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Analysis of a Dynamic Contact Problem for Electro-viscoelastic Materials

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Abstract

We consider a mathematical model which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. We model the material’s behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition. We derive variational formulation for the model which is in the form of a system involving the displacement field, the electric potential field, the damage field and the adhesion field. We prove the existence of a unique weak solution to the problem. The proof is based on arguments of time dependent variational inequalities, parabolic inequalities, differential equations and fixed point.

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Authors and Affiliations

  1. Department of Mathematics, University of Ferhat Abbas, Setif, 19000, Algeria

    Boutechebak Souraya

  2. Department of Mathematics, University of El Oued, El Oued, 39000, Algeria

    Azeb Ahmed Abdelaziz

Authors
  1. Boutechebak Souraya
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  2. Azeb Ahmed Abdelaziz
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Correspondence to Azeb Ahmed Abdelaziz.

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Souraya, B., Abdelaziz, A.A. Analysis of a Dynamic Contact Problem for Electro-viscoelastic Materials. Milan J. Math. 86, 105–124 (2018). https://doi.org/10.1007/s00032-018-0282-4

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  • DOI: https://doi.org/10.1007/s00032-018-0282-4

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