Variational principle and reciprocity theorem on the temperature-rate-dependent poro-thermoelasticity theory

Abstract

The present work is concerned with the temperature-rate-dependent theory of poro-thermoelasticity for anisotropic homogeneous medium and aims to establish the variational principle based on this theory for the fluid-saturated poro-thermoelastic medium. Here, the principle of virtual work is applied to derive the expressions for the generalized strain energy, Biot’s free energy, and the total work done by the system during the thermo-mechanical process. Further in view of this, the variational principle is established in the context of the temperature-rate-dependent poro-thermoelasticity. We also prove that a reciprocity theorem results for a general problem of poro-thermoelasticity of an anisotropic medium. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.