Bulletin of the Belgian Mathematical Society - Simon Stevin

On a frictional contact problem with adhesion in piezoelectricity

Mohamed Selmani and Lynda Selmani

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We consider a mathematical model describing the quasistatic frictional contact between an electro-elasto-viscoplastic body and an adhesive conductive foundation. The contact is described with a normal compliance condition with adhesion, the associated general version of Coulomb's law of dry friction in which the adhesion of contact surfaces is taken into account and a regularized electrical conductivity condition. The existence of a unique weak solution is established under smallness assumption on the surface conductance. The proof is based on arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 2 (2016), 263-284.

First available in Project Euclid: 31 May 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 74M15: Contact 74M10: Friction 74F15: Electromagnetic effects 74D10: Nonlinear constitutive equations

Electro-elasto-viscoplastic materials quasistatic process internal state variable frictional contact normal compliance adhesion weak solution fixed point


Selmani, Mohamed; Selmani, Lynda. On a frictional contact problem with adhesion in piezoelectricity. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 2, 263--284. doi:10.36045/bbms/1464710118. https://projecteuclid.org/euclid.bbms/1464710118

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