On a theory of thermoelasticity with the second gradient of temperature

Abstract This paper deals with a linear theory of non-simple thermoelastic materials based on Green–Naghdi thermomechanics. We use an entropy production inequality, a thermal displacement and the entropy flux tensor to establish a theory of thermoelasticity in which the second displacement gradient and the second temperature gradient are included in the classical set of independent constitutive variables. The reciprocity theorem, a variational theorem, a uniqueness and a structural stability result are established. The existence and the impossibility of localization are also investigated. In the equilibrium theory, the deformation of an elastic space with a spherical cavity is studied.