Applied Mathematics & Optimization

, Volume 69, Issue 2, pp 175–198 | Cite as

A Viscoplastic Contact Problem with Normal Compliance, Unilateral Constraint and Memory Term



We consider a mathematical model which describes the quasistatic contact between a viscoplastic body and a foundation. The material’s behavior is modelled with a rate-type constitutive law with internal state variable. The contact is frictionless and is modelled with normal compliance, unilateral constraint and memory term. We present the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. Then we prove its unique weak solvability. The proof is based on arguments of history-dependent quasivariational inequalities. We also study the dependence of the solution with respect to the data and prove a convergence result.


Viscoplastic material Frictionless contact Normal compliance Unilateral constraint Memory term History-dependent variational inequality Weak solution Fréchet space 



The work of the first two authors was supported within the Sectorial Operational Programme for Human Resources Development 2007-2013, co-financed by the European Social Fund, under the projects POSDRU/88/1.5/S/60185 and POSDRU/107/1.5/ S/76841, respectively, entitled Modern Doctoral Studies: Internationalization and Interdisciplinarity, at University Babeş-Bolyai, Cluj-Napoca, Romania.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et PhysiqueUniversité de Perpignan Via DomitiaPerpignanFrance
  2. 2.Tiberiu Popoviciu Institute of Numerical AnalysisCluj-NapocaRomania
  3. 3.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania

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