Geodesic
A viscoplastic contact problem with friction and adhesion
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 540-565

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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. 
@article{SEMR_2020_17_a89,
     author = {Abderrezak Kasri},
     title = {A viscoplastic contact problem with friction and adhesion},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {540--565},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a89/}
}
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Abderrezak Kasri. A viscoplastic contact problem with friction and adhesion. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 540-565. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a89/