In this paper, we consider a mathematical model of a contact problem in thermo-electro-viscoelasticity with the normal compliance conditions and Tresca’s friction law. We present a variational formulation of the problem, and we prove the existence and uniqueness of the weak solution. We also study the numerical approach using spatially semidiscrete and fully discrete finite element schemes with Euler’s backward scheme. Finally, we derive error estimates on the approximate solutions.
The aim of this paper is to study a Signorini?s problem with Coulomb?s
friction between a thermo-electro-viscoelasticity body and an electrically
and thermally conductive foundation. The materiel?s behavior is described by
the linear thermo-electro-viscoelastic constitutive laws. The variational
formulation is written as nonlinear quasivariational inequality for the
displacement field, a nonlinear family elliptic variational equations for
the electric potential and a nonlinear parabolic variational equations for
the temperature field. We prove under some assumption existence of a weak
solution to the problem. The thermo-electro-viscoelastic law with a some
temperature parameter ? > 0 is considered. Then we prove its unique solution
as well as the convergence of its solution to the solution of the original
problem as the temperature parameter ? ? 0.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.