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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Laboratoire de Mathématiques et Physique, Université de Perpignan Via Domitia, 52 Avenue de Paul Alduy, 66 860, Perpignan, France

    M. Sofonea

  2. Tiberiu Popoviciu Institute of Numerical Analysis, P.O. Box 68-1, 400110, Cluj-Napoca, Romania

    F. Pătrulescu

  3. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Kogălniceanu street, no. 1, 400084, Cluj-Napoca, Romania

    A. Farcaş

Authors
  1. M. Sofonea
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  2. F. Pătrulescu
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  3. A. Farcaş
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Correspondence to M. Sofonea.

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Sofonea, M., Pătrulescu, F. & Farcaş, A. A Viscoplastic Contact Problem with Normal Compliance, Unilateral Constraint and Memory Term. Appl Math Optim 69, 175–198 (2014). https://doi.org/10.1007/s00245-013-9216-2

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  • DOI: https://doi.org/10.1007/s00245-013-9216-2

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