, a mound structure can be formed with a characteristic length scale, or "wavelength" lambda, that describes the separation of the mounds. We show that the temporal evolution of lambda is distinctly different from that of the mound size, or lateral correlation length xi. The formation of a mound structure is due to nonlocal growth effects, such as shadowing, that lead to the breakdown of the self-affinity of the morphology described by the well-established dynamic scaling theory. We show that the wavelength grows as a function of time in a power law form, lambda approximately t(p), where p approximately equals 0.5 for a wide range of growth conditions, while the mound size grows as xi approximately t(1-z), where 1/z varies depending on growth conditions.     

Friction of wrinkles

Sufficiently thin elastic sheets wrinkle when they are in contact with a small adhesive counterbody. Despite significant progress on the dynamics of wrinkle formation and morphology, little is known about how wrinkles impede the relative sliding motion of the counterbody. Using molecular dynamics we demonstrate that instabilities are likely to occur during sliding when the wrinkle pattern has asymmetries not present in the counterbody. The instabilities then cause Coulomb's friction law. The behavior can be rationalized in terms of simple models for multistable elastic manifolds.     

A measurement of elastic moduli for tungsten films on polymer substrate using wrinkling analysis

The elastic moduli of ultra thin tungsten (W) films on polymers were assessed with wrinkling analysis. Thin W films with a range of thickness between 17 and 100 nm were deposited on compliant polymers and Si strips using DC magnetron sputtering method, causing the tensile stress in a few GPa scale with respect to the thickness of W films. By applying lateral compression on polymer, wrinkle patterns were developed in the W thin film with well-defined amplitude and wavelength. Using a simple equation on wrinkle analysis, the range of elastic moduli was estimated with increasing the thickness. It was found that the elastic modulus and the tensile stress decreased with increasing the film thickness.     

Self-similar structures near boundaries in strained systems

We study the buckling of thin elastic plates caused by residual strains concentrated near a free edge. This is a model for plant leaves and torn plastic sheet morphologies. We derive new governing equations explaining self-similar patterns reported earlier in experiments. We reveal the cascade mechanism, determine the bounds for its wavelengths, and predict a similarity factor of 3 in agreement with experiments. This is confirmed by numerical solutions with up to five generations of wrinkles.     

The wrinkle and its measurement--a skin surface Profilometric method

This study outlines a simple 'Profilometric' method for measuring the size and function of the wrinkles. Wrinkle size was measured in relaxed conditions and the representative parameters were considered to be the mean 'Wrinkle Depth', the mean 'Wrinkle Area', the mean 'Wrinkle Volume', and the mean 'Wrinkle Tissue Reservoir Volume' (WTRV). These parameters were measured in the wrinkle profiles under relaxed conditions. The mean 'Wrinkle to Wrinkle Distance', which measures the distance between two adjacent wrinkles, is an accurate indicator of the muscle relaxation level during replication. This parameter, identified as the 'Muscle Relaxation Level Marker', and its reduction are related to increased muscle tone or contraction and vice versa. The mean Wrinkle to Wrinkle Distance is very important in experiments where the effectiveness of an anti-wrinkle preparation is tested. Thus, the correlative wrinkles' replicas, taken during follow up in different periods, are only those that show the same mean Wrinkle to Wrinkle Distance. The wrinkles' functions were revealed by studying the morphological changes of the wrinkles and their behavior during relaxed conditions, under slight increase of muscle tone and under maximum wrinkling. Facial wrinkles are not a single groove, but comprise an anatomical and functional unit (the 'Wrinkle Unit') along with the surrounding skin. This Wrinkle Unit participates in the functions of a central neuro-muscular system of the face responsible for protection, expression, and communication. Thus, the Wrinkle Unit, the superficial musculoaponeurotic system (superficial fascia of the face), the underlying muscles controlled by the CNS and Psyche, are considered to be a 'Functional Psycho-Neuro-Muscular System of the Face for Protection, Expression and Communication'. The three major functions of this system exerted in the central part of the face and around the eyes are: (1) to open and close the orifices (eyes, nose, and mouth), contributing to their functions; (2) to protect the eyes from sun, foreign bodies, etc.; (3) to contribute to facial expression, reflecting emotions (real, pretended, or theatrical) during social communication. These functions are exercised immediately and easily, without any opposition ('Wrinkling Ability') because of the presence of the Wrinkle Unit that gives (a) the site of refolding (the wrinkle is a waiting fold, ready to respond quickly at any moment for any skin mobility need) and (b) the appropriate skin tissue for extension or compression (this reservoir of tissue is measured by the parameter of WTRV). The Wrinkling Ability of a skin area is linked to the wrinkle's functions and can be measured by the parameter of 'Skin Tissue Volume Compressed around the Wrinkle' in mm(3) per 30 mm wrinkle during maximum wrinkling. The presence of wrinkles is a sign that the skin's 'Recovery Ability' has declined progressively with age. The skin's Recovery Ability is linked to undesirable cosmetic effects of ageing and wrinkling. This new Profilometric method can be applied in studies where the effectiveness of anti-wrinkle preparations or the cosmetic results of surgery modalities are tested, as well as in studies focused on the functional physiology of the Wrinkle Unit.     

