Non-adhesive Contact Research Articles

Experimental and theoretical investigation of Chronic Lymphocytic Leukemia cell's viscoelastic contact mechanics using atomic force microscope

Chronic Lymphocytic Leukemia (CLL) is a type of cancer usually appearing in old age. In this research, a method for detecting CLL cells in young age through the analysis of geometrical and mechanical properties of human Leukocytes has been presented. For this purpose, the CLL cells are cultured and their geometric characteristics, adhesion force, and contact behavior have been examined using an Atomic Force Microscope (AFM) device. Subsequently, the obtained experimental results have been compared with the geometric and mechanical properties of Leukocytes. Furthermore, the manipulation process has been mathematically modeled using different adhesive and non-adhesive contact theories. The results showed that blood cancer cells have up to 8.17% smaller dimensions and up to 23.57% greater elastic modulus compared to leukocytes.

Non-adhesive and adhesive contacts of an elastic quarter-or eighth-space with freely sliding sides

The contact of an elastic quarter- or eighth-space is studied under the condition that the movement of the side surface of the quarter-space is constrained: It can slide freely along the plane of the side surface but its normal movement is blocked (for example, by a rigid wall). The solution of this contact problem can be easily achieved by additionally applying a mirrored load to an elastic half-space. Non-adhesive contact and the Johnson-Kendall-Roberts (JKR)-type adhesive contact between a rigid sphere and an elastic quarter-space under such a boundary condition is numerically simulated using the fast Fourier transform (FFT)-assisted boundary element method (BEM). Contacts of an elastic eighth-space are investigated using the same idea. Depending on the position of the sphere relative to the side edge, different contact behavior is observed. In the case of adhesive contact, the force of adhesion first increases with increasing the distance from the edge of the quarter-space, achieves a maximum, and decreases further to the JKR-value in large distance from the edge. The enhancement of the force of adhesion compared to the half-space-contact is associated with the pinning of the contact area at the edge. We provide the maps of the force of adhesion and their analytical approximations, as well as pressure distributions in the contact plane and inside the quarter-/eighth-space.

Load–displacement relation and gap distribution between rough surfaces: Partial differential equations approach

We develop a theoretical model to predict the load–displacement relation and probability density function for gaps between contacting rough surfaces. We derive partial differential equations from the previous model (Joe et al., 2018), and extend them to the non-adhesive contact problem. The predictions of the present theory are compared with numerical results using the Green’s function molecular dynamics algorithm, and a good agreement is obtained.

3D-printed hydrogels dressings with bioactive borate glass for continuous hydration and treatment of second-degree burns.

Recent advances in additive manufacturing have led to the development of innovative solutions for tissue regeneration. Hydrogel materials have gained significant attention for burn wound treatment in clinical practice among various advanced dressings due to their soothing and moisturizing activity. However, prolonged healing, pain, and traumatic removal due to the lack of long-term wound hydration are some of the challenges in the treatment of second-degree burn wounds. In this study, 3D-printed dressings were fabricated using gelatin, alginate, and bioactive borate glass (BBG) using an extrusion-based bioprinter. After ionic crosslinking, the 3D-printed dressings were characterized for mechanical properties, degradation rate, hydration activity, and in vitro cell viability using human fibroblasts. The results demonstrated that in 3D-printed dressings with 20 wt% BBG, Young's modulus increased by 105%, and 10-day degradation rate decreased by 62%. Addition of BBG prevented the burst release of water from hydrogel dressings and enabled the continuous water release for up to 10 days, which is crucial in treating second-degree burn wounds. 3D-printed hydrogel dressings with BBG showed long-term cell viability that can be a result of the accumulative release of therapeutic ions from BBG particulate. The in vivo wound healing functionality of the dressings was investigated using a rat model with a second-degree burn wound. Our animal study showed that the 3D-printed dressings with BBG exhibited faster wound closure, non-adhesive contact, non-invasive debridement, and non-traumatic dressing removal. Histological analysis suggested that 3D-printed dressings contributed to more uniform re-epithelialization and tissue remodeling compared to the non-printed hydrogels of the same compositions. Critically, 3D-printed dressings with BBG led to significant regeneration of hair follicles compared to the 3D-printed hydrogel, non-printed hydrogel, and the control groups. The superior outcome of the 3D-printed hydrogel-BBG20 dressings can be attributed to the bioactive formulation, which promotes moist wound healing for longer time periods, and the non-adhesive porous texture of the 3D-printed dressings with increased wound-dressing interactions. Our findings provided proof of concept for the synergistic effect of bioactive formulation and the porous texture of the 3D-printed hydrogel dressings incorporated with BBG on continuous water release and, consequently, on second-degree burn wound healing.

