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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]

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]

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]

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]

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]

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]

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]

[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]

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]

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]

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]

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]

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]

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]

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]

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]

A generalized double-Hertz (D-H) model has been proposed to consider the adhesive contact between an elastic cylinder and an elastic half space under inclined forces. The normal traction is exactly the same as that in the conventional D-H model. The shear traction of finite value is distributed into a slipping zone and a non-slipping zone. In the slipping zone, the shear traction is proportional to the compressive pressure. With the model, adhesive contact behaviour between cylinders has been numerically illustrated. The shear-induced peeling has been demonstrated. The value of the ratio for shear traction to normal traction larger than friction coefficient has been found in part of the non-slipping zone. Those altogether are consistent with experiments. [ABSTRACT FROM AUTHOR]

The surface micro-interaction model of Lennard-Jones (LJ) is used for adhesive contact problems (ACP). To address theoretical and numerical pitfalls of this model, a sequence of partitions of contact models is adaptively constructed to both extend and approximate the LJ model. It is formed by a combination of the LJ model with a sequence of shifted-Signorini (or, alternatively, -Linearized-LJ) models, indexed by a shift parameter field. For each model of this sequence, a weak formulation of the associated local ACP is developed. To track critical localized adhesive areas, a two-step strategy is developed: firstly, a macroscopic frictionless (as first approach) linear-elastic contact problem is solved once to detect contact separation zones. Secondly, at each shift-adaptive iteration, a micro-macro ACP is re-formulated and solved within the multiscale Arlequin framework, with significant reduction of computational costs. Comparison of our results with available analytical and numerical solutions shows the effectiveness of our global strategy. [ABSTRACT FROM AUTHOR]

In this study, the adhesive contact problem for a functionally graded coating with exponentially varying modulus is investigated. The MD model is used to describe the adhesion effect between a rigid cylindrical indenter and a functionally graded coated half-space. The method of Fourier integral transform is applied to convert the controlling equation of the two-dimensional adhesive contact problem to the singular integral equations with Cauchy kernel. The numerical calculation is conducted to achieve the effects of the adhesion parameter and the stiffness ratio on the pull-out force, indentation, contact stresses and adhesion region. The results provide a way to improve the performance of coating on contact phenomena. [ABSTRACT FROM AUTHOR]

Studying the collective behavior of adhesive particles with the discrete element method (DEM) requires well-founded force–displacement relations (force models). While the Johnson–Kendall–Roberts (JKR) theory reliably predicts the dependence of the contact radius a on the force F , it has remained a challenge in this framework to obtain a straightforward force–displacement relation F (δ) with physically meaningful parameters to calculate the force F from the displacement δ. We derive a novel force–displacement relation from the JKR theory as a composition of functions F (δ) = (F ∘ a ∘ λ) (δ) , with the intermediate functions contact radius a (λ) and effective adhesive contact radius λ (δ). We also analyze contact geometry errors in the Hertz and JKR models, derive the exact contact centroid to accurately calculate contact torques and relative tangential velocities, and propose a smoothed JKR model to avoid discontinuities in force and energy. We find that incorrect torques and relative tangential velocities are obtained when the stiffness quotient is neglected because it affects the exact location of the contact centroid. We also find that contact geometry errors can become non-negligible for nanoparticles due to their large relative contact size. In addition, we show from bouncing ball simulations that the JKR models with a nominal coefficient of restitution derived for the Hertz model result in higher damping and thus reduced actual coefficients of restitution. Our analysis serves as a foundation for contact-mechanics-based force models for DEM simulations of adhesive particles to investigate their collective behavior in the future. [Display omitted] • We derive a force–displacement relation from JKR theory as a composite function. • We propose a smoothed JKR model without discontinuities in force and energy. • We derive the exact contact centroid which depends on stiffness quotient. • Contact geometry errors may become non-negligible for some nano-sized particles. • Restitution coefficient tuned to Hertz model leads to higher damping in JKR model. [ABSTRACT FROM AUTHOR]

