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A One-Dimensional Problem of Nonlinear Thermo-Electroelasticity with Thermal Relaxation

  • Wael Mahmoud
  • Moustafa S. Abou-Dina
  • Amr R. El Dhaba
  • Ahmed F. Ghaleb
  • Enaam K. Rawy
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)

Abstract

We investigate a nonlinear, one-dimensional problem of thermoelectroelasticity with thermal relaxation and in quasi-electrostatics. The system of basic equations is a restriction to one spatial dimension of that proposed earlier in Abou-Dina et al (2017). This model is based on the introduction of the heat flow vector as an additional state variable, thus leading to a Cattaneo-type evolution equation. It includes several non-linear couplings and may be useful in studying problems of elastic dielectrics at low temperatures, as well as in problems of high-temperature heat conduction in dielectric solids subjected to strong high-frequency laser beams. For the present investigation, however, only a few nonlinearities have been retained in the equations for conciseness. A numerical solution is presented for the system of nonlinear equations using an iterative, quasilinearization scheme by finite differences. The numerical results are discussed.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Wael Mahmoud
    • 1
  • Moustafa S. Abou-Dina
    • 1
  • Amr R. El Dhaba
    • 2
  • Ahmed F. Ghaleb
    • 1
  • Enaam K. Rawy
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt
  2. 2.Department of Mathematics, Faculty of ScienceDamanhour UniversityDamanhurEgypt

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