Stress Concentrations at the Apex of a Plane Indenter Acting on an Elastic Half Plane

Gdoutos, E. E.; Theocaris, P. S.

doi:10.1115/1.3423663

Cited by 95 publications

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“…It is subject to a normal force P, possibly a moment M and a shearing force Q, and any of these may vary in time in an arbitrary way. The state of stress adjacent to a slipping corner for such a problem has been studied in detail by Gdoutos and Theocaris [1], but the question that is asked here is: 'What is the minimum value of the coefficient of friction to guarantee adhesion, in the neighbourhood of the contact corner A?' The most obvious way to approach the problem is to solve for the interfacial contact pressure distribution and the shear traction distribution.…”

Section: Introductionmentioning

confidence: 99%

What level of friction guarantees adhesion in a complete contact?

Hills

Dini

2004

The Journal of Strain Analysis for Engineering Design

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The Williams' solution for the state of stress near the apex of an elastic wedge is used to study the traction distribution adjacent to the tip of a complete contact. Assuming that the surfaces remain in contact during loading, the coefficient of friction needed to ensure local adhesion is found. This is compared with that predicted by an analysis of an elastic rectangle clamped between elastic halfplanes and is shown to be consistent. The results are appropriate to all complete contacts between elastically similar components.

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Section: Introductionmentioning

confidence: 99%

What level of friction guarantees adhesion in a complete contact?

Hills

Dini

2004

The Journal of Strain Analysis for Engineering Design

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“…They concluded that the singularity in stresses was never stronger than the inverse square root of the distance d, and it had no oscillatory multiplier corresponding to complex zeros of the characteristic determinant. The study was extended to a contact with the Coulomb law of dry friction by Gdoutos and Theocaris [7], Comninou [5] and, in more detail, by Churchman, Mugadu and Hills [4]. Still no complex roots was found, whereas the singularity in stresses appeared depending on the slip direction and could be stronger than O(1/ √ d).…”

Section: Fig 1 Interface Leyers With Finite Thickness Near An Commonmentioning

confidence: 96%

Interface conditions simulating influence of a thin elastic wedge with smooth contacts

Linkov

Rybarska-Rusinek

2010

Arch Appl Mech

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The paper presents a method for deriving interface conditions simulating the influence of a thin wedge in a multi-wedge system with smooth contacts. It consists in successive (i) employing the Mellin's transform, (ii) separation of the symmetric and anti-symmetric parts of a solution, (iii) distinguishing terms tending to infinity, when the wedge angle tends to zero, (iv) appropriate re-arrangement of the terms to avoid degeneration, (v) using truncated power series in equations for the thin wedge and (vi) inspection of the characteristic determinant and finding models simulating the influence of the thin wedge for various combinations of parameters. The paper extends and improves the results previously obtained by the authors for a harmonic problem. The analysis leads to three physical models of contact interaction, which cover all the ratios of shear modules of a thin wedge and neighbour wedges. Numerical examples illustrate the accuracy provided by the method employed and the models derived.

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“…For this class of problems further contributions are due to Dundurs [11], Bogy and Wang [12], Hein and Erdogan [13], Dundurs and Lee [14], Gdoutos and Theocaris [15], Theocaris and Gdoutos [16], and Rao [17]. The case of an TV-material composite wedge was treated by Dempsey and Sinclair [18], [19].…”

Section: Introductionmentioning

confidence: 99%

The singular wedge problem in the nonlinear elastostatic plane stress theory

Tarantino¹

1999

Quart. Appl. Math.

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Abstract.A finite elastostatic analysis of the singular equilibrium field in the proximity of the apex of a wedge, with clamped-free radial edges and general far-field loading conditions, is performed. The problem is formulated for compressible hyperelastic sheets under a plane stress condition. An asymptotic procedure is proposed to compute the deformation and stress singular fields. Emphasis is placed on the investigation of the dependence of the order of singularity in the asymptotic Piola-Kirchhoff and Cauchy stresses on the wedge angles. The case of a half-plane bounded to a rigid substrate is studied in detail. Introduction.In linear elastostatic theory, several methods of singularity analysis are available for wedge problems. Williams [1] employed the Airy stress function and separation of variables to study the single-material wedge under different boundary conditions, proposing a method of analysis that appeals in its simplicity and immediacy. Tranter Green and Zerna [7] employed the complex function representation of the solution, conformally mapped the wedge into an infinite strip, and applied Fourier transforms to solve the strip problem. Hetenyi [8] generated a series solutions for the wedge by overlapping known half-plane solutions. Babuska, et al. [9], used a variance of this technique to reduce the wedge problem to an integral equation.The Mellin transform was also employed by Bogy [10] to study bi-material isotropic wedges, providing conditions for a logarithmic stress singularity.

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Stress Concentrations at the Apex of a Plane Indenter Acting on an Elastic Half Plane

Cited by 95 publications

References 0 publications

What level of friction guarantees adhesion in a complete contact?

What level of friction guarantees adhesion in a complete contact?

Interface conditions simulating influence of a thin elastic wedge with smooth contacts

The singular wedge problem in the nonlinear elastostatic plane stress theory

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