The theory of nonsimple thermoelastic materials has been discussed in various articles.
The question of the interaction of electromagnetic fields with elastic solids has been the subject of important investigations. Some crystals (such as quartz) subjected to stress, become electrically polarized (piezoelectric effect). Conversely, an external electromagnetic field produces deformation in a piezoelectric crystal. The theory of thermopiezoelectricity has been studied in various works. Our contribution on the theory of thermopiezoelectricity of a body is divided into two papers. In the first one, we derive a theory in which the second displacement gradient and the second electric potential gradient are included in the set of independent constitutive variables. This theory may be useful for starting a series of observations, although the number of parameters to be determined is significant and there is no easy way to deduce them from current experiments. We obtain the appropriate thermodynamic restrictions and constitutive equations, with the help of an entropy production inequality proposed by Green&Laws. In the second one, starting from the linear theory, we consider in particular the case of center-symmetric materials, and we prove a number of useful results without using the definiteness assumptions on internal energy and with the help of the time convolution product.