A quasistatic unilateral and frictional contact problem with adhesion for elastic materials

Volume 36 / 2009

Arezki Touzaline Applicationes Mathematicae 36 (2009), 107-127 MSC: 74M10, 74M15, 47J20, 49J40. DOI: 10.4064/am36-1-8


We consider a quasistatic contact problem between a linear elastic body and a foundation. The contact is modelled with the Signorini condition and the associated non-local Coulomb friction law in which the adhesion of the contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation of the mechanical problem and prove existence of a weak solution if the friction coefficient is sufficiently small. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments, differential equations and the Banach fixed point theorem.


  • Arezki TouzalineLaboratoire de Systèmes Dynamiques
    Faculté de Mathématiques, USTHB
    BP 32 El Alia
    Bab Ezzouar, 16111, Algeria

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