Analytical and experimental study of a circular membrane in adhesive contact with a rigid substrate

The problem that is addressed here is that of a pressurized circular membrane in adhesive contact with a rigid substrate. A closed-form membrane analysis is developed for the JKR, DMT and Maugis regimes, which describes the relationships between adhesion energy, pressure, contact radius and contact force. The JKR–DMT transition is studied for this case of membrane contact by introducing an appropriate dimensionless parameter. Experiments are conducted with smooth and structured acrylate layers on a PET carrier film contacting a glass substrate using an apparatus based on moiré deflectometry to measure the contact radius and slope of these thin transparent films. They demonstrate that this analysis predicts the contact radius well. The adhesion energy extracted from the analysis of the measured pressure-contact radius response is constant during unloading but appears to increase during pressurization.     

Peeling behavior of a viscoelastic thin-film on a rigid substrate

In order to study the adhesion mechanism of a viscoelastic thin-film on a substrate, peeling experiment of a viscoelastic polyvinylchloride (PVC) thin-film on a rigid substrate (glass) is carried out. The effects of peeling rate, peeling angle, film thickness, surface roughness and the interfacial adhesive on the peel-off force are considered. It is found that both the viscoelastic properties of the film and the interfacial adhesive contribute to the rate-dependent peel-off force. For a fixed peeling rate, the peel-off force decreases with the increasing peeling angle. Increasing film thickness or substrate roughness leads to an increase of the peel-off force. Viscoelastic energy release rate in the present experiment can be further predicted by adopting a recently published theoretical model. It is shown that the energy release rate increases with the increase of peeling rates or peeling angles. The results in the present paper should be helpful for understanding the adhesion mechanism of a viscoelastic thin-film.     

Decohesion of a rigid punch from non-linear membrane undergoing finite axisymmetric deformation

Adhesion of flexible thin film or membrane plays an important role in many biological and industrial applications. In many physical systems, large deformation is often expected, especially for biological membranes, which suggests that non-linear analysis might be required. In this paper the adhesion and decohesion between a rigid flat punch and a non-linear membrane undergoing finite axisymmetric deformation is studied. The decohesion is assumed to obey the Griffith fracture criterion. The cases of initially stress-free and prestressed membrane are analyzed. A comparison with published works using the linear theory shows that the non-linear theory substantially deviates from the linear one, qualitatively and quantitatively. These results advocate the use of non-linear consideration when the membrane undergoes large deformation prior to and during the debonding process.     

Analytical and experimental study of a circular membrane in Hertzian contact with a rigid substrate

The problem that is addressed here is that of a pressurized circular membrane in contact with a rigid substrate. A closed-form membrane analysis with Hertz-type contact is developed to describe the relationship between pressure, contact radius and contact force. Both the variation in the slope of the deflection profile of the portion of the membrane outside the contact zone and the contact radius itself are measured by an apparatus based on moiré deflectometry. Contact experiments with a 3 μm PET film and a glass substrate show that this analysis predicts both the slope field and contact radius well.     

Adhesive contact of an elastic semi-infinite solid with a rigid rough surface: Strength of adhesion and contact instabilities

The effect of adhesion on the contact behavior of elastic rough surfaces is examined within the framework of the multi-asperity contact model of Greenwood and Williamson (1966), known as the GW model. Adhesive surface interaction is modeled by nonlinear springs with a force–displacement relation governed by the Lennard–Jones (LJ) potential. Constitutive models are presented for contact systems characterized by low and high Tabor parameters, exhibiting continuous (stable) and discontinuous (unstable) surface approach, respectively. Constitutive contact relations are obtained by integrating the force–distance relation derived from the LJ potential with a finite element analysis of single-asperity adhesive contact. These constitutive relations are then incorporated into the GW model, and the interfacial force and contact area of rough surfaces are numerically determined. The development of attractive and repulsive forces at the contact interface and the occurrence of instantaneous surface contact (jump-in instability) yield a three-stage evolution of the contact area. It is shown that the adhesion parameter introduced by Fuller and Tabor (1975) governs the strength of adhesion of contact systems with a high Tabor parameter, whereas the strength of adhesion of contact systems with a low Tabor parameter is characterized by a new adhesion parameter, defined as the ratio of the surface roughness to the equilibrium interatomic distance. Applicable ranges of aforementioned adhesion parameters are interpreted in terms of the effective surface separation, obtained as the sum of the effective distance range of the adhesion force and the elastic deformation induced by adhesion. Adhesive strength of rough surfaces in the entire range of the Tabor parameter is discussed in terms of a generalized adhesion parameter, defined as the ratio of the surface roughness to the effective surface separation.     