Wrinkle formations in axi-symmetrically stretched membranes

We study experimentally the main features of wrinkles that form in an initially stretched and flat elastic membrane when subjected to an axi-symmetric traction force at the center. The wavelength and amplitude of the wrinkle pattern are accurately characterized as the membrane tension and the traction forced are varied. We show that wrinkles are the result of a supercritical instability and appear for a well-defined critical traction force that is a function of the membrane tension. Wrinkle length and amplitude increase as the traction force is increased further. By contrast, both quantities decrease as the membrane tension is increased. Calculations based on symmetry arguments and elastic-energy minimization are in good agreement with experiments and provide a simple way to investigate configurations that are difficult to access experimentally. Such problems include wrinkles in elastic nano-films on finite-thickness viscous substrates used in semiconductor technology or in cellular forces detection.Received: 10 August 2004, Published online: 19 October 2004PACS: 46.32. + x Static buckling and instability - 87.19.St Movement and locomotion - 85.40.Ls Metallization, contacts, interconnects; device isolationJ.-C. Géminard: Permanent address: Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 64, Allée dItalie, 69364 Lyon cedex 07, France     

Wrinkling of vesicles during transient dynamics in elongational flow

Recent experiments by Kantsler et al. [Phys. Rev. Lett. 99, 178102 (2007)10.1103/PhysRevLett.99.178102] have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. The formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasispherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scaling laws for the temporal evolution of wrinkling wavelength and surface tension are established, confirmed numerically, and compared to experimental results.     

热氧化铜箔中的起皱和CuO纳米线的生长机

在500 oC大气条件下热氧化0.5 mm厚的铜箔0.5～10 h有起皱现象,且皱的大小随氧化时间的增加而增大,在皱的侧面和顶部均有生长CuO纳米线,皱侧面生长纳米线的长度比皱顶部的纳米线的长,密度也高;CuO纳米线的生长方向垂直于纳米线的生长表面. 通过计算波动阶段中皱内部的局部电场,发现皱的侧面和顶部的电场强度的数值相差很小,表明在CuO纳米线生长过程中驱动铜离子扩散的主要驱动力不是局部的电场力而是内应力.     

Plastic folding of buckling structures

Atomic force microscopy observations of the free surface of gold thin films deposited on silicon substrates have evidenced the buckling of the films and the formation of blister patterns undergoing plastic folding. The classical elastic buckling and plastic deformation of the films are analyzed in the framework of the F?ppl-Von Kármán theory of thin plates introducing the notion of low-angle tilt boundaries and dislocation distributions to describe this folding effect. It is demonstrated that, in agreement with elementary plasticity of bent crystals, the presence of such tilt-boundaries results in the formation of buckling patterns of lower energy than "classical" elastic blisters.     

Spontaneous wrinkling pattern of a constrained thin film membrane

The wrinkling morphology of an inhomogeneously constrained thin film membrane is explored using finite element simulations, where a small circular area in a thin sheet undergoes expansion, and buckles emerge due to differential in-plane deformation. The local wrinkling patterns are characterized by the normalized circular (inner) area size, the modulus mismatch between the inner and outer regions, and the normalized stress in the inner area. As the stress increases, the morphology transits from ripple-like to petal-like and finally to a branched pattern. Through parametric studies, the effect of the governing variables on the pattern evolution, wave number, and maximum deflection is discussed. The model is used to qualitatively explain the delamination/blister morphology observed in thin film/substrate systems. The study has the potential of inspiring new fabrication techniques based on mechanical self-assembly.     

Effect of pressure on the Ginzburg-Landau parameter kappa=lambda/xi in YB6

Measurements of the transition temperature Tc, the upper critical field Hc2, and the magnetic penetration depth lambda under hydrostatic pressure (up to approximately 9.2 kbar) in the YB6 superconductor were carried out. A pronounced and negative pressure effect (PE) on Tc and Hc2 with dTc/dp=-0.0547(4) K/kbar and micro0dHc2(0)/dp=-4.84(20) mT/kbar, and zero PE on lambda(0) were observed. The PE on the coherence length dxi(0)/dp=0.28(2) nm/kbar was calculated from the measured pressure dependence of Hc2(0). Together with the zero PE on the magnetic penetration depth lambda(0), our results imply that the Ginzburg-Landau parameter kappa(0)=xi(0)/lambda(0) depends on pressure and that pressure "softens" YB6, e.g., moves it to the type-I direction.     

Solid state solvation in amorphous organic thin films

The photoluminescence (PL) of the red laser dye DCM2, doped into blended thin films of polystyrene (PS) and the polar small molecule camphoric anhydride (CA), redshifts as the CA concentration increases. The DCM2 PL peaks at 2.20 eV (lambda=563 nm) for pure PS films and shifts to 2.05 eV (lambda=605 nm) for films with 24.5% CA (by mass). The capacitively measured electronic permittivity also increases from epsilon=2.4 to epsilon=5.6 with CA concentration. These results are consistent with the theory of solvatochromism developed for organic molecules in liquid solvents. To our knowledge, this work is the first application of a quantitative theory of solvation to organic molecules in amorphous thin films with continuously controllable permittivity, and demonstrates that "solid state solvation" can be used to predictably tune exciton energies in organic thin film structures.     

Elastic response and wrinkling onset of curved elastic membranes subjected to indentation test

Starting from a polymeric-fluid droplet, by vulcanization of the fluid free surface, curved elastic membranes, several nanometers thick and a few millimeters in diameter, which enclose a constant fluid volume, are produced. In an indentation-type test, carried out by pushing the membrane along its normal by means of a micro-needle, under some conditions, wrinkles are likely to appear around the contact region. Interestingly, we observe that the instability does not significantly alter the force-displacement relation: the relation between the force and the displacement remains linear and the associated stiffness is simply proportional to the tension of the membrane. In addition, we determine that the wrinkles develop when the stretching modulus of the membrane compares with its tension, which provides a useful method to estimate the elastic constant.