Axisymmetric Indentations of an Elastic Half-Space With Tensed Surface/Membrane in the Johnson–Kendall–Roberts Adhesive Approximation

Abstract Owing to the significant effects of adhesive force and surface/membrane tension, the classical contact models often fail to describe the indentation responses of soft materials and biological systems. This work addresses the axisymmetric indentation of an elastic substrate with constant surface/membrane tension by a spherical, conical, or cylindrical flat indenter in the Johnson–Kendall–Roberts adhesive approximation. On the basis of non-adhesive contact solutions accounting for the surface/membrane tension effect, explicit expressions for the external load and depth with respect to the contact radius are derived for the adhesive contact cases, which act as the theoretical fundamental for the accurate analysis of indentation tests. Despite using different correction functions, the results for spherical indentation are consistent with the solution of previous studies. It is found that the role of surface/membrane tension in the adhesive contact behavior is controlled by a dimensionless parameter. As the parameter gets larger, the pull-off force and the contact size at zero-external load for spherical and conical indentations are smaller, whereas the pull-off force for cylindrical flat indentation is higher.

Evolution of the real contact area of self-affine non-Gaussian surfaces

The impact of non-Gaussian height distribution on the real contact area evolution of elastic, frictionless and non-adhesive contact is studied. The Weibull probability function is used to model the height distribution, as it can capture surfaces of practical relevance. The set of variables needed to parametrise the problem is discussed, including the shape parameter of the height distribution, the topography’s wavelength ratio and the Hurst exponent. As the topographies become more non-Gaussian, a significant deviation from the Gaussian case is observed. Moreover, the spectral properties show a distinct effect on different non-Gaussian surfaces and the dependency on Nayak’s parameter is not inherited. A power-law evolution of the real contact area is found to fit the numerical results obtained with the boundary element method precisely. Finally, two semi-analytical asperity-based models are compared with numerical results, using the statistics of artificially generated topographies. The qualitative behaviour predicted with the numerical simulations is captured.

Fractal contact analysis for transversely isotropic piezoelectric materials: Theoretical and numerical predictions

This paper aims to investigate the micro frictionless and non-adhesive rough contact for transversely isotropic piezoelectric materials. The surface topography is formulated by the two-variable Weierstrass–Mandelbrot fractal function. The system of contact is subjected to light generalized loads. By virtue of the Hertzian solution of transversely isotropic piezoelectric materials and the size distribution function, the generalized loads-area relation is developed. The smallest truncated contact area in the theoretical model is determined by comparing the theoretical and simulation results. The present numerical solutions via the finite element method are validated in comparison to the numerical results in literature. The influence of various fractal parameters on the contact behavior of transversely isotropic piezoelectric solids are studied.

Adhesive depth-sensing indentation tests: Slopes of the force–displacement curves

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.

On the limitations of low‐rank approximations in contact mechanics problems

AbstractTypical strategies for reducing the computational cost of contact mechanics models use low‐rank approximations. The underlying hypothesis is the existence of a low‐dimensional subspace for the displacement field and a non‐negative low‐dimensional subcone for the contact pressure. However, given the local nature of contact, it seems natural to wonder whether low‐rank approximations are a good fit for contact mechanics or not. In this article, we investigate some of their limitations and provide numerical evidence showing that contact pressure is linearly inseparable in many practical cases. To this end, we consider various mechanical problems involving nonadhesive frictionless contacts and analyze the performance of the low‐rank models in terms of three different criteria, namely, compactness, generalization, and specificity.

A General Load–Displacement Relationship Between Random Rough Surfaces in Elastic, Non-adhesive Contact, with Application in Metal Additive Manufacturing

A General Load–Displacement Relationship Between Random Rough Surfaces in Elastic, Non-adhesive Contact, with Application in Metal Additive Manufacturing

Stress distribution of a cylindrical sandwich sector with FG-CNT core and piezoelectric face sheets subjected to low-velocity impact

A new theoretical solution based on Layerwise theory is presented to determine the stress distribution in a simply-supported cylindrical sandwich sector with a functionally graded carbon nanotube core and piezoelectric face sheets subjected to low-velocity impact. The spherical elastic ball hits the top face sheet of the sector at an initial velocity of 50 m/s. The classical non-adhesive elastic contact theory and Hunter's relationship were used to determine the normal contact pressure distribution in terms of time and distance of the contact location. Moreover, Hamilton's principle and Maxwell's static equation were used to obtain the nineteen equations of motion. The numerical code was written to solve these nonlinear equations and the stress components in each layer were calculated in terms of time. In addition, it was assumed that the out-of-shell displacement of the sector at each layer is a quadratic polynomial function of the radial component in addition to a function of the coordinate components within the shell. Due to this assumption, the normal out-of-shell strain is not only zero, or not even a constant, but it changes in the form of a linear function along with the thickness of each layer.

