Abstract
This paper presents the theory of fractional order generalized thermoelasticity with microstructure modeling for porous elastic bodies and synthetic materials containing microscopic components and micro- cracks. Built upon the micromorphic theory, the theory of fractional order generalized micromorphic ther- moelasticity (FOGTEmm)isfirstlyestablishedbyintroducingthefractionalintegraloperator.Togeneralizethe FOGTEmm theory, the general forms of the extended thermoelasticity, temperature rate dependent thermoelas- ticity,thermoelasticitywithoutenergydissipation,thermoelasticitywithenergydissipation,anddual-phase-lag thermoelasticity are introduced during the formulation. Secondly, the uniqueness theorem for FOGTEmm is established. Finally, a generalized variational principle of FOGTEmm is developed by using the semi-inverse method. For reference, the theories of fractional order generalized micropolar thermoelasticity (FOGTEmp) andmicrostretchthermoelasticity (FOGTEms)andthecorrespondinggeneralizedvariationaltheoremsarealso presented.
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