# A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate

Sami El-Borgi, Shameem Usman, Mehmet Ali Güler

Research output: Contribution to journalArticle

24 Citations (Scopus)

### Abstract

This paper investigates the plane problem of a frictional receding contact formed between an elastic functionally graded layer and a homogeneous half space, when they are pressed against each other. The graded layer is assumed to be an isotropic nonhomogeneous medium with an exponentially varying shear modulus and a constant Poisson's ratio. A segment of the top surface of the graded layer is subject to both normal and tangential traction while rest of the surface is devoid of traction. The entire contact zone thus formed between the layer and the homogeneous medium can transmit both normal and tangential traction. It is assumed that the contact region is under sliding contact conditions with the Coulomb's law used to relate the tangential traction to the normal component. Employing Fourier integral transforms and applying the necessary boundary conditions, the plane elasticity equations are reduced to a singular integral equation in which the unknowns are the contact pressure and the receding contact lengths. Ensuring mechanical equilibrium is an indispensable requirement warranted by the physics of the problem and therefore the global force and moment equilibrium conditions for the layer are supplemented to solve the problem. The Gauss-Chebyshev quadrature-collocation method is adopted to convert the singular integral equation to a set of overdetermined algebraic equations. This system is solved using a least squares method coupled with a novel iterative procedure to ensure that the force and moment equilibrium conditions are satisfied simultaneously. The main objective of this paper is to study the effect of friction coefficient and nonhomogeneity factor on the contact pressure distribution and the size of the contact region.

Original language English 4462-4476 15 International Journal of Solids and Structures 51 25-26 https://doi.org/10.1016/j.ijsolstr.2014.09.017 Published - 1 Dec 2014

### Fingerprint

Plane Problem
Contact Problem
Integral equations
traction
Substrate
Contact
Poisson ratio
singular integral equations
Substrates
Pressure distribution
Elasticity
Physics
Elastic moduli
Boundary conditions
Friction
Singular Integral Equation
moments
sliding contact
integral transformations
collocation

### Keywords

• Friction coefficient
• Frictional receding contact
• Least squares solution
• Nonhomogeneity parameter
• Singular integral equation of first kind

### ASJC Scopus subject areas

• Mechanical Engineering
• Mechanics of Materials
• Materials Science(all)
• Condensed Matter Physics
• Applied Mathematics
• Modelling and Simulation

### Cite this

A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate. / El-Borgi, Sami; Usman, Shameem; Güler, Mehmet Ali.

In: International Journal of Solids and Structures, Vol. 51, No. 25-26, 01.12.2014, p. 4462-4476.

Research output: Contribution to journalArticle

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