Uniqueness of Solutions in Thermopiezoelectricity of Nonsimple Materials.

This article presents the theory of thermopiezoelectricity in which the second displacement gradient and the second electric potential gradient are included in the set of independent constitutive variables. This is achieved by using the entropy production inequality proposed by Green and Laws. At first, appropriate thermodynamic restrictions and constitutive equations are obtained, using the well-established Coleman and Noll procedure.

Exponential stability in Mindlin's Form II gradient thermoelasticity with microtemperatures of type III.

In this paper, we derive a nonlinear strain gradient theory of thermoelastic materials with microtemperatures taking into account micro-inertia effects as well. The elastic behaviour is assumed to be consistent with Mindlin's Form II gradient elasticity theory, while the thermal behaviour is based on the entropy balance of type III postulated by Green and Naghdi for both temperature and microtemperatures. The work is motivated by increasing use of materials having microstructure at both mechanical and thermal levels.