| Issue |
ESAIM: M2AN
Volume 42, Number 6, November-December 2008
|
|
|---|---|---|
| Page(s) | 1021 - 1045 | |
| DOI | https://doi.org/10.1051/m2an:2008037 | |
| Published online | 25 September 2008 | |
Thick obstacle problems with dynamic adhesive contact
Department of Mathematics and Statistics, Arkansas State University, P.O. Box 70, State University, AR 72467, USA. jeongho.ahn@csm.astate.edu
Received:
4
October
2007
Revised:
2
April
2008
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.
Mathematics Subject Classification: 74M20 / 74M15 / 74K10 / 35L85
Key words: Adhesion / Signorini's contact / complementarity conditions / time-discretization.
© EDP Sciences, SMAI, 2008
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