Analysis of the adhesive contact of confined layers by using a Green's function approach

Carbone, Giuseppe; Mangialardi, L.

doi:10.1016/j.jmps.2007.05.009

Cited by 80 publications

(85 citation statements)

References 36 publications

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“…Of course for a infinitely thick layer (d → +∞ as in our case) the average displacement u m is also infinitely large except when the ν = 0.5, but the difference u (x) − u m is always finite [18], [19], and can be interpreted as the additional elastic displacement of the solid due to the presence of roughness at the interfaces. In order to close the system of equations we need ad additional condition to determine the yet unknown contact domain Ω.…”

Section: The Numerical Modelmentioning

confidence: 77%

“…For the numerical implementation the reader is referred to Ref. [18], here we just describe some numerical techniques which are peculiar to the problem we discuss in this paper. Let us assume that we know the solution of Eqs.…”

Section: The Numerical Modelmentioning

confidence: 99%

“…The methodology, already presented by one of us in Ref. [18], is based on a pure continuum mechanics approach and belongs to the class of Boundary Element Methods (BEM), since it also makes use of Green's function to solve the problem. This allows us to reduced the problem to Fredholm integral equation of the first kind with a logarithmic kernel.…”

Section: Introductionmentioning

confidence: 99%

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Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

2009

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The authors have employed a numerical procedure to analyze the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution of the problem, which belongs to the class of the free boundary problems, is obtained by calculating the Green's function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel, and the boundaries of the contact area are calculated by requiring that the energy of the system is stationary. The methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the prediction of an extended version of the Persson's contact mechanics theory, able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson's theory underestimates the contact area of about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than what is found for 2D rough surfaces in case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson's theory is a mean field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe, that the predicted value of separation is in very good agreement with our numerical results as well as the exponent of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson's theory captures almost exactly the main qualitative behavior of the rough contact phenomena.

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Section: The Numerical Modelmentioning

confidence: 77%

Section: The Numerical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

2009

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“…By following a path similar to the one proposed by Hunter [2], for the case of a rigid cylinder rolling on a viscoelastic half-space, we reformulate the problem in terms of a Fredholm integral equation of the first kind, where the logarithmic Kernel is exactly the same found for twodimensional elastic problems [34][35][36][37], plus a couple of first-order differential equations and the corresponding boundary conditions. This formulation allows to exploit some of the solutions already known for elastic materials [34], thus leading to a strong simplification of the viscoelastic contact problem at hand.…”

Section: Introductionmentioning

confidence: 99%

The sliding contact of a rigid wavy surface with a viscoelastic half-space

et al. 2014

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In this paper, the contact of a rigid sinusoid sliding on a viscoelastic half-space is studied. The solution of the problem is obtained by following the path drawn by Hunter for cylindrical contacts. Results show that depending on the remote applied load, a transition from full contact conditions to partial contact may occur depending on the sliding velocity. This effect, which is not observed in smooth single asperity contacts, is related to the viscoelastic stiffening of the material and to the periodicity of the contacts. Frictional properties as well as contact area, displacement and pressure distributions are discussed in detail.

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“…In fact, both the mean pull-off force and the work needed to detach the surfaces decrease with increasing roughness, and may even vanish above a certain roughness threshold [23,24]. However, it has been also shown [23,[25][26][27] that, if the contacting bodies are relatively soft in comparison with the surface energy and roughness length scales, the adhesion forces and the effective interfacial energy may, unexpectedly, increase when roughness is present, provided the contacting surfaces are not too rough. Indeed, in such cases, the adhesion forces may easily deform the elastic bodies to pull them into full contact with the substrate, thus increasing the contact area and the strength of adhesion.…”

Section: Introductionmentioning

confidence: 99%

Biomimetic surfaces with controlled direction-dependent adhesion

Afferrante

Carbone

2012

J. R. Soc. Interface.

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We propose a novel design of a biomimetic micro-structured surface, which exhibits controlled strongly direction-dependent adhesion properties. The micro-system consists of parallel elastic wall-like structures covered by a thin layer. Numerical calculations have been carried out to study the adhesive properties of the proposed system and to provide design criteria with the aim of obtaining optimized geometries. A numerically equivalent version of the double cantilever beam fracture experiment is, then, simulated by means of finite element analysis to investigate the anisotropic adhesion of the structure. We find that, because of inherent crack trapping properties of these types of structures, the wall-like geometry allows us to strongly enhance adhesion when the detachment direction is perpendicular to the walls. On the other hand, when the detachment occurs parallel to the walls, the system shows low adhesion. This controlled direction-dependent adhesive property of the proposed structure solves one of the key problems of biomimetic adhesive surfaces, which usually show very strong adhesion, even larger than biological systems, but are not suitable for object manipulation and locomotion, as detachment always occurs at high loads and cannot be controlled.

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Analysis of the adhesive contact of confined layers by using a Green's function approach

Cited by 80 publications

References 36 publications

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

The sliding contact of a rigid wavy surface with a viscoelastic half-space

Biomimetic surfaces with controlled direction-dependent adhesion

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