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A mixed variational problem with applications in contact mechanics

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Abstract

We provide an existence result in the study of an abstract mixed variational problem which involves a history-dependent operator and two nondifferentiable functionals depending on the solution. The proof relies on generalized saddle point theory and a fixed point argument. Then we consider a new mathematical model which describes the quasistatic frictionless contact process between a viscoplastic body and an obstacle. The contact is modeled with a multivalued normal compliance condition and unilateral constraint. We use our abstract result to prove the weak solvability of this contact problem.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Physique, Université de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860, Perpignan, France

    Mircea Sofonea

  2. Department of Mathematics, University of Craiova, A.I. Cuza 13, 200585, Craiova, Romania

    Andaluzia Matei

Authors
  1. Mircea Sofonea
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  2. Andaluzia Matei
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Correspondence to Mircea Sofonea.

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Sofonea, M., Matei, A. A mixed variational problem with applications in contact mechanics. Z. Angew. Math. Phys. 66, 3573–3589 (2015). https://doi.org/10.1007/s00033-015-0573-3

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  • DOI: https://doi.org/10.1007/s00033-015-0573-3

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