Non-uniform breaking of molecular bonds,peripheral morphology and releasable adhesion by elastic anisotropy in bio-adhesive contacts

Biological adhesive contacts are usually of hierarchical structures, such as the clustering of hundreds of sub-micrometre spatulae on keratinous hairs of gecko feet, or the clustering of molecular bonds into focal contacts in cell adhesion. When separating these interfaces, releasable adhesion can be accomplished by asymmetric alignment of the lowest scale discrete bonds (such as the inclined spatula that leads to different peeling force when loading in different directions) or by elastic anisotropy. However, only two-dimensional contact has been analysed for the latter method (Chen & Gao 2007 J. Mech. Phys. Solids 55, 1001–1015 (doi:10.1016/j.jmps.2006.10.008)). Important questions such as the three-dimensional contact morphology, the maximum to minimum pull-off force ratio and the tunability of releasable adhesion cannot be answered. In this work, we developed a three-dimensional cohesive interface model with fictitious viscosity that is capable of simulating the de-adhesion instability and the peripheral morphology before and after the onset of instability. The two-dimensional prediction is found to significantly overestimate the maximum to minimum pull-off force ratio. Based on an interface fracture mechanics analysis, we conclude that (i) the maximum and minimum pull-off forces correspond to the largest and smallest contact stiffness, i.e. ‘stiff-adhere and compliant-release’, (ii) the fracture toughness is sensitive to the crack morphology and the initial contact shape can be designed to attain a significantly higher maximum-to-minimum pull-off force ratio than a circular contact, and (iii) since the adhesion is accomplished by clustering of discrete bonds or called bridged crack in terms of fracture mechanics terminology, the above conclusions can only be achieved when the bridging zone is significantly smaller than the contact size. This adhesion-fracture analogy study leads to mechanistic predictions that can be readily used to design biomimetics and releasable adhesives.     

A linear model of elasto-plastic and adhesive contact deformation

Rigorous non-linear models of elasto-plastic contact deformation are time-consuming in numerical calculations for the distinct element method (DEM) and quite often unnecessary to represent the actual contact deformation of common particulate systems. In this work a simple linear elasto-plastic and adhesive contact model for spherical particles is proposed. Plastic deformation of contacts during loading and elastic unloading, accompanied by adhesion are considered, for which the pull-off force increases with plastic deformation. Considering the collision of a spherical cohesive body with a rigid flat target, the critical sticking velocity and coefficient of restitution in the proposed model are found to be very similar to those of Thornton and Ning’s model. Sensitivity analyses of the model parameters such as plastic, elastic, plastic-adhesive stiffnesses and pull-off force on work of compaction are carried out. It is found that by increasing the ratio of elastic to plastic stiffness, the plastic component of the total work increases and the elastic component decreases. By increasing the interface energy, the plastic work increases, but the elastic work does not change. The model can be used to efficiently represent the force-displacement of a wide range of particles, thus enabling fast numerical simulations of particle assemblies by the DEM.     

Simulation of synthetic gecko arrays shearing on rough surfaces

To better understand the role of surface roughness and tip geometry in the adhesion of gecko synthetic adhesives, a model is developed that attempts to uncover the relationship between surface feature size and the adhesive terminal feature shape. This model is the first to predict the adhesive behaviour of a plurality of hairs acting in shear on simulated rough surfaces using analytically derived contact models. The models showed that the nanoscale geometry of the tip shape alters the macroscale adhesion of the array of fibres by nearly an order of magnitude, and that on sinusoidal surfaces with amplitudes much larger than the nanoscale features, spatula-shaped features can increase adhesive forces by 2.5 times on smooth surfaces and 10 times on rough surfaces. Interestingly, the summation of the fibres acting in concert shows behaviour much more complex that what could be predicted with the pull-off model of a single fibre. Both the Johnson–Kendall–Roberts and Kendall peel models can explain the experimentally observed frictional adhesion effect previously described in the literature. Similar to experimental results recently reported on the macroscale features of the gecko adhesive system, adhesion drops dramatically when surface roughness exceeds the size and spacing of the adhesive fibrillar features.     

