A quasistatic unilateral and frictional contact problem with adhesion for elastic materials
Tom 36 / 2009
Applicationes Mathematicae 36 (2009), 107-127
MSC: 74M10, 74M15, 47J20, 49J40.
DOI: 10.4064/am36-1-8
Streszczenie
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.
