Analysis of an Antiplane Contact Problem with Adhesion for Electro-Viscoelastic Materials

Abstract

We consider a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The adhesion of the contact surfaces, caused by the glue, is taken into account. The material is assumed to be electro-viscoelastic and the foundation is assumed to be electrically conductive. We derive a variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field, a time-dependent variational equation for the electric potential field and a differential equation for the bonding field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of evolution equations with monotone operators and fixed point.

Quasistatic Adhesive Contact of Piezoelectric Cylinders

“…Piezoelectric materials for which the mechanical properties are elastic are called electro-elastic materials and those for which the mechanical properties are viscoelastic are called electro-viscoelastic materials. Antiplane contact problems for piezoelectric materials were considered in [13][14][15][16]. In [13,15,16] the contact was assumed to be frictional and in [14] is was assumed to be adhesive.…”

“…Antiplane contact problems for piezoelectric materials were considered in [13][14][15][16]. In [13,15,16] the contact was assumed to be frictional and in [14] is was assumed to be adhesive.…”

“…The present paper represents a continuation of [14]. There, a mathematical model which describes the antiplane shear deformation of a piezoelectric cylinder in adhesive contact with a rigid foundation was considered.…”

“…An existence and uniqueness result of the solution to the model was obtained by using arguments of evolution equations with monotone operators and fixed point. Unlike [14], in the present paper we model the material's behavior by an electro-viscoelastic constitutive law or by an electro-elastic constitutive law; also, we neglect the inertial term in the equation of motion and, therefore, we assume that the process is mechanically quasistatic. This leads to consider two mathematical models, different from that studied in [14], which represents the first trait of novelty of this paper.…”

“…Unlike [14], in the present paper we model the material's behavior by an electro-viscoelastic constitutive law or by an electro-elastic constitutive law; also, we neglect the inertial term in the equation of motion and, therefore, we assume that the process is mechanically quasistatic. This leads to consider two mathematical models, different from that studied in [14], which represents the first trait of novelty of this paper. We derive the variational formulation of the models and then we prove the existence of a unique weak solution, for each model.…”