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IMA Journal of Numerical Analysis Advance Access originally published online on February 16, 2008
IMA Journal of Numerical Analysis 2009 29(1):43-71; doi:10.1093/imanum/drm029
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Dynamic frictionless contact in linear viscoelasticity

Jeongho Ahn{dagger}

Department of Mathematics and Physics, Alfred State SUNY College of Technology, Alfred, NY 14802, USA

David E. Stewart

Department of Mathematics, University of Iowa, Iowa, IA 52242, USA

{dagger} Email: ahnj{at}alfredstate.edu

Received on 11 August 2006. Revised on 18 July 2007.


  Abstract

In this work, we formulate a dynamic frictionless contact problem with linear viscoelasticity of Kelvin–Voigt type, based on the Signorini contact conditions. We show existence of solutions, and investigate the possibility for obtaining an energy balance. Employing time discretization and the finite-element method, we compute numerical solutions. Our numerical scheme is implemented with non-smooth Newton's method which solves the complementarity problem. The numerical results support the idea that the energy losses in the limit of the numerical solution are equal to the losses due to viscosity.

Key Words: viscoelasticity; Signorini contact; complementarity condition; time discretization


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