Search

An analytical solution is presented for adhesive contact of a rigid disc inclusion embedded in a penny-shaped crack in a transversely isotropic piezoelectric material. By virtue of Hankel transforms and a method of potentials, the mixed boundary-value problem is formulated as dual and triple integral equations, which, in turn, are reduced to Fredholm integral equations. The results of primary interest to engineering applications, namely, the total indentation load, the total electric charge, and stress intensity factor at the tip of the crack are evaluated as integral equations in terms of dimensionless parameters. Finally, to reveal the efficacy of the proposed method and also to verify it, comparison is made with indentation solutions in transversely isotropic and isotropic media. [ABSTRACT FROM AUTHOR]

In soft lithography roof collapse is frequently observed on the stamp surface consisting of rectangular micro-grooves which yields unwanted contact between the sagged surface and the substrate. Deep understanding of the adhesive contact behavior is a key to design of high-performance collapse-resistant stamp. Both theoretical and numerical studies are presented for a single rectangular micro-groove in the middle of the stamp surface under applied pressure. The JKR-type adhesion solution is established by the principle of superposition and equivalent energy release rate, with a series of closed-form expressions derived which are consistent with previous studies. Finite element analysis (FEA) is performed based on virtual crack closure technique (VCCT) to investigate the roof collapse mechanism with interfacial adhesion and applied pressure considered. Comparison of theoretical, numerical, and experimental results demonstrates that both size effect and constitutive nonlinearity of the stamp on the self-collapse contact width are not obvious for shallow grooves but become prominent for deep grooves, so that the obtained analytical solution is limited to shallow grooves due to its assumptions of half-plane and linear elasticity adopted for the stamp. For deep grooves, the present FEA method shows potential to capture more accurate results. [ABSTRACT FROM AUTHOR]

The sharp morphological features of lunar dust particles generate significant elastic–plastic contact forces and deformations upon contact with material surfaces, which considerably affect the mechanical properties of lunar dust particles, including their contact, collision, adhesion, transport, and wear characteristics. Despite these severe effects, valid models considering the contact characteristics of typical sharp-featured lunar dust particles are currently lacking. This study proposes an elastic–plastic contact model for nonrotationally symmetric lunar dust particles showing typical sharp features. Detailed derivations of the expressions for various physical responses observed when lunar dust particles establish normal contacts with elastic and elastic–plastic half-spaces under adhesive conditions are also provided. These include derivations for elastic forces, elastic–plastic forces, contact areas, pull-off forces, residual displacements, and plastic deformation areas. Furthermore, the tangential pull-off force during the tangential loading of lunar dust particles is derived, and the tangential contact characteristics are explored. Comparisons of the results of the proposed model with those of previous experiments reveal that the proposed model shows errors of only 6.06 % and 1.03 % in the maximum indentation depth and residual displacement, respectively. These errors are substantially lower than those of conventional spherical models (60.30 % and 60.13 %, respectively), confirming the superior accuracy of the proposed model. Furthermore, the discrete element method is employed to analyze the effects of normal and tangential contacts, dynamic characteristics, and plastic deformations on the considered lunar dust particles. The results are then compared with those of existing contact models. They reveal that maximum elastic–plastic forces under normal contact conditions are positively correlated with the initial velocity but negatively correlated with the lateral angle. Furthermore, the tangential pull-off force is positively correlated with the normal force and surface energy. In addition, the contact duration of lunar dust particles is positively correlated with their initial velocities, while the residual displacement is negatively correlation. For instance, as the initial velocity increases from 10 to 50 m/s, the maximum elastic–plastic force increases from 37.64 to 321.72 mN. Comparisons of the proposed model with other contact models reveal that the maximum elastic–plastic force of the elastic–plastic triangular pyramid model is only 14.93 % that of the cylindrical model, 34.23 % that of the spherical model, and 76.27 % that of the conical model, indicating significant reductions in the maximum elastic–plastic force owing to the plastic deformations of particles with typical sharp features. Overall, the results of this study offer crucial insights into the mechanical characteristics of nonspherical lunar dust particles under various contact conditions, such as elastic–plastic and adhesive contacts, and can guide in situ resource utilization on the lunar surface and for craft landings. • Elastic–plastic contact forces and deformations of nonrotationally symmetric lunar dust particles. • Normal and tangential contacts, dynamic contact characteristics, and plastic deformations of particles. • Maximum elastic–plastic forces increase with initial velocities and decrease with lateral angles. • Increasing initial velocities increase contact durations and decrease residual displacements. [ABSTRACT FROM AUTHOR]