Effect of counterface roughness on adhesion of mushroom-shaped microstructure

In this study, the effect of the substrate roughness on adhesion of mushroom-shaped microstructure was experimentally investigated. To do so, 12 substrates having different isotropic roughness were prepared from the same material by replicating topography of different surfaces. The pull-off forces generated by mushroom-shaped microstructure in contact with the tested substrates were measured and compared with the pull-off forces generated by a smooth reference. It was found that classical roughness parameters, such as average roughness (R_a) and others, cannot be used to explain topography-related variation in pull-off force. This has led us to the development of an integrated roughness parameter capable of explaining results of pull-off measurements. Using this parameter, we have also found that there is a critical roughness, above which neither smooth nor microstructured surface could generate any attachment force, which may have important implications on design of both adhesive and anti-adhesive surfaces.     

Contact mechanics modeling of pull-off measurements: effect of solvent,probe radius,and chemical binding probability on the detection of single-bond rupture forces by atomic force microscopy

Pull-off forces for chemically modified atomic force microscopy tips in contact with flat substrates coated with receptor molecules are calculated using a Johnson, Kendall, and Roberts contact mechanics model. The expression for the work of adhesion is modified to account for the formation of discrete numbers of chemical bonds (nBonds) between the tip and substrate. The model predicts that the pull-off force scales as nBonds(1/2), which differs from a common assumption that the pull-off force scales linearly with nBonds. Periodic peak progressions are observed in histograms generated from hundreds of computed pull-off forces. The histogram periodicity is the signature of discrete chemical interactions between the tip and substrate and allows estimation of single-bond rupture forces. The effects of solvent, probe tip radius, and chemical binding probability on the detection of single-bond forces are examined systematically. A dimensionless parameter, the effective force resolution, is introduced that serves as a quantitative predictor for determining when periodicity in force histograms can occur. The output of model is compared to recent experimental results involving tips and substrates modified with self-assembled monolayers. An advantage of this contact mechanics approach is that it allows straightforward estimation of solvent effects on pull-off forces.     

The assessment of particle friction of a drug substance and a drug carrier substance

The centrifuge technique, which has been previously used in adhesion experiments, has been modified for use in single particle friction studies. Both flat compacted surfaces and large single particles were used as substrate surfaces to allow assessment of drug-drug, drug-drug carrier and drug carrier-drug carrier friction forces. Particle size, particle shape and surface roughness were identified as main factors influencing the change from a static into a dynamic friction process and the division between friction due to adhesion and ploughing. The forces of adhesion and friction were found to be proportional to the reversible energy of adhesion. The ratio between the force of adhesion and the press-on force applied and the ratio between the force of friction and the press-on force can be related to the yield stress and the reduced Young's modulus of the materials in contact.     

三维四向编织陶瓷基复合材料改进模型及刚度预报

基于对三维四向编织陶瓷基复合材料CT扫描结果的观察和理论分析, 参考现有交织模型, 建立了改进的胞元三维实体模型, 较为真实地反映了材料内部的细观结构。模型内部纤维束横截面沿纤维束轴向不断发生形状和面积的周期性变化, 纤维束横截面呈平行四边形、五边形交替变化, 不同纤维束轴线间呈交织关系, 接近材料内部纤维束间打紧后的挤压变形规律。通过测算平均纱线填充因子并配合有限元法获得了纤维束及材料的弹性性能, 与试验结果符合较好。有限元仿真显示在材料单胞内, 纤维束承担主要载荷, 纤维束与基体的某些交界处往往会出现应力集中现象, 可能是发生裂纹扩展及局部破坏的主要区域。该细观应力场的获得也为分析材料破坏机理和强度提供了基础。      

Grain-size dependence of fracture stress in anisotropic brittle solids

The stress concentrations that occur at grain boundaries due to thermal expansion anisotropy and elastic stress concentration are discussed, and the stress intensity factor that results from these stresses is estimated. The procedure for the stress intensity factor calculation is based on the model in which a spherical crystal (grain) is forced into a cavity of equal size possessing annular or radial cracks emanating from the boundary. The stress intensity factor equation thus obtained is extended to include the effect of elastic stress concentration due to the presence of a cavity, and is subsequently used to predict the grain-size dependence of strength in anisotropic brittle ceramics. In assessing the degradation of strength with increasing grain size in non-cubic ceramics, it is shown that, in addition to grain size, the effect of pre-existing crack size must also be considered. Cubic ceramics, on the other hand, are known to exhibit no thermal expansion anisotropy and, based on the present model, their strength is predicted to be governed by the pre-existing flaw size, rather than the grain size.     

