This article is cited in 2 papers

Differentical equations, dynamical systems and optimal control

A viscoplastic contact problem with friction and adhesion

Abderrezak Kasri

Département de Mathématiques, Faculté des sciences, Université 20 Août 1955 - Skikda, B.P.26 Route El-Hadaiek Skikda-Algérie

Abstract: The aim of this paper is to present a new result in the study of a contact problem between a viscoplastic body and an obstacle, the so-called foundation. The process is supposed to be quasistatic and the contact is modelled with a version of Coulomb's law of dry friction, normal compliance and an ordinary differential equation which describes the adhesion effect. We derive a variational formulation for the model and under smallness assumption, we establish the existence of a weak solution to the problem. The proof is based on the Rothe time-discretization method, the Banach fixed point theorem and arguments of monotonicity, compactness and lower semicontinuity.

Keywords: viscoplastic materials, adhesion, quasistatic process, Coulomb's law of dry friction, normal compliance, Rothe method, lower semicontinuity, the Banach fixed point theorem, variational inequalities.

UDC: 517.9

MSC: 74C10, 74M15, 49J40, 74H20, 74F25, 74A55

Received October 31, 2019, published April 16, 2020

Language: English

DOI: 10.33048/semi.2020.17.035

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