Computational mechanics modelling of cell-substrate contact during cyclic substrate deformation

Experimental testing carried out on various adherent cell types cultured on deformable substrates reveals specific patterns of cell reorientation in response to cyclic stretching of the substrate. In Wang et al. (2001. Specificity of endothelial cell reorientation in response to cyclic mechanical stretching. J. Biomech. 34, 1563), a number of substrate deformation modes were considered: in cases where lateral deformation of the substrate was prohibited (uniaxial case) cells were found to elongate perpendicular to the stretch direction, whereas in cases where the substrate was laterally unrestrained (biaxial case) cells were found to elongate at an angle to the stretch direction. The alignment directions in both cases corresponded to directions of minimum substrate strain. However, the mechanisms underlying such behaviour are not apparent from such in-vitro testing and consequently are not well understood. In this study finite element models are developed in order to investigate the role of cell viscoelasticity in cell debonding and cell realignment under conditions of cyclic substrate stretching using cohesive zone formulations to simulate cell-substrate interfacial behaviour. The characteristic length scale used in such models is based on the length of the receptor-ligand bonds at the cell-substrate interface. Two-dimensional simulations reveal that permanent debonding at the cell-substrate interface occurs due to the accumulation of strain concentrations in the cell. Inclusion of a nucleus in two-dimensional models is shown to have little effect on debonding while discrete cell-substrate contact at focal adhesion sites results in a completion of debonding in fewer cycles. Three-dimensional cohesive zone models are developed in order to compute changes in cell-substrate contact under the aforementioned uniaxial and biaxial modes of substrate deformation. Results reveal that, due to the accumulation of tensile and compressive strains in the cell under cyclic deformation, definite patterns of cell-substrate contact area evolution are computed. With continued cycling, equilibrium contact area profiles with definite orientations are established. These orientations are found to be coincidental with the preferential cell orientation directions seen in the experiments. As no changes in cell morphology are predicted by the models it is concluded that permanent breaking of cell-substrate bonds constitutes the first stage in the process of cell alignment under such mechanical loading.     

Elastic-plastic analysis of a flat plate with a circular rigid inclusion

Summary An elastic-plastic solution is presented for a circular rigid inclusion in a unidirectionally stressed flat plate of linearly strain hardening material. The results are compared to the results obtained for the free hole. It is postulated that for intermediate constraints the plastic flow would be less pronounced than in these limiting cases.     

Large deformation and electrochemistry of polyelectrolyte gels

Immersed in an ionic solution, a network of polyelectrolytes imbibes the solution and swells, resulting in a polyelectrolyte gel. The swelling is reversible, and the amount of swelling is regulated by ionic concentrations, mechanical forces, and electric potentials. This paper develops a field theory to couple large deformation and electrochemistry. A specific material model is described, including the effects of stretching the network, mixing the polymers with the solvent and ions, and polarizing the gel. We show that the notion of osmotic pressure in a gel has no experimental significance in general, but acquires a physical interpretation within the specific material model. The theory is used to analyze several phenomena: a gel swells freely in an ionic solution, a gel swells under a constraint of a substrate, electric double layer at the interface between the gel and the external solution, and swelling of a gel of a small size.     

