A frictional contact problem with adhesion for viscoelastic materials with long memory. (English) Zbl 1538.49013

Kasri, Abderrezak

Appl. Math., Praha 66, No. 4, 479-508 (2021).

Summary: We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb’s law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization method, the Banach fixed point theorem and arguments of lower semicontinuity, compactness and monotonicity.

MSC:

49J40	Variational inequalities
74H20	Existence of solutions of dynamical problems in solid mechanics
74A55	Theories of friction (tribology)
74D05	Linear constitutive equations for materials with memory
74F25	Chemical and reactive effects in solid mechanics

Keywords:

viscoelastic material; long memory; adhesion; quasistatic process; Coulomb’s law of dry friction; normal compliance; the time-discretization method; variational inequality

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