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Contact Mechanics

Modeling of Quasistatic Thermoviscoelastic Frictional Contact Problems

[+] Author and Article Information
Ahmed G. El-Shafei1

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

1

On sabbatical leave to College of Engineering, Jazan University, Jazan 45142, Saudi Arabia.

J. Tribol 134(1), 011403 (Mar 06, 2012) (12 pages) doi:10.1115/1.4005522 History: Received March 28, 2011; Accepted December 13, 2011; Published March 05, 2012; Online March 06, 2012

Frictional contacts of thermoviscoelastic bodies are complicated nonlinear temperature- and time-dependent problems. The introduction of friction with its irreversible character makes the problem more difficult. Additionally, the consideration of temperature, as an independent variable, destroys the convolution integral form of the viscoelasticity constitutive relations. This paper presents a computational model capable of predicting the nonlinear quasistatic response of uncoupled thermoviscoelastic frictional contact problems. The contact problem, as a variational inequality constrained model, is handled by using the Lagrange multiplier method to incorporate the inequality contact constraints. A local nonlinear friction law is adapted to model friction at the contact interface. This, in turn, eliminates difficulties that arise with the application of the classical friction laws. The temperature-dependency of viscoelasticity is modeled by applying the time-temperature superposition principle. The constitutive equations are transformed to be a function of the reduced time as the only independent variable, maintaining the convolution integral form. Two different illustrative examples are presented to demonstrate the applicability of the proposed model to analyze both nonconformal and conformal thermoviscoelastic frictional contact problems.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Contact of two deformable bodies

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Figure 2

Representation of the local nonlinear friction model

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Figure 3

Geometry of the contact interface, (a) a contactor node K in contact with a target segment S, and (b) contact forces at the contact interface

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Figure 4

Contact of a viscoelastic cylinder and an elastic substrate

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Figure 5

VE and THVE contact pressure distribution at different instants of time

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Figure 6

VE and THVE tangential contact stress distribution at different instants of time

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Figure 7

Relaxation of maximum contact stresses for VE and THVE responses

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Figure 8

Relative tangential displacements throughout the contact interface at different time instants

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Figure 9

A viscoelastic block resting on a flat rigid foundation

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Figure 10

VE and THVE contact pressure distributions at different instants of time

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Figure 11

VE and THVE tangential contact stress distributions at different instants of time

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Figure 12

Relaxation of maximum contact stresses for VE and THVE responses

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Figure 13

Relative tangential displacements throughout the contact interface at different time instants

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