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Memory-dependent derivatives theory of thermo-viscoelasticity involving two-temperature

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Abstract

A new model of two-temperature generalized thermo-viscoelasticity theory based on memory-dependent derivative is constructed. The equations of the new model are applied to one-dimensional problem of a half-space. The bounding surface is taken to be traction free and subjected to a time dependent thermal shock. Laplace transforms technique is used. A direct approach is applied to obtain the exact formulas of heat flux, temperature, stresses, displacement and strain in the Laplace transform domain. Application is employed to our problem to get the solution in the complete form. The considered variables are presented graphically and discussions are made.

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Authors and Affiliations

  1. Dep. of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt

    M. A. Ezzat

  2. Arab Academy for Science and Technology, P.O. Box 1029, Alexandria, Egypt

    A. A. El-Bary

Authors
  1. M. A. Ezzat
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  2. A. A. El-Bary
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Correspondence to M. A. Ezzat.

Additional information

Recommended by Associate Editor Seong Beom Lee

Magdy A. Ezzat is a professor of Applied Mathematics. He received his Ph.D. at Russia from Georgia University in 1988 and now he is a lecture in faculty of Education, Alexandria University. His current research is focused on MHD and generalized thermoelasticity theory. He published a review of state space approach to solids and fluids in Canadian Journal of Physics, 2008 and participated in the research encyclopedia of Thermal stresses, 2014.

Alaa Abdelbary El-Bary is a profeessor of Computational and Applied Mathematics. He obtained his B.sc., Msc. and Ph.D. in 1988, 1996 and 1999, respectively. Abdelbary interested and research oriented in the field of Applied Mathematics (Hydrodynamics and Thermoelasticity) in general and published more than 70 research papers in international reviewed journals and conferences.

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Ezzat, M.A., El-Bary, A.A. Memory-dependent derivatives theory of thermo-viscoelasticity involving two-temperature. J Mech Sci Technol 29, 4273–4279 (2015). https://doi.org/10.1007/s12206-015-0924-1

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  • DOI: https://doi.org/10.1007/s12206-015-0924-1

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