Stick-slip analysis of a circular point contact between a rigid sphere and a flat unidirectional composite with cylindrical fibers

The stick-slip contact problem is investigated here when at least one of the contacting bodies behaves as an ideal composite material with long fibers perpendicular to the direction of movement. Cylindrical inhomogeneous inclusions within a homogeneous media and with axes parallel to the contact surface are considered. The Eshelby’s equivalent inclusion method is used to solve the problem numerically. Interactions between close inclusions are taken into account in the numerical procedure, as well as the coupling between the normal and tangential contact problems. It is found that the presence of heterogeneities in the vicinity of the surface contact affects significantly the contact pressure distribution and subsequently the distribution of shear and slip at the interface.     

Large deformation of circular membrane under the concentrated force

1　AxisymmetryLargeDeformationofCircularMembraneTheproblemofaxisymmetrylargedeformationofcircularmembraneisonewithpracticalsignificance.Hencky (1 91 5) [1]gaveasolutionofpowerseriesundertheuniformforce ;Alekseev (1 951 ) [2 ]gaveananalyticsolutionofcircularmembraneundertheconcentratedforce ,whichisexactonlywhenν=1 3 .ChienWei_zangetal.(1 981 ) [3]gaveananalyticsolutionofthesymmetricalcircularmembraneundertheactionofuniformlydistributedloadsinitscentralportion .Asfortheresultsorotherauthor…     

Thermoelastic contact mechanics for a flat punch sliding over a graded coating/substrate system with frictional heat generation

The problem of thermoelastic contact mechanics for the coating/substrate system with functionally graded properties is investigated, where the rigid flat punch is assumed to slide over the surface of the coating involving frictional heat generation. With the coefficient of friction being constant, the inertia effects are neglected and the solution is obtained within the framework of steady-state plane thermoelasticity. The graded material exists as a nonhomogeneous interlayer between dissimilar, homogeneous phases of the coating/substrate system or as a nonhomogeneous coating deposited on the substrate. The material nonhomogeneity is represented by spatially varying thermoelastic moduli expressed in terms of exponential functions. The Fourier integral transform method is employed and the formulation of the current thermoelastic contact problem is reduced to a Cauchy-type singular integral equation of the second kind for the unknown contact pressure. Numerical results include the distributions of the contact pressure and the in-plane component of the surface stress under the prescribed thermoelastic environment for various combinations of geometric, loading, and material parameters of the coated medium. Moreover, in order to quantify and characterize the singular behavior of contact pressure distributions at the edges of the flat punch, the stress intensity factors are defined and evaluated in terms of the solution to the governing integral equation.     

Non-slipping adhesive contact between mismatched elastic spheres: A model of adhesion mediated deformation sensor

A generalized JKR model is established for non-slipping adhesive contact between two dissimilar elastic spheres subjected to a pair of pulling forces and a mismatch strain. We discuss the full elastic solution to the problem as well as the so-called non-oscillatory solution in which tension and shear tractions along the contact interface is decoupled from each other. The model indicates that the mismatch strain has significant effect on the contact area and the pull-off process. Under a finite pulling force, a pair of adhering spheres is predicted to break apart spontaneously at a critical mismatch strain. This study suggests an adhesion mediated deformation sensing mechanism by which cells and molecules can detect mechanical signals in the environment via adhesive interactions.     

Bio-inspired mechanics of reversible adhesion: Orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials

Geckos and many insects have evolved elastically anisotropic adhesive tissues with hierarchical structures that allow these animals not only to adhere robustly to rough surfaces but also to detach easily upon movement. In order to improve our understanding of the role of elastic anisotropy in reversible adhesion, here we extend the classical JKR model of adhesive contact mechanics to anisotropic materials. In particular, we consider the plane strain problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic elastic half space with the axis of symmetry oriented at an angle inclined to the surface. The cylinder is then subjected to an arbitrarily oriented pulling force. The critical force and contact width at pull-off are calculated as a function of the pulling angle. The analysis shows that elastic anisotropy leads to an orientation-dependent adhesion strength which can vary strongly with the direction of pulling. This study may suggest possible mechanisms by which reversible adhesion devices can be designed for engineering applications.     

