Thick obstacle problems with dynamic adhesive contact
Department of Mathematics and Statistics, Arkansas State University, P.O. Box 70, State University, AR 72467, USA. email@example.com
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