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ESAIM: Mathematical Modelling and Numerical Analysis ESAIM: Mathematical Modelling and Numerical Analysis

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Thick obstacle problems with dynamic adhesive contact

Published online by Cambridge University Press:  25 September 2008

Jeongho Ahn
Jeongho Ahn*
Affiliation:
Department of Mathematics and Statistics, Arkansas State University, P.O. Box 70, State University, AR 72467, USA. jeongho.ahn@csm.astate.edu
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Abstract

In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the Kelvin-Voigt type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate the convergence of numerical trajectories. The fully discrete approximation which satisfies the complementarity conditions is computed by using the nonsmooth Newton's method with the Kanzow-Kleinmichel function. Numerical simulations of a viscoelastic beam clamped at two ends are presented.

Keywords

AdhesionSignorini's contactcomplementarity conditionstime-discretization.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 6 , November 2008 , pp. 1021 - 1045
Copyright
© EDP Sciences, SMAI, 2008

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