A Mathematical Model for the Electrothermomechanical Behavior of Dielectric Viscoelastic Materials

Abstract

This study examines the behavior of a material under electro-mechanical loads arising of the external medium in a viscoelastic and dielectric material, provided that isotropy constraint is imposed on the material. The reaction of the object to external loads is expressed in elastic stress, dissipative stress and electrical polarization. Based on constitutive axioms and concepts pertaining to the symmetry group of the material, constitutive functionals have been obtained. To materially determine arguments of these functionals, findings of the theory of invariants have been used as a routine method. As a result constitutive equations pertaining to elastic stress, polarization field and dissipative stress have been found in material and spatial coordinates whereas symmetric and asymmetric stresses have been found in terms of displacement gradient and its derivative by using the expressions of elastic stress, polarization field and dissipative stress.

A Mathematical Model for the Electrothermomechanical Mechanical Behavior of Viscoelastic Piezoelectric Body having Hexagonal Symmetry

“…* + P ' + P (23) Polarization vector per unit of mass here is defined as follows: (24) 156 Brought to you by | University of California Authenticated Download Date | 6/9/15 5:12 AM…”

On Constitutive Equations for Anisotropic Nonlinearly Piezoelectric Materials

“…In all of our previous studies [11,12,13,14], since the material is viscoelastic, the symmetric stress was obtained as the sum of elastic and dissipative stresses. In our study [15], the constitutive equations determining the linear electro-thermomechanical behavior of a thermoelastic-piezoelectric medium have been obtained.…”