The current research on theoretical modeling of the surface roughness of brittle materials generally regards the tool as a rigid body. Incorporating tool factors into theoretical models of surface roughness is challenging because the influence of tool-workpiece coupling contact on surface roughness remains unclear. This paper investigates the tool-workpiece coupling contact mechanism using contact mechanics analysis: collision contact between the rake face and the material, adhesive contact between the cutting edge roundness and the material, and hertz contact between the flank face and the material. The tool-workpiece coupling contact causes the material to fracture and break, and the tool undergoes collision wear, adhesive wear, and abrasive wear. The formation of pits is attributed to the tool's cutting action on the workpiece, whereas the presence of hard convex peaks is a consequence of the workpiece's reverse cutting into the tool. A quantitative description of hard convex peaks and pits on machined surfaces was based on contact mechanics, fracture mechanics, and tribology. A novel theoretical model is developed for characterizing the surface roughness of brittle materials. Turning verification experiments were carried out using different tools, workpieces, and tool parameters. The predicted values and experimental measurements are similar and have the same trend, indicating that the model is accurate. This paper is the first to consider both the tool and the workpiece as the influencing objects of the surface roughness of brittle materials, and it innovatively incorporates tool wear and tool material properties into the parameters of the theoretical model of surface roughness. It offers a fresh perspective on predicting the theoretical surface roughness model for brittle materials. [ABSTRACT FROM AUTHOR]

Non-axisymmetric frictionless JKR-type adhesive contact between a rigid body and a thin incompressible elastic layer bonded to a rigid base is considered in the framework of the leading-order asymptotic model, which has the form of an overdetermined boundary value problem. Based on the first-order perturbation of the Neumann operator in the Dirichlet problem for Poisson's equation, the decohesion initiation problem is formulated in the form of a variational inequality. The asymptotic model assumes that the contact zone and its boundary contour during the detachment process are unknown. The absence of the solvability theorem is illustrated by an example of the instability of an axisymmetric flat circular contact. [ABSTRACT FROM AUTHOR]

The classical adhesive contact models belong to isothermal adhesion theories, where the effect of temperature on adhesion was neglected. However, a number of experimental results indicated that the adhesion behaviors can be significantly affected by temperature. In this paper, the two-dimensional non-slipping anisothermal adhesion behaviors between two orthotropic elastic cylinders are investigated within the framework of the Johnson–Kendall–Roberts theory. The stated problem is reduced to the coupled singular integral equations by virtue of the Fourier integral transform, which are solved analytically with the analytical function theory. The closed-form solutions for the stress fields in the presence of thermoelastic effect are obtained. The stable equilibrium state of contact system is determined by virtue of the Griffith energy balance. The effect of temperature difference on adhesion behaviors between orthotropic solids is discussed. It is found that the difference between the oscillatory and non-oscillatory solutions increases with increasing the degree of anisotropy of orthotropic materials. The oscillatory solution cannot be well approximated by the non-oscillatory solution for the orthotropic materials with relatively high anisotropy. [ABSTRACT FROM AUTHOR]

This paper developed a finite element model based on the Derjaguin approximation and the Lennard–Jones potential to describe a single loading-remaining-unloading cycle of adhesive contact in elastoplastic and viscoelastic media. The effects of tangent modulus, the Prony coefficient, and the times on the adhesive contact behaviors were examined. Some complicated phenomena on rate-dependent adhesion in viscoelastic media and history-dependent adhesion in elastoplastic media were understood. The simulation results showed that both the pull-off force and final central gap were negatively correlated with tangent modulus while positively with the Prony coefficient; the pull-off force and the final central gap synchronously rose as the loading time or the remaining time increased; the effect of the remaining time on the pull-off force is stronger than the loading time. [ABSTRACT FROM AUTHOR]

The adhesive contact between a rigid cylinder and an elastic layer bonded on a rigid half-space is investigated. In the past, several analytical models were proposed in the frame of the JKR model. In this research, boundary element method is employed. The traction is derived on the basis of the Lennard-Jones potential and the Derjaguin approximation. The whole solutions are obtained. The effects of Tabor parameter and layer thickness are investigated. The results are compared with the analytical models. The limitations of the analytical models are obtained. The empirical formulas for pull-off forces, jump-in distance, and pull-off distance are proposed. [ABSTRACT FROM AUTHOR]

Contact behaviors of medical devices, such as guidewires and catheters, are critical in endovascular surgeries. In this work, a new method to predict adhesive contact force between catheter and vascular artery is presented. Multi-asperity adhesion on the surface of vascular artery, deformation of asperity and deformation of vascular substrate are all considered. The single asperity behavior is described with Johnson-Kendall-Roberts (JKR) contact model. The multi-asperity behavior is based on Greenwood–Williamson (GW) asperity model. Vascular substrate is considered as elastic bulk substrate and its deformation is determined with Hertzian pressure from asperity on a circular region on the elastic half space. The model shows that the deformation of vascular substrate accounts for the majority of the total contact deformation and significantly affects the predicted contact force. The model is verified with published experimental data. The comparison shows that the model produces very accurate prediction of contact force between catheter and vascular artery when the contact force is compressive. Parametric analysis based on asperity topography is carried out. The analysis shows that the diameter of the circular region of the interface between asperity and vascular substrate has more significant effect on the estimation of contact force than the radius of asperity. Further validation of prediction accuracy of the model under experiment is needed. [ABSTRACT FROM AUTHOR]

The frictional responses of graphene and boron nitride lubricants is studied from the perspective of the potential energy evolution. At a low normal load regime and high interface adhesion, friction can be effectively characterized by investigating the interfacial energy barrier formation process. By decomposing the energy evolution into strain and interfacial cohesive components, we find that the oscillation phase difference plays an essential role in the friction response and is controlled by the energy conversion between them. Analyses further reveal that the energy oscillations are excited by the vertical motion of the sliding asperity that induces periodic deformation and position changes in the lubrication systems. These new findings suggest the study of potential energy evolution is advantageous for understanding adhesive friction and infers the potential to leverage adhesion in 2D lubricant application through high conversion efficiency and out-of-phase oscillations between strain and cohesive energies.

