On the Issue of Variational Formulation of Problems of Generalized GN-Thermoelasticity

Issues related to the formulation of the variational principles of generalized thermoelasticity based on the Green–Naghdi (GN-thermoelasticity or GN theory) theory are investigated. Variants of the Green–Naghdi theory are considered: classical coupled thermoelasticity and hyperbolic thermoelasticity. To construct functionals of the linear theory of thermoelasticity, the variational principle, which is a generalization of Hamilton’s principle in the linear theory of elasticity, is used. Conditions for the stationarity of the constructed functionals are formulated leading to differential formulations of thermoelasticity problems.