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An Algorithmic Perspective on the Thermoelasticity of the Micromorphic Materials Using Fractional Order Strain

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Algorithms as a Basis of Modern Applied Mathematics

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 404))

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Abstract

The chapter is dealing with the approach to the micromorphic materials linear thermoelasticity, its purpose being to present an algorithmic perspective in obtaining, on the one hand, the constitutive equations of this linear theory and the non-Fourier heat equation form, and on the other hand, in obtaining a reciprocal relation, by using the Caputo fractional derivative. This algorithmic perspective allows the creation of a technical scheme that can be followed in determining these basic relations of the linear thermoelasticity of the micromorphic materials, providing a model that can be used to determine these equations for other materials, thus the theory can be extended to various materials. The algorithmic transposition of a mathematical model always leads to a relaxation of the mathematical solution and to its systematization, the mathematical reasoning being presented in the form of concrete steps to be followed in order to obtain the solution of a problem.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Transilvania University of Braşov, Bd. Eroilor 29, 500036, Braşov, Romania

    Lavinia Codarcea-Munteanu & Marin Marin

Authors
  1. Lavinia Codarcea-Munteanu
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  2. Marin Marin
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Corresponding author

Correspondence to Lavinia Codarcea-Munteanu .

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Editors and Affiliations

  1. Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Brno, Czech Republic

    Šárka Hošková-Mayerová

  2. Faculty of Mathematics and Computer Science, Ovidius University, Constanta, Romania

    Cristina Flaut

  3. Department of Mathematics and Physics, University of Campania “Luigi Vanvitelli”, Caserta, Italy

    Fabrizio Maturo

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Codarcea-Munteanu, L., Marin, M. (2021). An Algorithmic Perspective on the Thermoelasticity of the Micromorphic Materials Using Fractional Order Strain. In: Hošková-Mayerová, Š., Flaut, C., Maturo, F. (eds) Algorithms as a Basis of Modern Applied Mathematics. Studies in Fuzziness and Soft Computing, vol 404. Springer, Cham. https://doi.org/10.1007/978-3-030-61334-1_8

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