The nanoindentation technique plays a significant role in characterizing the mechanical properties of materials at nanoscale, where the adhesion effect becomes very prominent due to the high surface-to-volume ratio. For this paper, the classical adhesion theories were generalized to study the contact behaviors of various piezoelectric materials indented by conical punches with different electric properties. With the use of the Hankel integral transform, dual integral equations, and superposing principle, the closed-form solutions of the physical fields for the Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (M-D) models were obtained, respectively. The contribution of the electrical energy to the energy release rate under the conducting punch was taken into consideration. The relationships between the contact radius, the indentation load, and the indentation depth were set up using the total energy method for the JKR model and the Griffith energy balance for the M-D model, respectively. Numerical results indicate that increasing the half cone angle of the conical punch enhances the adhesion effect, which can significantly affect the accuracy of the results of characterization in nanoindentation tests. It was found that the effect of electric potential on adhesion behaviors is sensitive to different material properties, which are not revealed in the existing studies of axisymmetric adhesive contact of piezoelectric materials and multiferroic composite materials. The load-displacement curves under conical punches with different half cone angles have very different slopes. These results indicate that the half cone angle has a prominent effect on the characterization of mechanical properties of piezoelectric solids in nanoindentation tests. [ABSTRACT FROM AUTHOR]

Considering the elastoplastic deformation of a single-crystal copper substrate, based on the atomic scale, a mixed potential function (EAM and Morse) and the Verlet algorithm were used to simulate the adhesion contact and separation process between a hemispherical diamond indenter and a single-crystal copper substrate at low temperatures. The influences of the temperature on the micro/nanomechanical properties of the material surface and on the mechanism of the subsurface deformation process were analysed. The results show that as the simulated temperature decreases, the time for adhesion to occur is delayed, and the adhesion forces increase slightly. While the indenter is being pressed, the temperature affects the generation and interaction of the dislocations in the substrate. As the temperature decreases, a large number of dislocations in the substrate are generated and then relatively reduced, and the load on the indenter fluctuates. A calculation of the mechanical properties of the material found that the contact stiffness was related to the elastic recovery energy. A smaller elastic recovery energy leads to a greater contact stiffness; thus, the indentation hardness is related to the plastic deformation energy. An increased plastic deformation energy results in a decreased indentation hardness. [ABSTRACT FROM AUTHOR]

This paper develops the adhesive contact theory for a one-dimensional hexagonal quasicrystal half-space punched by a spherical indenter on the basis of the classical adhesive contact models involving the Johnson–Kendall–Roberts (JKR) model, the Maugis–Dugdale (MD) model and the Derjaguin–Muller–Toporov (DMT) model. By using the superposition principle combined with the Griffith energy balance, all the significant physical quantities for adhesive contact, such as the energy release rate, indentation force, penetration depth, contact radius and pull-out force, are obtained for different models. The result for the DMT model is derived from the MD solution through a limiting procedure. A numerical calculation is carried out to verify the present analytical solutions, to compare different contact models, and to analyze the influence of the phason field on the results. It is indicated that the effect of the phason field on the result for the MD model is pronounced, especially for a small contact radius. However, the phason effect on the JKR and DMT results is not significant. The present solution can serve as a theoretical basis for nano-indentation and atomic force microscopy to measure the material properties of quasicrystals. [ABSTRACT FROM AUTHOR]

Mechanical transformation of rough diamonds into brilliant ones is usually achieved by polishing using microsized abrasive diamond particles. It is shown that in addition to formation of periodic pattern of 'partial' Hertzian cone cracks on the diamond surface, nano-sized domains (50–150 nm in diameter) of crumbled material are observed. Because these domains are located in the centres of the regions (250–500 nm in diameter) partially surrounded by the Hertzian cone cracks, where the stresses are close to the stress field of hydrostatic compression, the material removal cannot be explained by creation of tensile or shear cracks. It is argued that the creation of these domains of crumbled material is due to adhesive interactions between sliding diamond particles and the diamond surface. Employing a two-term law of friction, the scheme of ultimate equilibrium between the particle and the surface is presented. The distributions of contact stresses are calculated for two approaches: (i) the extended Johnson–Kendall–Roberts model and (ii) the 'soft' model of adhesive contact. Thus, adhesion between the sliding diamond particle and the surface leads to creation of periodic pattern of the crumbling domains with the steps 500–1000 nm and adhesive tearing out of the material from the domains. This article is part of the theme issue 'Nanocracks in nature and industry'. [ABSTRACT FROM AUTHOR]

