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Quasistatic Elastic Contact with Adhesion

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  • Boudjemaa Teniou
  • Sabrina Benferdi

Abstract

The aim of this paper is the variational study of the contact with adhesion between an elastic material and a rigid foundation in the quasistatic process where the deformations are supposed to be small. The behavior of this material is modelled by a nonlinear elastic law and the contact is modelled with Signorini's conditions and adhesion. The evolution of bonding field is described by a nonlinear differential equation. We derive a variational formulation of the mechanical problem, and we prove the existence and uniqueness of the weak solution using a theorem on variational inequalities, the theorem of Cauchy-Lipschitz, a lemma of Gronwall, as well as the fixed point of Banach.

Suggested Citation

  • Boudjemaa Teniou & Sabrina Benferdi, 2011. "Quasistatic Elastic Contact with Adhesion," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-13, October.
    • Handle: RePEc:hin:jijmms:686139
    DOI: 10.1155/2011/686139
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