Roof Deformation and Collapse of Stamps With Isolated Grooves: A Contact Mechanics Approach

Abstract 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 α 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 α.

Attractive forces slow contact formation between deformable bodies underwater

Thermodynamics tells us to expect underwater contact between two hydrophobic surfaces to result in stronger adhesion compared to two hydrophilic surfaces. However, the presence of water changes not only energetics but also the dynamic process of reaching a final state, which couples solid deformation and liquid evacuation. These dynamics can create challenges for achieving strong underwater adhesion/friction, which affects diverse fields including soft robotics, biolocomotion, and tire traction. Closer investigation, requiring sufficiently precise resolution of film evacuation while simultaneously controlling surface wettability, has been lacking. We perform high-resolution in situ frustrated total internal reflection imaging to track underwater contact evolution between soft-elastic hemispheres of varying stiffness and smooth-hard surfaces of varying wettability. Surprisingly, we find the exponential rate of water evacuation from hydrophobic-hydrophobic (adhesive) contact is three orders of magnitude lower than that from hydrophobic-hydrophilic (nonadhesive) contact. The trend of decreasing rate with decreasing wettability of glass sharply changes about a point where thermodynamic adhesion crosses zero, suggesting a transition in mode of evacuation, which is illuminated by three-dimensional spatiotemporal height maps. Adhesive contact is characterized by the early localization of sealed puddles, whereas nonadhesive contact remains smooth, with film-wise evacuation from one central puddle. Measurements with a human thumb and alternatively hydrophobic/hydrophilic glass surface demonstrate practical consequences of the same dynamics: adhesive interactions cause instability in valleys and lead to a state of more trapped water and less intimate solid-solid contact. These findings offer interpretation of patterned texture seen in underwater biolocomotive adaptations as well as insight toward technological implementation.

Explicit transformation between non-adhesive and adhesive contact problems by means of the classical Johnson-Kendall-Roberts formalism.

The classic Johnson-Kendall-Roberts (JKR) contact theory was developed for frictionless adhesive contact between two isotropic elastic spheres. The advantage of the classical JKR formalism is the use of the principle of superposition of solutions to non-adhesive axisymmetric contact problems. In the recent years, the JKR formalism has been extended to other cases, including problems of contact between an arbitrary-shaped blunt axisymmetric indenter and a linear elastic half-space obeying rotational symmetry of its elastic properties. Here the most general form of the JKR formalism using the minimal number of a priori conditions is studied. The corresponding condition of energy balance is developed. For the axisymmetric case and a convex indenter, the condition is reduced to a set of expressions allowing explicit transformation of force-displacement curves from non-adhesive to corresponding adhesive cases. The implementation of the developed theory is demonstrated by presentation of a two-term asymptotic adhesive solution of the contact between a thin elastic layer and a rigid punch of arbitrary axisymmetric shape. Some aspects of numerical implementation of the theory by means of Finite-Element Method are also discussed. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Numerical moving mesh solution for the JKR adhesive contact between an incompressible layer and an axisymmetric rigid indenter

Recent research extended the non-adhesive contact problems between an incompressible layer and a rigid indenter to adhesive cases in the limit of the Johnson–Kendall–Roberts (JKR) model, where it simply changes the boundary condition. The governing equation of this problem is in the form of Poisson’s equation, and there are two boundary conditions, one of which serves to determine the extent of the contact area. This makes it possible to develop a numerical solution of an adhesive thin incompressible layer indentation problem. For a numerical implementation, we have devised a finite element formulation with a moving mesh technique satisfying the slope boundary condition, which determines the actual extent of the contact area. We shall apply the proposed numerical method to an adhesive contact problem by a spherical rigid indenter to demonstrate the validity of the method. Furthermore, we will compare the characteristics of the JKR indentation solutions between a half-space and a thin incompressible layer.

Coefficients of Restitution in Normal Adhesive Impact between Smooth and Rough Elastic Bodies

n 1975, Fuller and Tabor have shown that roughness can destroy macroscopic adhesion. This means that in spite of the presence of adhesion at the microscopic scale, the macrosopic force of adhesion vanishes. The mechanism of vanishing macroscopic adhesion is very simple: during approach of elastic bodies, asperities are elastically deformed so strongly that after unloading they destroy the microscopic adhesive junctions. However, both in the moment of formation of microscopic adhesive junctions in the loading phase and their destruction during unloading, mechanical energy disappears. This means that the microscopic adhesion makes the contact dissipative even if there is no macroscopic force of adhesion. In particular, the force-distance dependency during indentation and pull-off do not coincide with each other showing some "adhesive hysteresis". When a ball rolls on such rough surface, there will be a final energy dissipation due to formation of a new contact at the frontline of the contact and its destruction at the rear part. Thus, microscopic adhesion will lead to appearance of rolling friction in an apparently non-adhesive contact. In the present paper, we calculate the approach and pull-off dependencies of force on distance, the dissipated energy in one loading-unloading cycle and estimate the force of rolling friction due to microscopic adhesion.