In the conventional adhesive contact mechanics, the value of the Tabor parameter μ provides criterion for the applicability of the JKR and the DMT models. While the JKR model is an appropriate approximation for a large Tabor parameter (μ > 5), Ciavarella et al. demonstrated that the JKR theory overestimates the hysteresis loss during an approach-retraction period, even though the Tabor parameter is high enough. The present study investigates how surface tension affects the hysteretic loss in an approach-retraction cycle of spherical adhesive contact. With surface tension, Wu's solution is invalid in terms of the prediction of the jump-in position. Based on Civarella's research, we developed a hybrid model to approximate the hysteretic loss. This model used direct numerical solution from the Lennard-Jones potential Law. The same method can also be generalized to the spherical contact system with finite stiffness, in terms of hysteretic loss determination. [ABSTRACT FROM AUTHOR]

This paper has revisited the roof deformation and collapse of stamps with isolated grooves based on a contact mechanics approach, with emphasis on establishing the nonadhesive and adhesive contact solutions for surfaces containing a shallow rectangular groove with the effects of applied load and interfacial adhesion taken into account. By solving singular integral equations and using the energy release rate approach, closed-form solutions are derived analytically for the deformed groove shapes, interfacial stress distributions, and equilibrium relations between load and contact size, which reduce to the previously proposed solutions without adhesion or without applied load. Finite element (FE) analysis is performed to validate the nonadhesion solutions, while experiment results of stamp collapse reported in the literature are adopted to examine the adhesion solutions. By introducing the Johnson parameter a to represent a competition between surface energy and elastic strain energy of the groove, four kinds of contact behaviors of the groove roof can be characterized appropriately: nonadhesion, weak adhesion, intermediate adhesion, and strong adhesion. Hysteresis loop and energy loss due to distinct load/unloading paths are revealed in the cases of intermediate and strong adhesion. We have also provided the critical applied pressure to achieve roof collapse and the corresponding equilibrium contact size for full range of a. [ABSTRACT FROM AUTHOR]

There exist many well-known analytical models for adhesive contact for spherical asperities. However, in many situations, the asperities are not spherical and may be better described by a power-law function. Thus, these well-known analytical models were extended to power-law-shaped axisymmetric asperities in the past decades. In this paper, numerical simulation is employed for the adhesive contact between a rigid power-law axisymmetric asperity and an elastic half-space. The realistic Lennard-Jones potential and the Derjaguin approximation are used for the surface traction. Numerical simulations are performed with different shape indexes and different Tabor parameters. The whole solution is obtained. Semi-empirical formulas for the pull-off forces, the contact radius at zero loads, the jump-in distance, and the pull-off distance are proposed. All these equations are both simple and as accurate as of the numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a multiscale moving contact line (MMCL) theory is presented and employed to simulate liquid droplet spreading and capillary motion. The proposed MMCL theory combines a coarse-grained adhesive contact model with a fluid interface membrane theory, so that it can couple molecular scale adhesive interaction and surface tension with hydrodynamics of microscale flow. By doing so, the intermolecular force, the van der Waals or double layer force, separates and levitates the liquid droplet from the supporting solid substrate, which avoids the shear stress singularity caused by the no-slip condition in conventional hydrodynamics theory of moving contact line. Thus, the MMCL allows the difference of the surface energies and surface stresses to drive droplet spreading naturally. To validate the proposed MMCL theory, we have employed it to simulate droplet spreading over various elastic substrates. The numerical simulation results obtained by using MMCL are in good agreement with the molecular dynamics results reported in the literature.

The prediction of tensile strength properties of powder compacts remains an important industrial issue. In particular, one of the main problems of the powder compaction process is the failure of compacts. Indeed, some powder compacts exhibit cracks which appear during compaction. Such defects occur due to localised tensile or shear stresses, for example close to geometrical singularities. They are also related to the ability of a powder to create enough adhesion at contacts between particles to withstand tensile stresses. Therefore, cracks are a consequence of phenomena occurring at the particle scale and below, down to the molecular scale. To help understanding this mechanism, a particle-scale, numerical method called the multi-particle finite-element method was developed using the finite-element software suite Abaqus (Abaqus 6.14 Documentation, 2016). Such a method allowed to explicitly model the microstructure of a granular media idealised as an assembly of elastic–plastic spheres. The particles were meshed such that their deformations were fully taken into account, using a continuum-mechanics-based material model. The interactions between particles were managed using finite-element contact formulations. A multi-scale, adhesive contact model was developed based on the literature and implemented into the multi-particle finite-element code. The contact model was based on a surface energy formulation weighted by the roughness model developed by Pullen and Williamson (1972). It introduced a novel aspect, the development of adhesion under the effect of external mechanical loads, which is consistent with the cold compaction process. This model was then applied to predict the mesoscopic properties of a packing of spheres, i.e. its response to mechanical stresses of any type, in particular strongly deviatoric stress paths. Such a method intends to be a help toward the development of an efficient continuum model for the modelling of the powder compaction process. • Contact adhesion was implemented into the multi-particle finite-element method. • A new adhesive contact model including the effect of surface roughness was developed. • It was validated against existing adhesive, elastic–plastic contact models. • Adhesion had an influence on yield properties under tensile and shear loading paths. [ABSTRACT FROM AUTHOR]

