A theory of thermopiezoelectricity with strain gradient and electric field gradient effects

This paper is concerned with a theory of thermopiezoelectricity in which the second gradient of displacement and the second gradient of electric potential are included in the set of independent constitutive variables. First, the basic equations of a linear theory are derived. The field equations for homogeneous and isotropic solids are established and the boundary-initial-value problems are formulated. Then, a uniqueness result for the mixed boundary-initial-value problem and a reciprocity relation are presented. This relation forms the basis of a reciprocal theorem and a new uniqueness result. Finally, the fundamental solutions in the stationary theory and representations of Somigliana type are derived.