An existing hyperelastic membrane model for graphene calibrated from ab-initio data (Kumar and Parks, 2014) is adapted to curvilinear coordinates and extended to a rotation-free shell formulation based on isogeometric finite elements. Therefore, the membrane model is extended by a hyperelastic bending model that reflects the ab-inito data of Kudin et al. (2001). The proposed formulation can be implemented straight-forwardly into an existing finite element package, since it does not require the description of molecular interactions. It thus circumvents the use of interatomic potentials that tend to be less accurate than ab-initio data. The proposed shell formulation is verified and analyzed by a set of simple test cases. The results are in agreement to analytical solutions and satisfy the FE patch test. The performance of the shell formulation for graphene structures is illustrated by several numerical examples. The considered examples are indentation and peeling of graphene and torsion, bending and axial stretch of carbon nanotubes. Adhesive substrates are modeled by the Lennard–Jones potential and a coarse grained contact model. In principle, the proposed formulation can be extended to other 2D materials. [ABSTRACT FROM AUTHOR]

Recently proposed formulation of the boundary element method for adhesive contacts has been generalized for contacts of power-law graded materials with and without adhesion. Proceeding from the fundamental solution for single force acting on the surface of an elastic half space, first the influence matrix is obtained for a rectangular grid. The inverse problem for the calculation of required stress in the contact area from a known surface displacement is solved using the conjugate-gradient technique. For the transformation between the stresses and displacements, the Fast Fourier Transformation is used. For the adhesive contact of graded material, the detachment criterion based on the energy balance is proposed. The method is validated by comparison with known exact analytical solutions as well as by proving the independence of the mesh size and the grid orientation. [ABSTRACT FROM AUTHOR]

A closed-form general analytic solution is presented for the adhesive normal contact of convex axisymmetric power-law graded elastic bodies using a Dugdale-Maugis model for the adhesive stress. The case of spherical contacting bodies is studied in detail. The known JKR- and DMT-limits can be derived from the general solution, whereas the transition between both can be captured introducing a generalized Tabor parameter depending on the material grading. The influence of the Tabor parameter and the material grading is studied. [ABSTRACT FROM AUTHOR]

A full self-consistent model (FSCM) for the adhesive contact between an axisymmetric rigid punch and a Gibson solid (an incompressible, linear graded elastic material) is established, which gives a self-consistent relation between the surface gap and interaction. Power-law shaped indenters and the Lennard–Jones interaction law are studied as representative cases, and the self-consistent equation is expressed in a dimensionless form with two independent parameters, namely the shape index and the Tabor number. The self-consistent equation for Gibson solid is a higher order polynomial equation with respect to the surface gap, which differs from the nonlinear integral equation for power-law graded elastic material. By taking the surface gap as the independent variable instead of the radius, the self-consistent equation is solved explicitly, which gives the first explicit form of the solution to an FSCM. When the Tabor number exceeds a critical value, jump-in instability and adhesion hysteresis occur, and the folding phenomenon that the Gibson solid surface is flipped and folded along the radial direction is observed. The critical Tabor number is determined in an explicit form and it is found to be independent of the surface index. The extended Maugis–Dugdale (M–D) model for Gibson solid is invalid when the Tabor number is large enough and the extended Johnson–Kendall–Roberts (JKR) model does not present the soft limit, due to their assumption of simple contact. An asymptotic solution is derived for the soft limit of the FSCM, which gives a power-law asymptotic relation between the dimensionless pull-off force and the Tabor number. This study provides a self-consistent toy model for the adhesive contact of Gibson solid and may deepen the understanding on the adhesion of graded materials. [Display omitted] • A full self-consistent model for the adhesive contact of Gibson solid is established. • The explicit form of self-consistent relation is obtained by exchanging variables. • The adhesion hysteresis and folding deformation appear over a critical Tabor number. • The restriction of Tabor number in the M–D- n -G model stems from contact hypothesis. • The JKR- n -G solution is proved not to be the soft limit through asymptotic analysis. [ABSTRACT FROM AUTHOR]

