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: adhesion, Signorini's contact, complementarity conditions, time-discretization
@article{M2AN_2008__42_6_1021_0, author = {Ahn, Jeongho}, title = {Thick obstacle problems with dynamic adhesive contact}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {1021--1045}, publisher = {EDP-Sciences}, volume = {42}, number = {6}, year = {2008}, doi = {10.1051/m2an:2008037}, mrnumber = {2473318}, zbl = {1149.74043}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008037/} }
TY - JOUR AU - Ahn, Jeongho TI - Thick obstacle problems with dynamic adhesive contact JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 1021 EP - 1045 VL - 42 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008037/ DO - 10.1051/m2an:2008037 LA - en ID - M2AN_2008__42_6_1021_0 ER -
%0 Journal Article %A Ahn, Jeongho %T Thick obstacle problems with dynamic adhesive contact %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 1021-1045 %V 42 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008037/ %R 10.1051/m2an:2008037 %G en %F M2AN_2008__42_6_1021_0
Ahn, Jeongho. Thick obstacle problems with dynamic adhesive contact. ESAIM: Modélisation mathématique et analyse numérique, Volume 42 (2008) no. 6, pp. 1021-1045. doi : 10.1051/m2an:2008037. http://www.numdam.org/articles/10.1051/m2an:2008037/
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