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TECHNICAL PAPERS

# Linear Viscoelastic Creep Model for the Contact of Nominal Flat Surfaces Based on Fractal Geometry: Standard Linear Solid (SLS) Material

[+] Author and Article Information
Osama M. Abuzeid

Mechanical Engineering Department,  University of Jordan, Amman-11942, Jordanoabuzeid@ju.edu.jo

Peter Eberhard

Institute of Engineering and Computational Mechanics,  University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germanyeberhard@itm.uni-stuttgart.de

J. Tribol 129(3), 461-466 (Feb 16, 2007) (6 pages) doi:10.1115/1.2736427 History: Received May 03, 2006; Revised February 16, 2007

## Abstract

The objective of this study is to construct a continuous mathematical model that describes the frictionless contact between a nominally flat (rough) viscoelastic punch and a perfectly rigid foundation. The material’s behavior is modeled by assuming a complex viscoelastic constitutive law, the standard linear solid (SLS) law. The model aims at studying the normal compliance (approach) of the punch surface, which will be assumed to be quasistatic, as a function of the applied creep load. The roughness of the punch surface is assumed to be fractal in nature. The Cantor set theory is utilized to model the roughness of the punch surface. An asymptotic power law is obtained, which associates the creep force applied and the approach of the fractal punch surface. This law is only valid if the approach is of the size of the surface roughness. The proposed model admits an analytical solution for the case when the deformation is linear viscoelastic. The modified analytical model shows a good agreement with experimental results available in the literature.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 1

The fractal CB structure constructed with s=2

Figure 2

The fractal CB structure constructed with s=3

Figure 3

Standard linear solid model (SLS)

Figure 4

Nondimensional time-strain creep curves for the SLS model

Figure 5

Experimental and isochronous stress-strain curves for D=1.4

Figure 6

Experimental and isochronous stress-strain curves for D=1.5

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