Large scale manufacture of magnetic polymer particles using membranes and microfluidic devices

Magnetic polymer particles have found applications in diverse areas such as biomedical treatments, diagnosis and separation technology. These applications require the particles to have controlled sizes and narrow size distributions to gain better control and reproducibility in use. This paper reviews recent developments in the preparation of magnetic polymer particles at nano- and micro-scales by encapsulating magnetic components with dissolved or in situ formed polymers. Particle manufacture using emulsification and embedment methods produces magnetic polymer particles at micro-scale dimensions. However, the production of particles in this range using conventional emulsification methods affords very limited control over particle sizes and polydispersity. We report on alternative routes using membrane and microfluidics emulsification techniques, which have a capability to produce monodisperse emulsions and polymer microspheres （with coefficients of variation of less than 10%） in the range from submicrometer to a few 100 μm. The performance of these manufacturing methods is assessed with a view to future applications.     

Inplane deformation of a circular inhomogeneity with imperfect interface

The plane elastic problem of a circular inhomogeneity with an imperfect interface of spring-constant-type is reduced to the solution of a Somigliana dislocation problem, when the solution for the corresponding problem with a perfect interface is known. The Burger's vector of the Somigliana dislocation is determined so that its components satisfy two interfacial conditions involving the traction components of the corresponding problem with a perfect interface. Employing complex variables, a two-phase potential solution to the Somigliana dislocation inhomogeneity problem is developed for a general form of the Burger's vector. Detailed results are reported for a uniform eigenstrain in the inhomogeneity, and for a remote uniform heat flow in the matrix. In the latter case, the inhomogeneity behaves as a void, when it begins to slide.     

Discrete contact mechanics of a fibrillar surface with backing layer interactions

The contact mechanics of a fibrillar micro-fabricated surface structure made of poly(dimethyl siloxane) (PDMS) is studied. The attachment and detachment of individual fibrils to and from a spherical indenter upon approach and retraction are detected as jumps in force and stiffness. A quantitative model describes the stiffness values by taking into account the deformation of the fibrils and the backing layer. The results emphasize the importance of long-range interactions in the contact mechanics of elastic materials and confirm some of the important concepts underlying the development of fibrillar adhesive materials.     

Adhesion and friction of an elastic half-space in contact with a slightly wavy rigid surface

The paper deals with the estimation of the pressure distribution, the shape of contact and the friction force at the interface of a flat soft elastic solid moving on a rigid half-space with a slightly wavy surface. In this case an unsymmetrical contact is considered and justified with the adhesion hysteresis. For soft solids as rubber and polymers the friction originates mainly from two different contributions: the internal friction due to the viscoelastic properties of the bulk and the adhesive processes at the interface of the two solids. In the paper the authors focus on the latter contribution to friction. It is known, indeed, that for soft solids, as rubber, the adhesion hysteresis is, at least qualitatively, related to friction: the larger the adhesion hysteresis the larger the friction. Several mechanisms may govern the adhesion hysteresis, such as the interdigitation process between the polymer chains, the local small-scale viscoelasticity or the local elastic instabilities. In the paper the authors propose a model to link, from the continuum mechanics point of view, the friction to the adhesion hysteresis. A simple one-length scale roughness model is considered having a sinusoidal profile. For partial contact conditions the detached zone is taken to be a mode I propagating crack. Due to the adhesion hysteresis, the crack is affected by two different values of the strain energy release rate at the advancing and receding edges respectively. As a result, an unsymmetrical contact and a friction force arise. Additionally, the stability of the equilibrium configurations is discussed and the adherence force for jumping out of contact and the critical load for snapping into full contact are estimated.     

Axisymmetric indentation of curved elastic membranes by a convex rigid indenter

Motivated by applications to seed germination, we consider the transverse deflection that results from the axisymmetric indentation of an elastic membrane by a rigid body. The elastic membrane is fixed around its boundary, with or without an initial pre-stretch, and may be initially curved prior to indentation. General indenter shapes are considered, and the load-indentation curves that result for a range of spheroidal tips are obtained for both flat and curved membranes. Wrinkling may occur when the membrane is initially curved, and a relaxed strain-energy function is used to calculate the deformed profile in this case. Applications to experiments designed to measure the mechanical properties of seed endosperms are discussed.