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.
@article{M2AN_2008__42_6_1021_0,
author = {Ahn, Jeongho},
title = {Thick obstacle problems with dynamic adhesive contact},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {42},
year = {2008},
pages = {1021-1045},
doi = {10.1051/m2an:2008037},
mrnumber = {2473318},
zbl = {1149.74043},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2008__42_6_1021_0}
}
Ahn, Jeongho. Thick obstacle problems with dynamic adhesive contact. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) pp. 1021-1045. doi : 10.1051/m2an:2008037. http://gdmltest.u-ga.fr/item/M2AN_2008__42_6_1021_0/
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