Atomic force microscopy (AFM) studies of living biological cells is one of main experimental tools that enable quantitative measurements of deformation of the cells and extraction of information about their structural and mechanical properties. However, proper modelling of AFM probing and related adhesive contact problems are of crucial importance for interpretation of experimental data. The Johnson-Kendall-Roberts (JKR) theory of adhesive contact has often been used as a basis for modelling of various phenomena including cell-cell interactions. However, strictly speaking the original JKR theory is valid only for contact of isotropic linearly elastic spheres, while the cell membranes are often prestressed. For the first time, effects caused by molecular adhesion for living cells are analytically studied taking into account the mechanical properties of cell membranes whose stiffness depends on the level of the tensile prestress. Another important question is how one can extract the work of adhesion between the probe and the cell. An extended version of the Borodich-Galanov method for non-direct extraction of elastic and adhesive properties of contacted materials is proposed to apply to experiments of cell probing. Evidently, the proposed models of adhesive contact for cells with prestressed membranes do not cover all types of biological cells because the structure and properties of the cells may vary considerably. However, the obtained results can be applied to many types of smooth cells and can be used to describe initial stages of contact and various other processes when effects of adhesion are of crucial importance. [ABSTRACT FROM AUTHOR]

We investigate experimentally and numerically the influence of chemical heterogeneity and of third-body particles on adhesive contact. Chemical heterogeneity is generated by chemical treatment of the contacting bodies changing locally the surface energy. For studying the influence of the third body, two types of particles are used: sand particles with various geometrical shapes and sizes, and steel spheres of equal radius. Dependencies of the normal force on the indentation depth at both indenting and pull-off as well as the evolution of the contact configuration are investigated. Corresponding numerical simulations are carried out using the boundary element method (BEM).

Using the well-known Lennard–Jones potential and a recently proposed surface energy density-based elastic theory, we analyze the adhesive contact behavior between a rigid spherical nano-indenter and an elastic half-space in this paper. With the help of Newton's method of iterations and arc-length continuation algorithm, both contact pressure and normal displacement at the indented surface are obtained numerically, based on which the load–approach curves are further achieved. It is found that the surface effect could be characterized by only one intrinsic length, i.e., the ratio of bulk surface energy density to shear modulus of the indented material. Comparison of the results with or without surface effect shows that the surface effect leads to a smaller pull-off force. Moreover, for the case of a zero-external loading, the corresponding approaches become smaller than the classical predictions, which qualitatively agree with the existing experimental findings. This indicates the elastic substrate becomes hardened due to the surface effect. All the study should have contributions to the deep understanding of surface effect on nanoscale adhesive contact behaviors. [ABSTRACT FROM AUTHOR]

We report a series of experiments on the indentation of steel indenters into a soft layer of transparent rubber with relatively high adhesion. The roughness properties of the steel indenters are varied by undergoing preparation using sandpaper with different grain sizes. Starting from a smooth surface, additional roughness increases the adhesive strength up to a critical roughness value, after which it significantly decreases. Furthermore, we look at the evolution of the contact area during slow indentation and detachment. It was found that, during indentation, the contact area changes more sharply compared to detachment (pull-off).

The bearing behavior of suction caissons supporting offshore wind turbines under two-way cyclic lateral loading and dead load in clay was investigated with consideration of soil strength degradation and adhesive interface friction between caisson walls and heterogeneous clay using the finite-element package ABAQUS. An ABAQUS built-in user subroutine was programmed to calculate the adhesive interface friction between clay and caisson walls. The results of parametric studies showed that the degradation of bearing capacity could be aggravated by the decrease of the aspect ratio. The offset between the rotation point of the soil inside the caisson and the central axis of the caisson increased with the increasing vertical load and number of cycles. The linearly increasing strength profile and adhesive interface led to the formation of an inverted spoon failure zone inside the caisson. The settlement-rotation curves in each cycle moved downwards with increasing number of cycles due to the soil strength degradation. [ABSTRACT FROM AUTHOR]

By incorporating the adhesive force as a body force in the finite element method, the adhesive contact between a diamond sphere and the iron substrate is studied. The adhesive force is derived from Morse potential by integrating the pair potential function over the spherical domain. Based on the tensile behaviors of iron nanowires, the elastic and elastoplastic material parameters are obtained for the substrate. As the radius of the sphere is larger than 320 nm and the maximum depth of indentation is one-tenth of the radius of the sphere, the adhesion caused by interatomic interaction between diamond and iron is small enough to ignore. Then take the sphere whose radius is 20 nm as an example, the results of a single load–unload cycle and multiple load–unload cycles are discussed. In the contact process between the sphere and the surface, the phenomena jump-to-contact and jump-off-contact were observed. Further, the stress distributions inside the substrate and the pressure distribution are investigated. With the analysis of the results, the proposed method can be used to simulate the mechanical behaviors under micro-nano scale contact. [ABSTRACT FROM AUTHOR]

