Analysis of a thermopiezoelectric isotropic problem with Green and Laws model

In this paper, we consider the linear theory for a model of a thermopiezoelectric nonsimple body as presented in Passarella (Entropy 24:1229, 2022) in which the second displacement gradient and the second gradient of electric potential are included in the set of independent constitutive variables and in which an entropy production inequality model proposed by Green and Laws is considered. After recalling the constitutive equations of the theory, the focus is on isotropic materials, for which the constitutive coefficients were first derived and used to determine the constitutive and field equations. An exponential stability result will be established and a qualitative analysis of plane harmonic wave propagation in the isothermal case will be discussed. Exponential stability will be proved, through the Hurwitz criterion, for a one-dimensional system of a thermopiezoelectric material whose equations involve as unknown fields the displacement, the relative temperature and the electric potential. The qualitative properties of wave propagation for some specific piezoelectric materials (quartz, tourmaline, PZT and LGS), of which values of constitutive constants are known, will be shown.