Glasnik Matematicki, Vol. 45, No.1 (2010), 109-124.

A QUASISTATIC FRICTIONAL CONTACT PROBLEM WITH NORMAL COMPLIANCE AND FINITE PENETRATION FOR ELASTIC MATERIALS

Arezki Touzaline

Abstract.   We consider a quasistatic unilateral contact problem with finite penetration between an elastic body and an obstacle, say a foundation. The constitutive law is assumed to be nonlinear and the contact is modelled with normal compliance associated to a version of Coulomb's law of dry friction. Under a smallness assumption on the contact functions, we establish the existence of a weak solution to the problem. The proofs are based on arguments of time-dicretization, compactness and lower semicontinuity.

2000 Mathematics Subject Classification.   35J85, 47J20, 74M10, 74M15.

Key words and phrases.   Elastic material, quasistatic process, frictional contact, incremental, normal compliance, Signorini condition, variational inequality, weak solution.

DOI: 10.3336/gm.45.1.09

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