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Fractional order theory of thermo-viscoelasticity and application

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Abstract

In this work, we derive a new fractional order theory for thermo-viscoelasticity. A uniqueness theorem for these equations is proved. A reciprocity theorem is also proved. A 1D problem for a viscoelastic half space is solved by using the Laplace transform technique. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained by using a numerical method. The temperature, displacement and stress distributions are computed and represented graphically.

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Authors and Affiliations

  1. Department of Mathematics, University of Alexandria, Alexandria, Egypt

    Hany H. Sherief

  2. Department of Mathematics, Damiatta University, New Damiatta, Egypt

    Mohammed A. El-Hagary

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  1. Hany H. Sherief
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  2. Mohammed A. El-Hagary
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Correspondence to Mohammed A. El-Hagary.

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Sherief, H.H., El-Hagary, M.A. Fractional order theory of thermo-viscoelasticity and application. Mech Time-Depend Mater 24, 179–195 (2020). https://doi.org/10.1007/s11043-019-09415-2

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  • DOI: https://doi.org/10.1007/s11043-019-09415-2

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