Thick obstacle problems with dynamic adhesive contact
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 6, p. 1021-1045

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.

DOI : https://doi.org/10.1051/m2an:2008037
Classification:  74M20,  74M15,  74K10,  35L85
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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {6},
     year = {2008},
     pages = {1021-1045},
     doi = {10.1051/m2an:2008037},
     zbl = {1149.74043},
     mrnumber = {2473318},
     language = {en},
     url = {http://www.numdam.org/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, Volume 42 (2008) no. 6, pp. 1021-1045. doi : 10.1051/m2an:2008037. http://www.numdam.org/item/M2AN_2008__42_6_1021_0/

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