Some basic theorems on the modified Green–Lindsay model of linear generalized thermoelasticity

The present paper is concerned with a theory of thermoelasticity based upon a newly developed temperature-rate-dependent thermoelastic model that was proposed by Yu et al. [Meccanica. 2018;53:2543–2554], which has eliminated the discontinuity observed in the displacement field during transient motion. The basic governing equations for a homogeneous and isotropic medium are formulated to deduce the significant theorems. Firstly, we prove the uniqueness theorem concerning a mixed initial and boundary value problem within the framework of linear thermoelasticity. Furthermore, we establish a reciprocity theorem utilizing the Laplace transform, which provides insight into the mutual influence between different aspects of the system under consideration. Consequently, we proved the Somigliana and Green theorems. This generalized theorem extends the applicability and versatility of the classical theorems and also assists the issue of thermal and mechanical fields as well as is beneficial for geophysics and mining.