The adhesive contact between a rigid sphere and a thin elastic layer bonded on a rigid foundation is investigated using boundary element method (BEM). Surface profile is approximated parabolic. The Lennard-Jones potential and the Derjaguin approximation are used for the surface traction. In the past, the adhesive contact between a sphere and a thin layer was analyzed only in the frame of the JKR theory. In this article, the adhesive contact is investigated with different Tabor parameters and different layer thickness. The whole solutions are obtained. The results are compared with the current analytical models and the simulation for the adhesive contact between spheres. The restrictions of the analytical models are obtained. The empirical formulas for jump-in and pull-off distance are proposed. [ABSTRACT FROM AUTHOR]

This paper investigates a feasible nondestructive method for micron-sized kissing defects in the composite insulators, which are commonly utilized in ultra-high voltage (UHV) power grid. In this paper, cylindrical adhesive contact model was established to describe the obvious distortion of ultrasound propagation caused by kissing defects on the polymeric interface of composite insulators. The ultrasonic nonlinearity parameter was measured for each of the kissing defective and intact specimens. Moreover, the theoretical analysis has been proved by the test results on the kissing defective samples, which indicates that the 0.7 μm kissing defects existed in the composite insulators could be successfully recognized by the nonlinear ultrasonic methods and the nonlinearity is reduced by interface roughness. [ABSTRACT FROM AUTHOR]

The adhesive contact problem of a half-space indented by a rigid cylindrical punch in the theory of couple-stress elasticity is investigated. Both the size effect and adhesion are considered to analyze the two-dimensional frictionless contact problem. The method of Mindlin's stress function and the technology of Fourier transform are applied to reduce the mixed boundary value problem to the singular integral equations. Efficient computational techniques is used to obtain the influence of the size effect and adhesion parameter on the adhesive contact behavior. Results indicated that the size effect play an important role in contact with adhesion and can help understanding the mechanism of adhesion. [ABSTRACT FROM AUTHOR]

[Display omitted] • Surface roughness affects the droplet profile, which then affects the wet adhesion. • A JKR mechanical model combined with thermodynamic method is proposed. • Precise pull-off force is obtained by dynamic meniscus surface and capillary force. • Experiments in different liquid environments verified the theoretical findings. Understanding wet adhesion is vital for advancing technologies such as underwater robotics, aquatic microsystems, and sweat-interfaced devices. It involves the formation of a liquid bridge with a meniscus between two solid surfaces. This phenomenon has a significant impact on surface adhesion, particularly in relation to roughness. Determining the profile of this liquid bridge is critical for accurately characterizing wet adhesion. In this paper, we propose a JKR mechanical model combined with a thermodynamic approach to investigate adhesive contact between a spherical indenter and an axisymmetric wavy surface in a wetting environment. The numerical solution for the pull-off force is obtained by considering parameters such as waviness, roughness, liquid volume, and liquid surface energy. The theoretical findings validated by experimental results provide insights into wet adhesion mechanisms on rough surfaces. [ABSTRACT FROM AUTHOR]

• A 3D numerical model for solving the adhesive contact problem of heterogeneous materials. • A new adhesive displacement driven CGM. • Coupling effects of inhomogeneity and adhesion on normal traction and adhesive zones. • Interaction of surface roughness and inhomogeneity and its on normal traction and adhesive zones. This paper reports a three-dimensional numerical model to solve adhesive elastic contact problem of heterogeneous materials with an engineered rough surface. This model integrates the Maugis-Dugdale (MD) adhesive contact model, the Boussinesq-Cerruti integral equations, the equivalent inclusion method (EIM), and the discrete convolution and fast Fourier transform (DC-FFT) algorithm, aiming at accurate determination of contact results for heterogeneous materials. An adhesive displacement-driven conjugate gradient method (CGM) was also developed to support rapid solutions of contact pressure and contact area. Four cases were analyzed to verify this model with satisfaction. This model was used to analyze the effects of inhomogeneity (location, size, and material properties) and adhesion on micro-adhesive-elastic contact, and the results lead to a curve-fitting equation for quick evaluation of the effects of inhomogeneity properties and adhesion characteristics on normal traction. It was also utilized to study the influence of the roughness level of a type of rough surface on the surface adhesion behavior. [Display omitted] [ABSTRACT FROM AUTHOR]