Simulation of Adhesive–Dissipative Behavior of a Microparticle Under the Oblique Impact

The adhesive–dissipative behavior of a microparticle under the oblique impact is investigated numerically and the new discrete element method (DEM)-compatible interaction model is elaborated. The modeling approach is based on the Derjaguin–Muller–Toporov model of normal interaction for the adhesive elastic contact. Adhesion hysteresis is specified by the loss of the kinetic energy governed by the fixed amount of the adhesion work, required to separate two adhesive contacting surfaces. This effect is captured in the new interaction model by adding an additional dissipative force component to normal contact during unloading and detachment. The essential feature of this approach, differing from that of the viscous damping model, is that, according to the proposed method, the amount of the dissipated energy is not influenced by the actual initial velocity during the entire contact. The influence of adhesion on slip friction is reflected by considering the adhesive normal force components in the Coulomb's law of friction. The contribution of the adhesion-related dissipation is illustrated by a comparison of the behavior of the attractive–dissipative and attractive–non-dissipative models. The oblique impact of a microparticle on the plane surface at the intermediate impact angle is also investigated numerically. The link between adhesion and friction is supported by the numerical results.     

From Single Particle AFM Studies of Adhesion and Friction to Bulk Flow: Forging the Links

The atomic force microscope (AFM) has been used to study inter-particle contacts in air for a range of model particles and cohesive granular materials of commercial importance. Adhesion (or pull-off force), friction and its load dependence, and particle size, morphology and roughness were measured for glass ballotini, fumed silica, alumina, limestone, titania and zeolite. Particle-wall contacts and effects of relative humidity were also studied. Most of the results, after allowing for roughness, are consistent with JKR contact mechanics and capillary bridge theory; however, the main object of the present work is to demonstrate semi-quantitative links between the AFM measurements and related bulk flow and cohesion measurements performed in parallel on the same materials. A simple model of a particle assembly will be used to compare average contact forces in typical single-particle AFM experiments and typical bulk experiments, and thus identify those regimes of powder flow where the two approaches overlap, and AFM measurements may be used with some confidence in more sophisticated modeling based on distinct element analysis (DEA). Four areas will be discussed briefly: (1) The apparent analogy between bulk yield loci and single-particle friction-load data; (2) Cohesion data and particle size effects; (3) Bulk tensile strength and single particle pull-off force; (4) Bulk wall friction and single-particle-wall friction. It is found that typical single-particle AFM experiments and bulk shear experiments converge for small particles (～ 4 μm) and low consolidation stress, when the average inter-particle contact forces are of the order 20–100nN, involve single or few asperities, and are not much larger than pull-off forces. For large particles and high consolidation loads the data do not overlap and AFM measurements may be less useful as input to simulations where sliding friction is less important, and where large normal contact forces dominate over tangential forces and are responsible for the shear strength.     

Effect of residual surface tension on the stress concentration around a nanosized spheroidal cavity

The effect of residual surface tension on the stress concentration around a nanosized spheroidal cavity in an isotropic elastic medium is analyzed based on the surface elasticity. Using the method of Boussinesq-Sadowsky’s potential functions, we obtained the solutions for the elastic field around the nanosized spheroidal cavity subjected to a uniformly uniaxial tension. It is shown that when the size of the cavity reduces to the same order of the ratio of residual surface tension to applied stress, the contribution from residual surface tension becomes important. Both the shape and the size of the cavity significantly affect the stress field and stress concentration around a nanosized cavity. The results are evidently different from the classical results, and are useful to the damage analysis and prediction of the effective moduli of heterogeneous materials containing nanosized cavities.     

