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On the analysis of a viscoplastic contact problem with time dependent Tresca’s friction law. (English) Zbl 1154.74325

Summary: This paper deals with the study of a nonlinear problem of frictional contact between an elastic-viscoplastic body and a rigid obstacle. We model the frictional contact by a version of Tresca’s friction law where the friction bound depends on time. Firstly, we obtain an existence and uniqueness result in a weak sense for a model including the bilateral contact. To this end we use a time discretization method and the Banach fixed-point theorem. Secondly, we show an existence result for a mechanical problem with the unilateral contact conditions (Signorini’s contact) using an iterative method

MSC:

74D10 Nonlinear constitutive equations for materials with memory
74A55 Theories of friction (tribology)
49J40 Variational inequalities
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