Nanoindentation technique has been widely applied to characterize the electromechanical properties of piezoelectric materials, where the adhesion effect induced by different surface forces becomes very prominent. The indenter tip should have more general profile rather than just three common simple shapes (flat, cone and sphere) in practical testing. In this study, the classical Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (M-D) models are extended to investigate the adhesion behaviors of a piezoelectric half-space indented by the power-law shaped punches with different electric properties, whose shape index is denoted as n. The JKR- n and M-D- n adhesion models for both the electrically conducting and electrically insulating punches are set up by means of Griffith energy balance. The Derjaguin-Muller-Toporov- n (DMT- n) adhesion solutions are derived from the corresponding M-D- n adhesion models as the limiting cases. The generalized Tabor parameter and interfacial adhesion strength applicable to piezoelectric materials are defined for the first time, with the former being used to describe the transition behavior from JKR- n model to DMT- n model. The impacts of the electric loading and the shape index on adhesion behaviors are discussed in detail. It is found that the pull-off force increases with the electric potential, which reveals the adhesion strengthening effect caused by electric loading. The shape index has a prominent influence on the pull-off force, interfacial adhesion strength, contact radius at pull-off moment, indentation depth and contact radius at self-equilibrium state, and the transition behavior from JKR- n model to DMT- n model. The results derived from this work not only are helpful to understand the contact behaviors of piezoelectric materials at micro/nano scale, but also provide a theoretical basis for nanoindentation technique in evaluating material properties of piezoelectric mediums. • The JKR-n and M-D-n adhesive contact models for piezoelectric materials under the power-law shaped indenters with different electric properties are established. • A generalized Tabor parameter is defined for the first time to describe the transition behaviors from JKR-n model to DMT-n model. • The pull-off force increases with increasing the electric potential, but it is not a monotonical function with respect to the shape index of the indenter. • The shape index has a significant effect on the pull-off force and the interfacial adhesion strength. [ABSTRACT FROM AUTHOR]

To model the deep penetration process of T-bar in soft clay, an adhesive contact algorithm was developed in conjunction with the Coupled Eulerian–Lagrangian approach with consideration of the effect of strain softening. Numerical results show the simulated penetration resistance agrees well with the previous centrifuge experimental data. The failure mechanisms of the clay around the T-bar can be divided into three stages, including shallow penetration stage with global failure mechanism, partially and fully back-flow stages with local failure mechanism. Fluctuations of the penetration resistance can be explained by the formation and evolution of shear bands around the T-bar. Newly formed shear bands would intersect the previously formed shear bands in the partially back-flow stage, which results in the formation of "ear-shaped" areas rotating anticlockwise around the T-bar. The evolution of shear bands would form a similar fabric structure in the fully back-flow stage. [ABSTRACT FROM AUTHOR]

The paper deals with an equilibrium problem of two bodies adhesively bonded to each other along the part of interface between them. There is a crack on the rest part of the interface. The bonding between the bodies is described by "spring type" condition modeling a soft and thin material layer. We also impose non-penetration conditions and Tresca's friction conditions on the interface including both the adhesive layer and the crack. The non-penetration condition excludes mutual penetration of bodies. A formula for the derivative of the energy functional with respect to the crack length is obtained. It is shown that the derivative can be represented as a path-independent integral (J -integral). Moreover, a non-overlapping domain decomposition method for the bonded structure is proposed and its convergence is studied theoretically and numerically. The numerical study shows the efficiency of the proposed method and the importance of the non-penetration condition. [ABSTRACT FROM AUTHOR]

We present a new formulation of the boundary element method for simulating the nonadhesive and adhesive contact between an indenter of arbitrary shape and an elastic half-space coated with an elastic layer of different material. We use the Fast Fourier Transform-based formulation of boundary element method, while the fundamental solution is determined directly in the Fourier space. Numerical tests are validated by comparison with available asymptotic analytical solutions for axisymmetric flat and spherical indenter shapes. [ABSTRACT FROM AUTHOR]

In the paper, we consider the tangential contact of single microasperities of the interacting surfaces the mechanical characteristics of which are close to the characteristics of typical rail steels. Using computer simulation by the method of discrete elements, we study the influence of the parameters of adhesive interaction of both external and internal surfaces on the regime of wear of asperities. It has been established that with increasing adhesion work, the wear regime changes from slipping (low wear) to grinding or brittle fracture of asperities (high wear), and this change is of threshold nature. An empirical sigmoid dependence of the location of the boundary between the two wear regimes (namely, the threshold value of the adhesive stress) on the value of the material hardening coefficient has been established. It is shown that the logistic nature of this dependence is due to the competition of two mechanisms of elastic strain energy dissipation, which determine the wear regime. These are plastic deformation and adhesion of the contacting surfaces. Special discussion is devoted to the influence of the scale factor on the threshold values of the mechanical characteristics of the material which provide the change of the wear regime. [ABSTRACT FROM AUTHOR]

Indentation of a thin elastic film attached through an interlayer to a rigid support is studied. Because the common interpretations of depth-sensing indentation tests are not applicable to such structured coatings, usually various approximating functions are employed to take into account influence of the interlayer. Contrary to the common approaches, a strict mathematical approach is applied here to study the problems under consideration assuming that the thickness of the two-layer structure is much less than characteristic dimension of the region of contact between the indenter and the coating. A simple derivation of asymptotic relations for displacements and stresses is presented. It is shown that often the leading term approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler-Fuss elastic foundation with an effective elastic constant. Because the contact between the indenter and the film at nanoscale may be greatly affected by adhesion, the adhesive problem for these bilayer coatings is studied in the framework of the JKR (Johnson, Kendall, and Roberts) theory of adhesion. Assuming the indenter shape near the tip has some deviation from its nominal shape and using the leading term approximation of the layered coatings, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius of adhesive contact region. • The proposed method may straightforwardly be applied to the bilayer systems. • Equivalency of leading order approximation to a Winkler-Fuss elastic foundation • Certain advantages of the proposed method to Argatov's method • Discussion of indentation by a spherical indenter and an equivalent conical one • The indentation problems should take into account the effects of adhesion. [ABSTRACT FROM AUTHOR]

