On fractional order generalized thermoelasticity with micromodeling

This paper presents the theory of fractional order generalized thermoelasticity with microstructure modeling for porous elastic bodies and synthetic materials containing microscopic components and microcracks. Built upon the micromorphic theory, the theory of fractional order generalized micromorphic thermoelasticity (FOGTE_mm) is firstly established by introducing the fractional integral operator. To generalize the FOGTE _mm theory, the general forms of the extended thermoelasticity, temperature rate dependent thermoelasticity, thermoelasticity without energy dissipation, thermoelasticity with energy dissipation, and dual-phase-lag thermoelasticity are introduced during the formulation. Secondly, the uniqueness theorem for FOGTE_mm is established. Finally, a generalized variational principle of FOGTE_mm is developed by using the semi-inverse method. For reference, the theories of fractional order generalized micropolar thermoelasticity (FOGTE_mp) and microstretch thermoelasticity (FOGTE_ms) and the corresponding generalized variational theorems are also presented.