A normal adhesive contact between a flat-ended cylindrical punch with elliptical cross-section and the surface of an elastic substrate, which can be regarded as an elastic layer of finite thickness, is considered. The experimental evidence published elsewhere indicates that the initiation of detachment can occur at the ends of the minor axis of the elliptical contact area, which eventually comes into contradiction with the surface energy theory developed so far. This paradox of adhesive detachment is examined in the framework of the JKR-type model formulated in terms of the stress intensity factor (SIF) of the contact normal stress. Based on the asymptotic model for a relatively thick elastic layer, the contact SIFs at the ends of the minor axis are shown to grow with decreasing the relative layer thickness faster than those at the ends of the major axis of the initial contact area. A plausible explanation for the observed inconsistency between experiment and state-of-the-art theory is found in the effect of the nonuniform elastic deformations on the square root singularity of the contact pressure at the punch edge. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a system for brittle delamination between two visco-elastic bodies, also subject to inertia, which can be interpreted as a model for dynamic fracture. The rate-independent flow rule for the delamination parameter is coupled with the momentum balance for the displacement, including inertia. This model features a nonsmooth constraint ensuring the continuity of the displacements outside the crack set, which is marked by the support of the delamination parameter. A weak solvabi- lity concept, generalizing the notion of energetic solution for rate-independent systems to the present mixed rate-dependent/rate-independent frame, is proposed. Via refined variational convergence techniques, existence of solutions is proved by passing to the limit in approximating systems which regularize the nonsmooth constraint by conditions for adhesive contact. The presence of the inertial term requires the design of suitable recovery spaces small enough to provide compactness but large enough to recover the information on the crack set in the limit. [ABSTRACT FROM AUTHOR]

This work aims at developing a computational stochastic multiscale methodology to quantify the uncertainties of the adhesive contact problems due to capillary effects and van der Waals forces in MEMS. Because the magnitudes of the adhesive forces strongly depend on the surface interaction distances, which in turn evolve with the roughness of the contacting surfaces, the involved structural behaviors suffer from a scatter. To numerically predict the probabilistic behaviors of structures involving adhesion, the proposed method introduces stochastic meso-scale random apparent contact forces which can be integrated into a stochastic finite element model. Because the evaluation of their realizations is expensive, a generator for the random apparent contact force using the polynomial chaos expansion is constructed in an efficient way. [ABSTRACT FROM AUTHOR]

Previous delamination mechanism maps for coatings/substrates system cannot predict the critical conditions for delamination nucleation under adhesive contact loads, because the effects of surface adhesion on delamination are not considered. In this paper, the finite element simulation of a rigid sphere in adhesive contact with an elastic coating on an elastic-plastic substrate is undertaken to clarify interface crack initiation and growth, in which the surface adhesion of the indenter/coating contact system is modeled by nonlinear spring elements with a force-displacement relationship derived from a Lennard-Jones potential, and the coating/substrate interface is represented by an irreversible cohesive zone law. By conducting parametric studies, delamination mechanism maps considering surface adhesion are constructed. It is found that increasing the adhesion work will initiate delamination nucleation, and the critical indentation depth increases with increasing the interfacial cohesive energy in the presence of the surface adhesion. For relatively stronger adhesion, the higher the coating elastic modulus or the coating thickness is, the greater the critical indentation depth becomes. However, for relatively weaker adhesion, increasing the coating elastic modulus will decrease the critical indentation depth, and increasing the coating thickness will increase the critical indentation depth for lower indentation depths, but an opposite trend occurs for higher indentation depths. [ABSTRACT FROM AUTHOR]

The current paper revisits the adhesive contact between a rigid nanoscale sphere and an elastic half-space. Using analytical solution for traction and a modified numerical scheme, a new simulation is proposed. The adhesive contact is simulated faster and more easily than previous researches. The effect of sphere size is investigated. A modified spherical JKR model and spherical DMT model are proposed. The results are compared with spherical JKR, spherical DMT, and rigid sphere model. The load–approach and contact radius–load relations can be predicted by the modified spherical JKR model for sphere radius larger than 50ɛ. Finally, approximation equations for pull-off force vs. Tabor parameter and jump-in distance vs. Tabor parameter are proposed. [ABSTRACT FROM PUBLISHER]

