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

Sami El-Borgi, R. Abdelmoula, L. Keer

Research output: Contribution to journalArticle

90 Citations (Scopus)

Abstract

In this paper, we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress-strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using integral transforms, the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half-length. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half-length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact.

Original languageEnglish
Pages (from-to)658-674
Number of pages17
JournalInternational Journal of Solids and Structures
Volume43
Issue number3-4
DOIs
Publication statusPublished - Feb 2006
Externally publishedYes

Fingerprint

Plane Problem
Contact Problem
Integral equations
traction
Substrate
Contact
singular integral equations
Substrates
Elasticity
Polynomials
integral transformations
Singular Integral Equation
half spaces
polynomials
inhomogeneity
elastic properties
Plane Elasticity
Integral Transform
Iterative Scheme
Half-space

Keywords

  • Functionally graded layer
  • Receding contact
  • Singular integral equation

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials

Cite this

A receding contact plane problem between a functionally graded layer and a homogeneous substrate. / El-Borgi, Sami; Abdelmoula, R.; Keer, L.

In: International Journal of Solids and Structures, Vol. 43, No. 3-4, 02.2006, p. 658-674.

Research output: Contribution to journalArticle

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