Uniqueness of solutions in thermopiezoelectricity of nonsimple materials

TL;DR

This paper develops a thermopiezoelectricity theory for nonsimple materials incorporating second gradients, establishing thermodynamic restrictions, constitutive equations, and proving solution uniqueness for the boundary-initial value problem.

Contribution

It introduces a novel thermopiezoelectricity model with second gradient effects and proves the uniqueness of solutions, advancing the theoretical understanding of nonsimple materials.

Findings

Derived thermodynamic restrictions and constitutive equations.

Established basic equations of linear thermopiezoelectricity.

Proved uniqueness of solutions for the mixed boundary-initial value problem.

Abstract

In this paper, using the entropy production inequality of Green and Laws, the theory of thermopiezoelectricity is presented, in which the second gradient of displacement and the second gradient of electric potential are included in the set of independent constitutive variables. At first, the appropriate thermodynamic restrictions and constitutive equations are obtained. Then, the basic equations of linear theory are derived and a uniqueness result for the mixed boundary-initial value problem is presented.