On Abstract Variational Inequalities in Viscoplasticity with Frictional Contact


DOI: 10.1007/s10957-007-9176-2

Cite this article as:
Delost, M. & Fabre, C. J Optim Theory Appl (2007) 133: 131. doi:10.1007/s10957-007-9176-2


In this paper, we study quasistatic abstract variational inequalities with time-dependent constraints. We prove existence results and present an approximation method valid for nonsmooth constraints. Then, we apply our results to the approximation of the quasistatic evolution of an elastic body in bilateral contact with a rigid foundation. The contact involves viscous friction of the Tresca or Coulomb type. We prove existence results for approximate problems and give a full asymptotic analysis, proving strong or weak convergence results. Our work is motivated by the numerical study in the paper [Delost, M.: Quasistatic Problem with Frictional Contact: Comparison between Numerical Methods and Asymptotic Analysis Related to Semi Discrete and Fully Discrete Approximations. University of Nice, Nice (2007, to appear)] and explains the choice of the approximation made in it.


Frictional contacts Viscoplasticity Variational inequalities Asymptotic analysis 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Observatoire OcanologiqueVillefranche sur MerFrance
  2. 2.Université Paris SudOrsayFrance

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