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Analysis of electroelastic frictionless contact problems with adhesion

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  • Mircea Sofonea
  • Rachid Arhab
  • Raafat Tarraf

Abstract

We consider two quasistatic frictionless contact problems forpiezoelectric bodies. For the first problem the contact ismodelled with Signorini's conditions and for the second one ismodelled with normal compliance. In both problems the material'sbehavior is electroelastic and the adhesion of the contactsurfaces is taken into account and is modelled with a surfacevariable, the bonding field. We provide variational formulationsfor the problems and prove the existence of a unique weak solutionto each model. The proofs are based on arguments of time-dependentvariational inequalities, differential equations, and fixed point.Moreover, we prove that the solution of the Signorini contactproblem can be obtained as the limit of the solution of thecontact problem with normal compliance as the stiffnesscoefficient of the foundation converges to infinity.

Suggested Citation

  • Mircea Sofonea & Rachid Arhab & Raafat Tarraf, 2006. "Analysis of electroelastic frictionless contact problems with adhesion," Journal of Applied Mathematics, Hindawi, vol. 2006, pages 1-25, August.
    • Handle: RePEc:hin:jnljam:064217
    DOI: 10.1155/JAM/2006/64217
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