Strain gradient thermopiezoelectric materials

Results from the linear theory of thermopiezoelectricity are discussed in this article. A brief introduction to dielectric materials and the phenomenon of direct and inverse piezoelectricity is given. Then, a general theory of thermopiezoelectricity for strain gradient materials is given, where the second gradient of the displacement field and electric potential enter into the set of independent constitutive variables. The second law of thermodynamics is formulated following an entropy production inequality proposed by Green and Laws. The thermodynamics restrictions are obtained, then the linear constitutive equations and the mixed initial-boundary value problem are established. On the basis of this theory, a uniqueness result and a variational principle are obtained.