Theory of uniformity applied to elastic dielectric materials and piezoelectricity

Abstract

Building on the celebrated works by Toupin (1963) on non-linear elastic dielectric materials and by Noll (1967) on the theory of material uniformity, we use the method of linear perturbations to obtain a generalised form of the equations of piezoelectricity in the linear regime, i.e., below the ferroelectric threshold. More specifically, in their most general form, the piezoelectric constitutive equations that we obtain include an anelastic strain and an anelastic polarisation, both arising from the intrinsic inhomogeneity of the body and according to the theory of material uniformity. These are distinct from the irreversible strain and polarisation that occur at values of stress and electric field above the ferroelectric threshold. Some of the known standard forms of the piezoelectricity equations are retrieved as particular cases.