In this paper we study the equations of the nonlinear theory of type II Thermoelasticity proposed by Green and Naghdi. We propose a constitutive framework for the free energy function arising in this theory and study various consequences including the existence and uniqueness of quasistatic solutions and the possibility of thermally activated instability.
Quintanilla, R., & Sivaloganathan, J. (2012). Aspects of the nonlinear theory of type II thermoelastostatics. European Journal of Mechanics - A/Solids, 32(1), 109-117. https://doi.org/10.1016/j.euromechsol.2011.09.002