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On fractional order generalized thermoelasticity with micromodeling

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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 microcracks. Built upon the micromorphic theory, the theory of fractional order generalized micromorphic thermoelasticity (FOGTEmm) is firstly established by introducing the fractional integral operator. To generalize the FOGTEmm 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 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) and microstretch thermoelasticity (FOGTEms) and the corresponding generalized variational theorems are also presented.

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Authors and Affiliations

  1. State Key Laboratory for Mechanical Structure Strength and Vibration, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Ya Jun Yu, Xiao Geng Tian & Tian Jian Lu

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  1. Ya Jun Yu
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  2. Xiao Geng Tian
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  3. Tian Jian Lu
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Correspondence to Xiao Geng Tian.

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Yu, Y.J., Tian, X.G. & Lu, T.J. On fractional order generalized thermoelasticity with micromodeling. Acta Mech 224, 2911–2927 (2013). https://doi.org/10.1007/s00707-013-0913-3

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