Some Variational Principles for Coupled Thermoelasticity

The nonlinear thermoelasticity of type II proposed by Green and Naghdi is considered. The thermoelastic structural model is formulated in a quasistatic range, and the related thermoelastic variational formulation in the complete set of state variables is recovered. Hence a consistent framework to derive all the variational formulations with different combinations of the state variables is provided, and a family of mixed variational formulations, with different combinations of state variables, is provided starting from the general variational formulation. A uniqueness condition is provided on the basis of a suitable variational formulation.