Adhesion paradox: Why adhesion is usually not observed for macroscopic solids.

The adhesion paradox refers to the observation that for most solid objects no adhesion can be detected when they are separated from a state of molecular contact. The adhesion paradox results from surface roughness, and we present experimental and theoretical results that show that adhesion in most cases is "killed" by the longest-wavelength roughness. In addition, adhesion experiments between a human finger and a clean glass plate were carried out, and for a dry finger no macroscopic adhesion occurred. We suggest that the observed decrease in the contact area with increasing shear force results from nonadhesive finger-glass contact mechanics, involving large deformations of complex layered material.

Macroscopic Modeling of Fingerpad Friction Under Electroadhesion: Possibilities and Limitations

Electrovibration is one of the key technologies in surface haptics. By inducing controlled electrostatic forces, the friction within a sliding contact between the human finger and a capacitive screen is modulated, which in turn gives effective tactile feedback to the user. Such powerful haptic displays can be built into mobile phones, tablets, navigation devices, games consoles and many other devices of consumer electronics. However, due to the layered structure and complex material of human skin, the underlying contact mechanical processes have not yet been fully understood. This work provides new continuum-based approaches to macroscopic modeling of the electro-adhesive frictional contact. A solution of pure normal contact between a human finger and a rigid, smooth plane under electroadhesion is derived by applying Shull's compliance method in the extended regime of large deformations. Based on these results and assuming pressure-controlled friction, a model for the sliding electro-adhesive contact is developed, which adequately predicts the friction force and coefficient of friction over the whole range of relevant voltages and applied normal forces. The experimentally observed area reduction caused by the tangential force is incorporated in a more empirical than profound contact mechanical way. This effect is studied with the help of a two-dimensional finite element model of the fingertip, assuming non-linear elastic material for the skin tissue. Although the simulations are restricted to non-adhesive tangential contacts, they show a significant reduction of the contact area, which is caused by large deformations of the non-linear elastic material around the distal phalanx. This result indicates that adhesion is only of secondary importance for the area reduction.

Representative contact element size determination for micromechanical contact analysis of self-affine topographies

A generic and straightforward numerical strategy for the determination of the size of Representative Contact Elements (RCEs), which are employed in finite element contact homogenization procedures, is proposed in this contribution. The approach enables the determination of the length, height and mesh discretisation of RCEs that provide a good statistical representation of the contact interface, described by a given set of topography properties. The case of Gaussian self-affine and elastic rough profiles under normal, frictionless and non-adhesive contact is analysed in detail. A collection of conditions has been derived for two-dimensional problems, based on a trade-off between the convergence of the real contact area and the computational cost. With the increasing width of the roughness power spectrum, the restrictions imposed on the length and mesh size can be relaxed, allowing to reduce the size of numerical models. The corresponding class of problems in three-dimensions has also been studied. In this case, the influence of the numerical scheme adopted for the evaluation of the contact area has been analysed leading to the identification of two bounds, which converge for the same value with progressively finer meshes. State-of-the-art numerical results fall within the bounded region, and the application of the area correction technique proposed by Yastrebov et al. to the upper node-based bound, accelerates the convergence of the mesh and renders a good agreement with reference data.

Non-adhesive Contacts With Different Surface Tension Inside and Outside the Contact Area

In the last decade, the influence of surface tension on properties has attracted much atten-tion, especially in the context of of very soft materials (like gels) or contacts at the na-noscale. However, in the most current studies it is assumed that the tension of the surface inside and outside the area is the same. This practically means that the considered object is an elastic body coated with a tensed membrane. In real contacts, there is no reasons why the sur-face tension of the free and the contact should be equal. On the contrary, especially in contacts of soft bodies with hard solid indenters one can await that they are com-pletely different. In the present paper, we consider an elastic with account of different surface tension inside and outside the area. However, the considered contacts are still non-adhesive. This means that the three surface energies in play (two surface energies of both bodies outside the and the interface energy in the region) fulfil the criterion that the work of separation vanishes. A numerical model based on the FFT assisted BEM is implemented and is illustrated with a few examples.