Finite element analysis of frictionless contact between a sinusoidal asperity and a rigid plane: Elastic and initially plastic deformations

A series of finite element simulations of frictionless contact deformations between a sinusoidal asperity and a rigid flat are presented. Explicit expressions of critical variables at plastic inception including interference, contact radius, depth of first yielding, and pressures are obtained from curve fitting of simulation results as a function of material and geometrical parameters. It is found Hertz solution is not applicable to the critical contact variables at plastic inception for sinusoidal contact, although contact responses of initially plastic deformation follow the same trend as that of purely elastic deformation. The contact pressure at incipient plasticity, which is defined as yield strength, is dependent on Poisson’s ratio, yield stress, and geometrical parameters, but independent of elastic modulus. It is not yield stress, but yield strength that correlates with indentation hardness. The results yield the insight into the specification of material properties to realize elastic contact. A larger ratio of yield stress to elastic modulus is beneficial to sustain a larger load before plastic deformation.     

Influence of friction and adhesion on the onset of plasticity during normal loading of spherical contacts

Increasing contact loading causes early transformation from elastic to elastic–plastic deformations in many conventional systems as well as micro/nano-electro-mechanical systems. The load required for yielding and the location of the onset of plasticity is critical in the robustness of systems with contacts. For frictionless (such as fully-lubricated) contacts, inception of plastic yielding occurs beneath the contact surface. However, frictional slip (contact shear) and adhesion push the inception of plastic yielding toward the contact surface. The influence of elastic mismatch, shear tractions and adhesive normal tractions on the subsurface stress field is studied analytically by superposition of the Hertzian stress field and the stress field created by the shear and additional (due to adhesion) normal tractions. Specifically, three contact conditions have been studied in this work: (i) frictionless, (ii) finite friction, and (iii) infinite friction (full stick). Also, a finite-element model is developed to verify certain assumptions in the analytical solution for the contact with finite friction. The results obtained are applied to two sets of in situ nanoindentation experiments to explain the change in the yielding behavior of submicrometer polycrystalline aluminum grains.     

Peeling dynamics of fluid membranes bridged by molecular bonds: moving or breaking

Biological adhesion is a critical mechanical function of complex organisms. At the scale of cell–cell contacts, adhesion is remarkably tunable to enable both cohesion and malleability during development, homeostasis and disease. It is physically supported by transient and laterally mobile molecular bonds embedded in fluid membranes. Thus, unlike specific adhesion at solid–solid or solid–fluid interfaces, peeling at fluid–fluid interfaces can proceed by breaking bonds, by moving bonds or by a combination of both. How the additional degree of freedom provided by bond mobility changes the mechanics of peeling is not understood. To address this, we develop a theoretical model coupling diffusion, reactions and mechanics. Mobility and reaction rates determine distinct peeling regimes. In a diffusion-dominated Stefan-like regime, bond motion establishes self-stabilizing dynamics that increase the effective fracture energy. In a reaction-dominated regime, peeling proceeds by travelling fronts where marginal diffusion and unbinding control peeling speed. In a mixed reaction–diffusion regime, strengthening by bond motion competes with weakening by bond breaking in a force-dependent manner, defining the strength of the adhesion patch. In turn, patch strength depends on molecular properties such as bond stiffness, force sensitivity or crowding. We thus establish the physical rules enabling tunable cohesion in cellular tissues and in engineered biomimetic systems.     

Cohesive Fracture Model Based on Necking

A linear hardening model together with a linear elastic background material is first used to discuss some aspects of the mathematical and physical limitations and constraints on cohesive laws. Using an integral equation approach together with the cohesive crack assumption, it is found that in order to remove the stress singularity at the tip of the cohesive zone, the cohesive law must have a nonzero traction at the initial zero opening displacement. A cohesive zone model for ductile metals is then derived based on necking in thin cracked sheets. With this model, the cohesive behavior including peak cohesive traction, cohesive energy density and shape of the cohesive traction–separation curve is discussed. The peak cohesive traction is found to vary from 1.15 times the yield stress for perfectly plastic materials to about 2.5 times the yield stress for modest hardening materials (power hardening exponent of 0.2). The cohesive energy density depends on the critical relative plate thickness reduction at the root of the neck at crack initiation, which needs to be determined by experiments. Finally, an elastic background medium with a center crack is employed to re-examine the shape effect of cohesive traction–separation curve, and the relation between the linear elastic fracture mechanics (LEFM) and cohesive zone models by considering the cohesive zone development and crack growth in the infinite elastic medium. It is shown that the shape of the cohesive curve does affect the cohesive zone size and the apparent energy release rate of LEFM for the crack growth in the elastic background material. The apparent energy release rate of LEFM approaches the cohesive energy density when the crack extends significantly longer than the characteristic length of the cohesive zone.     

