Some results on thermopiezoelectricity of nonsimple materials

TL;DR

This paper develops a theoretical framework for thermopiezoelectric nonsimple materials, establishing reciprocity, variational principles, and uniqueness results within a linear, anisotropic, and symmetric setting.

Contribution

It introduces new reciprocity theorems and a variational principle for thermopiezoelectric nonsimple materials, extending previous theories with a focus on entropy production and symmetry.

Findings

Established reciprocity theorems for the model

Formulated a variational principle for the system

Proved uniqueness without energy definiteness assumptions

Abstract

In this paper, we consider the linear theory for a model of a thermopiezoelectric nonsimple material adopting the entropy production inequality proposed by Green and Laws as presentated in Passarella (2022). We establish reciprocity theorems and a variational principle for homogeneous and anisotropic thermopiezoelectric nonsimple materials with a center of symmetry. The proof of these theorems use the time convolution product and an alternative formulation of the field equations. Moreover, a uniqueness result is established without using the definiteness assumptions on internal energy.