Thick obstacle problems with dynamic adhesive contact

Jeongho Ahn

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 6, page 1021-1045
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Ahn, Jeongho. "Thick obstacle problems with dynamic adhesive contact." ESAIM: Mathematical Modelling and Numerical Analysis 42.6 (2008): 1021-1045. <http://eudml.org/doc/250284>.

@article{Ahn2008,
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. },
author = {Ahn, Jeongho},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Adhesion; Signorini's contact; complementarity conditions; time-discretization.; Signorini conditions; time discretization; convergence},
language = {eng},
month = {9},
number = {6},
pages = {1021-1045},
publisher = {EDP Sciences},
title = {Thick obstacle problems with dynamic adhesive contact},
url = {http://eudml.org/doc/250284},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Ahn, Jeongho
TI - Thick obstacle problems with dynamic adhesive contact
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/9//
PB - EDP Sciences
VL - 42
IS - 6
SP - 1021
EP - 1045
AB - 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.
LA - eng
KW - Adhesion; Signorini's contact; complementarity conditions; time-discretization.; Signorini conditions; time discretization; convergence
UR - http://eudml.org/doc/250284
ER -

References

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