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Thick obstacle problems with dynamic adhesive contact

Published online by Cambridge University Press:  25 September 2008

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2008

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References

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