Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 85, pp. 1-23.

Title: Dynamic contact of viscoelastic bodies with two obstacles: mathematical
       and  numerical approaches
        
Authors: Jeongho Ahn (Arkansas State Univ., Arkansas, USA)
         Jon Calhoun (University of Illinois,  Urbana-Champaign, IL, USA)

Abstract:
 The motion of viscoelastic (Kelvin-Voigt model) bodies
 between an upper and a lower obstacle is studied both mathematically and
 numerically. The two obstacles are assumed to be stationary perfect
 rigid, therefore, Signorini contact conditions are imposed at each
 obstacle, which can be interpreted as a couple of complementarity
 conditions (CCs). The convergence of numerical trajectories for general
 dimensional problems is shown based on the box constrained
 variational inequality (VI) which is equivalent to the two CCs. A
 one-dimensional example is provided. Unlike higher dimensional cases,
 different perspectives are used to prove the results of its existence.
 Numerical results are also presented and discussed, showing a typical
 behavior of the system


Submitted September 05, 2012. Published April 05, 2013.
Math Subject Classifications: 74M20, 74K10, 35L85.
Key Words: Dynamic contact; variational inequality; 
           signorini contact conditions; complementarity conditions; 
           strong pointedness; numerical scheme.