Depth-sensing indentation experiments are a very important tool for estimating mechanical properties of modern materials. A review of various aspects of contact problems that used as the theoretical basis for interpretation of depth-sensing nanoindentation experiments is presented. Usually, analytical treatment of the indentation tests is based on analysis of the slopes of the force–displacement curves according to the non-adhesive Hertz contact theory. However, molecular adhesion is crucially important for many physical processes at the micro/nano-scales. Here, depth-sensing indentation techniques are reviewed and analyzed using the recent results obtained for adhesive contact problems. Fundamental relations for adhesive nanoindentation tests are derived for both frictionless and no-slip boundary conditions within the contact region. It is argued that the adhesive effects may be very important for treatment of the nanoindentation tests because the slopes of the force–displacement curves may considerably differ from the slopes derived using the non-adhesive contact theory. [ABSTRACT FROM AUTHOR]

The interface behavior of a thin-film adhering to an elastic half-plane with an arbitrarily graded transition layer is analyzed by a linearly unified model when the interface between the thin-film and the graded layer is subjected to a mismatch strain. A series of continuous but piecewise linear functions are adopted to describe different graded variation laws of the transition layer's modulus. The fundamental solution of a graded-layer coated half-plane under a pair of normal and tangential concentrated forces is obtained first, and then the mismatch problem of a thin-film bonded to an elastic half-plane with an arbitrarily graded transition layer is further investigated. Solving the obtained integral governing equation of Cauchy singularity leads to the interfacial shear stress, the normal stress in the film, as well as the stress intensity factor near the bonded edge. It is found that the interfacial mechanics of a thin-film bonded to a graded layer is significantly affected by varying gradient law, stiffness of the film, ratio of shear modulus and length scale of the graded transition layer. The results should be helpful for the design of systems with thin-films and functional graded materials and could guide engineers to choose proper graded materials for particular applications. [ABSTRACT FROM AUTHOR]

The paper presents solutions to the periodic adhesive contact problem between an elastic anisotropic layer and a wavy rigid half-space. Different systems including rigid, soft substrate and infinite elastic layer with orientation effect are considered in the paper. The periodic Green function in the form of Fourier series is obtained to formulate an integral equation of the contact pressure. The relation between the contact pressure and the relative approach is derived analytically. The results show that the adhesion effect depends strongly on both material orientation of the elastic layer and the substrate stiffness. These results are in particular useful for the design of new tunable adhesive systems. [ABSTRACT FROM AUTHOR]

The unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter and an elastic half-space is considered in the framework of the Johnson-Kendall-Roberts theory. In the case of a semi-fixed annular contact area, when one of the contact radii is fixed, while the other varies during indentation, we obtain the asymptotic solution of the adhesive contact problem based on the solution of the corresponding unilateral non-adhesive contact problem. In particular, the adhesive contact problem for Barber's concave indenter is considered in detail. In the case when both contact radii are variable, we construct the leading-order asymptotic solution for a narrow annular contact area. It is found that for a v-shaped generalized toroidal indenter, the pull-off force is independent of the elastic properties of the indented solid. [ABSTRACT FROM AUTHOR]

In the present work, the adhesive contact between elastic cylinders subject to a temperature difference under a specified applied force is studied. By adopting the concept that the contact size is governed by the balance between the energy release rate and the equivalent work of adhesion, the explicit expression for the applied force with respect to the contact half-width is derived analytically. The pull-off force and the contact half-width at zero applied force as functions of the temperature difference are obtained. The effect of the thermoelastic properties is accounted. Numerical results indicate that both the normal and the tangential thermoelastic effects influence the contact behaviors significantly. The present results may cast light on the evaluation and improvement of some thermal bonding technologies. [ABSTRACT FROM AUTHOR]

The stress and displacement fields of a complete contact problem are investigated using a finite element analysis (FEA) and a Moiré experiment, respectively. Asymptotic analysis of an adhered contact condition is preceded for comparison. Aluminum and copper alloys are used as the contact materials, from which specimens of different contact angles are fabricated. The FEA scheme is validated through comparison with the displacement distributions that are measured in the Moiré experiment. In turn, the generalized stress intensity factors are calculated using the validated FE models. These factors are used to evaluate the dimensional stress distributions in the asymptotic analysis, which are then compared with the FEA results. Excellent agreement in stress components is found between the asymptotic and FE methodologies. The relative error of the stress components σ rr and σ θθ between the methodologies was less than 3.8% within the range from the contact edge to 1 mm, and it increased gradually as the distance from the contact edge increased. In addition, a slight discrepancy is found in the contact of an elastically dissimilar case. [ABSTRACT FROM AUTHOR]