### 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 language | English |
---|---|

Pages (from-to) | 658-674 |

Number of pages | 17 |

Journal | International Journal of Solids and Structures |

Volume | 43 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Feb 2006 |

Externally published | Yes |

### Fingerprint

### Keywords

- Functionally graded layer
- Receding contact
- Singular integral equation

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials

### Cite this

*International Journal of Solids and Structures*,

*43*(3-4), 658-674. https://doi.org/10.1016/j.ijsolstr.2005.04.017

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

Research output: Contribution to journal › Article

*International Journal of Solids and Structures*, vol. 43, no. 3-4, pp. 658-674. https://doi.org/10.1016/j.ijsolstr.2005.04.017

}

TY - JOUR

T1 - A receding contact plane problem between a functionally graded layer and a homogeneous substrate

AU - El-Borgi, Sami

AU - Abdelmoula, R.

AU - Keer, L.

PY - 2006/2

Y1 - 2006/2

N2 - 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.

AB - 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.

KW - Functionally graded layer

KW - Receding contact

KW - Singular integral equation

UR - http://www.scopus.com/inward/record.url?scp=28244477119&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28244477119&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2005.04.017

DO - 10.1016/j.ijsolstr.2005.04.017

M3 - Article

VL - 43

SP - 658

EP - 674

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 3-4

ER -