A bilateral contact problem with nonlocal friction, damage and adhesion
Volume 48 / 2021
Applicationes Mathematicae 48 (2021), 37-63
MSC: 74C10, 49J40, 74A55, 74H20, 74M15, 74F25.
DOI: 10.4064/am2402-2-2021
Published online: 12 May 2021
Abstract
We consider a bilateral contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The process is quasistatic and the contact is modelled with a general nonlocal friction law in which the adhesion of contact surfaces is taken into account. We derive a variational formulation of the problem and, under smallness assumptions, we establish an existence and uniqueness theorem of a weak solution, including a regularity result. We also study the dependence of the solution on the data.