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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January 2008
Research Papers
A Numerical Solution for Quasistatic Viscoelastic Frictional Contact Problems
Fatin F. Mahmoud,
Fatin F. Mahmoud
Mem. ASME
Department of Mechanical Engineering, College of Engineering,
Zagazig University
, Zagazig 44511, Egypt
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Ahmed G. El-Shafei,
Ahmed G. El-Shafei
Department of Mechanical Engineering, College of Engineering,
e-mail: agelshafei@yahoo.com
Zagazig University
, Zagazig 44511, Egypt
Search for other works by this author on:
Amal E. Al-Shorbagy,
Amal E. Al-Shorbagy
Department of Mechanical Engineering, College of Engineering,
Zagazig University
, Zagazig 44511, Egypt
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Alaa A. Abdel Rahman
Alaa A. Abdel Rahman
Department of Mechanical Engineering, College of Engineering,
Zagazig University
, Zagazig 44511, Egypt
Search for other works by this author on:
Fatin F. Mahmoud
Mem. ASME
Department of Mechanical Engineering, College of Engineering,
Zagazig University
, Zagazig 44511, Egypt
Ahmed G. El-Shafei
Department of Mechanical Engineering, College of Engineering,
Zagazig University
, Zagazig 44511, Egypte-mail: agelshafei@yahoo.com
Amal E. Al-Shorbagy
Department of Mechanical Engineering, College of Engineering,
Zagazig University
, Zagazig 44511, Egypt
Alaa A. Abdel Rahman
Department of Mechanical Engineering, College of Engineering,
Zagazig University
, Zagazig 44511, EgyptJ. Tribol. Jan 2008, 130(1): 011012 (13 pages)
Published Online: December 26, 2007
Article history
Received:
February 7, 2007
Revised:
August 13, 2007
Published:
December 26, 2007
Citation
Mahmoud, F. F., El-Shafei, A. G., Al-Shorbagy, A. E., and Abdel Rahman, A. A. (December 26, 2007). "A Numerical Solution for Quasistatic Viscoelastic Frictional Contact Problems." ASME. J. Tribol. January 2008; 130(1): 011012. https://doi.org/10.1115/1.2806202
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