Sliding-induced adhesion of stiff polymer microfibre arrays. II. Microscale behaviour.

The adhesive pads of geckos provide control of normal adhesive force by controlling the applied shear force. This frictional adhesion effect is one of the key principles used for rapid detachment in animals running up vertical surfaces. We developed polypropylene microfibre arrays composed of vertical, 0.3 microm radius fibres with elastic modulus of 1 GPa which show this effect for the first time using a stiff polymer. In the absence of shear forces, these fibres show minimal normal adhesion. However, sliding parallel to the substrate with a spherical probe produces a frictional adhesion effect which is not seen in the flat control. A cantilever model for the fibres and the spherical probe indicates a strong dependence on the initial fibre angle. A novel feature of the microfibre arrays is that adhesion improves with use. Repeated shearing of fibres temporarily increases maximum shear and pull-off forces.     

Elastic-plastic adhesive contact of non-Gaussian rough surfaces

The paper describes an analysis of adhesion at the contact between non-Gaussian rough surfaces using the Weibull distribution with skewness as the key parameter to characterize asymmetry. The analysis uses an improved elastic-plastic model of contact deformation that is based on accurate Finite Element Analysis (FEA) of an elastic-plastic single asperity contact. Large range of interference values is considered starting from fully elastic through elastic-plastic to fully plastic regime of contacting asperities. The well-established elastic and plastic adhesion indices are used to consider the different conditions that arise as a result of varying load and material parameters. The loading and unloading behaviour for different combinations of the adhesion indices and skewness values are obtained as functions of mean separation between the surfaces. Transitional values of adhesion indices and skewness at which the influence of surface forces becomes insignificant are found to depend on material and surface parameters. Comparison with studies using previous elastic-plastic model that was based on some arbitrary assumptions shows significant differences in loading behaviour.     

具有曲面接触斑弹性体滚动接触理论及其数值方法

该文基于了Kalker三维弹性体非Hertz滚动接触理论模型,考虑滚动接触物体具有曲面接触斑,利用有限元法,推导出物体柔度系数,即力与位移之间的关系,将理论模型转化为数学上的非线性规划问题。结合拉格朗日乘子法,求解非线性方程组,从而得到接触斑力学行为。该模型是考虑曲面接触斑三维弹性体滚动接触理论模型,考虑了滚动接触物体的真实几何尺寸和接触区外边界因素对滚动接触行为的影响。为解决任何几何形状弹性体滚动接触问题提供了方法。该文主要对二维问题的数值模拟,所得数据结果较为合理。并结合商业有限元软件计算结果对静态问题进行对比验证,两种模型的分析结果吻合的较好。该文的模型和数值方法进一步完善后将适用于任意曲面接触斑滚动接触问题的求解。     

In situ elasticity and adhesion measurement of biomembrane by a video enhanced depth-sensing indentation technique

Elasticity and adhesion of a prestressed circular biomembrane to planar graphite surface was investigated by a video enhanced depth-sensing indentation technique. This biomembrane was a combination of human skin cells and biodegradable polymer. Using this kind of membrane as a skeleton facilitated the easy formation of the hybrid sponges into desired shapes that had a high mechanical strength, while the collagen micro sponges nested in the pores, which allowed the cells to interact with the collagen surfaces. A homemade indenter apparatus was constructed to meet force and displacement resolutions of 0.1 μN and 10.0 nm. The indenter possessed the capability of measuring the applied force and resultant displacement simultaneously. By armed with a high magnification side-view system, it could record lateral profile variation of biomembrane, which was essential for observing and analyzing its gradually rupture. A linear theoretical elastic solution was applied to quantitatively interpret the measured central displacement of the membrane under a central point load. Elastic modulus of the biomembrane could be easily determined once the applied force and the central displacement, together with the essential dimensions were known. The biomembrane “jump-into” an adhesion contact when the punch approached the range of the intersurfaces force across the punch-membrane gap. A “pull-off” event was observed at a nonzero contact circle when the tensile load reaching a critical threshold. This technique provided the capability of measuring mechanical behaviors of prestressed ultra thin tissue and thin-walled biocapsules with a residual stress.