The problem of multiple adhesive contact is considered for an elastic substrate modeled as a transversely isotropic elastic half-space. It is assumed that a large number of the Kendall-type microcontacts are formed between the substrate and circular rigid (i.e., nondeformable) and frictionless micropads, which are interconnected between themselves, thereby establishing a load sharing. The effect of microcontacts interaction is accounted for in the formulation of the detachment criterion for each individual microcontact. A number of different asymptotic models are presented for the case of dilute clusters of microcontacts with their accuracy tested against a special case of two-spot contact, for which an analytical solution is available. The pull-off force has been estimated and the effects of the array size and the microcontact spacing are studied. It is shown that the flexibility of the micropads fixation, which is similar to that observed in mushroom-shaped fibrils, significantly increases the pull-off force. The novelty of the presented approach is its ability to separate different effects in the multi-scale contact problem, which allows one to distinguish between different mathematical models developed for bioinspired fibrillar adhesives. [ABSTRACT FROM AUTHOR]

For compliant adhesive contact problems based on the Lennard-Jones potential, the non-convexity of the latter leads to jump-in and jump-off instabilities which can hardly be traced by using classical algorithms. In this work, we combine an adapted Asymptotic Numerical Method (ANM) and the multiscale Arlequin method to trace efficiently these instabilities. The ANM is used to trace the entire unstable solution path in a branch-by-branch manner. The Arlequin method is used to achieve a refined resolution in the vicinity of the contact surface and to reduce possible spurious numerical oscillations due to coarse surface discretizations. Numerical results, validated by comparison with available ones, reveal the accuracy, efficiency and robustness of the proposed global methodology. [ABSTRACT FROM AUTHOR]

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations for displacements and stress is presented. The proposed approach is compared with other published approaches. The cases are established when the leading-order approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler–Fuss elastic foundation. For this elastic foundation, the axisymmetric adhesive contact is studied in the framework of the Johnson–Kendall–Roberts (JKR) theory. The JKR approach has been generalized to the case of the punch shape being described by an arbitrary blunt axisymmetric indenter. Connections of the results obtained to problems of nanoindentation in the case that the indenter shape near the tip has some deviation from its nominal shape are discussed. For indenters whose shape is described by power-law functions, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius. [ABSTRACT FROM AUTHOR]

Highlights • A piece-wise exponential multi-layered (PWEML) model is used to simulate the functionally graded materials. • The adhesion effect can be altered by adjusting the gradient index. • The appropriate gradual variation of the shear modulus can improve the performance of the coating. Abstract The paper aims at the contact mechanics of functionally graded coated substrate by taking into the adhesion effect. The coating-substrate structure is indented by a cylindrical punch to form a contact region where the adhesion forces are described by using the Maugis adhesion model. A piece-wise exponential multi-layered (PWEML) model is used to simulate the functionally graded materials with arbitrary spatial variation of material properties. This model divided the functionally graded coating into several sub-layers in which the elastic parameter varies as exponential form. Using the Fourier transform technique and the Transfer matrix method, the boundary value problem for adhesive contact of graded coated substrate is reduced to the singular integral equation. Some numerical results are presented to analyze the influence of gradient index on the pull-out force, contact stresses and adhesion region. The results can be applied to improve the performance of the coating by adjusting the gradient index. [ABSTRACT FROM AUTHOR]

The effect of temperature on adhesion is neglected in classical adhesive contact theories. However, an increasing number of experimental results indicate that temperature has a prominent effect on adhesion behaviors. In this study, the anisothermal adhesive contact behaviors between two transversely isotropic piezoelectric cylinders with different initial temperatures is investigated by virtue of the generalized JKR model, where the contact interface is assumed to be perfectly bonded. The considered problem is reduced to coupled singular integral equations, which is derived by using the Fourier integral transform. The closed-form solutions of anisothermal generalized stress fields are obtained by taking the series expansion of the integrand induced by temperature difference. The effect of temperature difference on adhesion behaviors of two different types of layered piezoelectric structures under the action of mechanical-electro loadings is revealed. It is found that the pull-off force and contact size at pull-off moment decrease with increasing the temperature difference. The adhesion weakening effect induced by temperature difference diminishes when the electric loading is exerted. The results derived from this paper shed lights on understanding the adhesive contact behaviors of piezoelectric materials in the presence of temperature difference. • The anisothermal non-slipping JKR model for piezoelectric materials is established. • The effect of temperature difference on adhesion behavior of different types of layered piezoelectric structure is revealed. • The closed-form solutions for the contact stresses and normal electric displacement in the presence of temperature difference are obtained. • The presence of temperature difference can weaken the adhesion effect between dissimilar piezoelectric solids. • The adhesion weakening effect induced by temperature difference diminishes when the exerting electric loading is exerted. [ABSTRACT FROM AUTHOR]