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

M. Rhimi, Sami El-Borgi, W. Ben Saïd, F. Ben Jemaa

Research output: Contribution to journalArticle

46 Citations (Scopus)

### Abstract

In this paper, we consider the axisymmetric 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 is subjected over a part of its top surface to normal tractions while the rest of it 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 Hankel transform, the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using orthogonal Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact 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 language English 3633-3642 10 International Journal of Solids and Structures 46 20 https://doi.org/10.1016/j.ijsolstr.2009.06.008 Published - 1 Oct 2009 Yes

### Fingerprint

Integral equations
traction
Substrate
Contact
singular integral equations
Substrates
Elasticity
Polynomials
Singular Integral Equation
half spaces
polynomials
inhomogeneity
elastic properties
Hankel transform
Iterative Scheme
Orthogonal Polynomials
Half-space
Unknown

### Keywords

• Axisymmetric receding contact
• Singular integral equation

### ASJC Scopus subject areas

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

### Cite this

A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate. / Rhimi, M.; El-Borgi, Sami; Ben Saïd, W.; Ben Jemaa, F.

In: International Journal of Solids and Structures, Vol. 46, No. 20, 01.10.2009, p. 3633-3642.

Research output: Contribution to journalArticle

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N2 - In this paper, we consider the axisymmetric 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 is subjected over a part of its top surface to normal tractions while the rest of it 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 Hankel transform, the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using orthogonal Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact 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.

AB - In this paper, we consider the axisymmetric 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 is subjected over a part of its top surface to normal tractions while the rest of it 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 Hankel transform, the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using orthogonal Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact 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.

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