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Research Papers

A Numerical Solution for Quasistatic Viscoelastic Frictional Contact Problems

[+] Author and Article Information
Fatin F. Mahmoud, Amal E. Al-Shorbagy, Alaa A. Abdel Rahman

Department of Mechanical Engineering, College of Engineering, Zagazig University, Zagazig 44511, Egypt

Ahmed G. El-Shafei1

Department of Mechanical Engineering, College of Engineering, Zagazig University, Zagazig 44511, Egyptagelshafei@yahoo.com

1

Corresponding author.

J. Tribol 130(1), 011012 (Dec 26, 2007) (13 pages) doi:10.1115/1.2806202 History: Received February 07, 2007; Revised August 13, 2007; Published December 26, 2007

The tribological aspects of contact are greatly affected by the friction throughout the contact interface. Generally, contact of deformable bodies is a nonlinear problem. Introduction of the friction with its irreversible character makes the contact problem more difficult. Furthermore, when one or more of the contacting bodies is made of a viscoelastic material, the problem becomes more complicated. A nonlinear time-dependent contact problem is addressed. The objective of the present work is to develop a computational procedure capable of handling quasistatic viscoelastic frictional contact problems. The contact problem as a convex programming model is solved by using an adaptive incremental procedure. The contact constraints are incorporated into the model by using the Lagrange multiplier method. In addition, a local-nonlinear nonclassical friction model is adopted to model the friction at the contact interface. This eliminates the difficulties that arise with the application of the classical Coulomb’s law. On the other hand, the Wiechert model, as an effective model capable of describing both creep and relaxation phenomena, is adopted to simulate the linear behavior of viscoelastic materials. The resulting constitutive integral equations are linearized; therefore, complications that arise during the integration of these equations, especially with contact problems, are avoided. Two examples are presented to demonstrate the applicability of the proposed method.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Nonlinear function of Φε and (b) variation of the tangential contact stress according to Function A

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Figure 2

Contact of two deformable bodies

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Figure 3

Geometry of the contact interface. (a) A contactor node K in contact with a target segment Sl. (b) Contact forces at the contact interface.

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Figure 4

A viscoelastic block resting on a flat rigid foundation

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Figure 5

Variation of the contact pressure throughout the contact interface with different values of ε at different time instants

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Figure 6

Variation of the tangential contact stress throughout the contact interface with different values of ε at different time instants

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Figure 7

Relaxation of the maximum contact stresses at different values of ε

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Figure 8

Variation of the relative tangentialdisplacement throughout the contact interface with different ε at different time instants

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Figure 9

Contact of a viscoelastic block pressed against a rigid foundation with a gap

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Figure 10

Variation of the contact pressure throughout the contact interface at different time instants

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Figure 11

Variation of the tangential contact stress throughout the contact interface at different time instants

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Figure 12

Relaxation of the maximum contact stresses

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Figure 13

Variation of the relative tangential displacement throughout the contact interface at different time instants

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