Second gradient theory of thermopiezoelectricity

This paper is concerned with a linear theory of thermopiezoelectricity in which the second gradient of the displacement, the second gradient of the electric potential and the second temperature gradient are included in the classic set of independent constitutive variables. The present paper is based on Green–Naghdi thermomechanics. The introduction of the entropy flux tensor leads to constitutive equations that depend on the second temperature gradient. The fundamental boundary-initial-value problems are formulated and the uniqueness of the solution is studied. Two applications of the theory are presented. We study the problem of a concentrated charge density acting in an unbounded region, as well as the effects of a concentrated heat source.