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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Mahmoud, W., Abou-Dina, M.S., El Dhaba, A.R., Ghaleb, A.F., Rawy, E.K. (2018). A One-Dimensional Problem of Nonlinear Thermo-Electroelasticity with Thermal Relaxation. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 1. Advanced Structured Materials, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-72440-9_26
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DOI: https://doi.org/10.1007/978-3-319-72440-9_26
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