Rachid Guettaf, Arezki Touzaline
abstract:
This paper deals with the study of a mathematical model that describes a
frictional contact between a piezoelectric body and an obstacle. The material
behavior is described with an electro-elastic constitutive law with long memory
and the contact is modelled with Signorini conditions associated with the
non-local friction law in which the adhesion between the contact surfaces is
taken into account. We establish a variational formulation of the model in the
form of a system involving the displacement, stress, electric displacement,
electric potential and adhesion field. Under the assumption that the coefficient
of friction is small enough, we prove the existence of a unique weak solution to
the problem. The proof is based on arguments of variational inequalities,
nonlinear evolutionary equations with monotone operators, differential equations
and the Banach fixed-point theorem.
Mathematics Subject Classification: 74M15, 74H10, 74F25, 49J40, 35D30
Key words and phrases: Electro-elastic, adhesion, variational inequalities, fixed point, weak solution