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Exact solutions of generalized thermoelastic medium with double porosity under L–S theory

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Abstract

In this paper, a general solution to the field equations of a generalized thermoelastic medium with double porosity has been obtained. To investigate the problem, we use the Lord–Shulman theory in the thermoelasticity. The half-space of an isotropic homogeneous thermoelastic material is considered. Using the normal mode analysis and the numerical inversion technique, the analytic expressions of the physical quantities are obtained. Numerically, computed results for these quantities and its depicted graphically lead to study the effect of porosity. Comparisons in the presence and absence of double porosity, in two different times, are obtained. Although the problem has been solved theoretically, it is possible for researchers to benefit from their results in many different sciences, for example, in the field of geophysics, earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

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Abbreviations

λ, μ :

Lame’ parameters

δ ij :

Kronecker delta

c e :

The specific heat at constant strain

T 0 :

The reference temperature

σ i :

The equilibrated stress corresponding to v1

τ i :

The equilibrated stress corresponding to v2

b, d, b1, γ, γ1, γ2 :

The constitutive coefficients

v 1 :

The volume fraction field corresponding to pores and v2 is the volume fraction field corresponding to fissures

Ψ, Φ:

The volume fraction fields corresponding to v1 and v2, respectively

K1 and K2 :

The coefficients of equilibrated inertia

T :

The temperature change measured form the absolute temperature T0

u i :

The displacement vector

ρ :

The mass density

τ ij :

The stress tensor

τ 0 :

The relaxation time

K ≥ 0:

The thermal conductivity

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    Mohamed I A Othman, Ramadan S Tantawi & Nehal T Mansour

  2. Mathematics Department, Faculty of Education, Alexandria University, Alexandria, Egypt

    M A Abdou

  3. Basic Sciences Department, Al Safwa High Institute of Engineering, Cairo, Egypt

    Nehal T Mansour

Authors
  1. M A Abdou
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  2. Mohamed I A Othman
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  3. Ramadan S Tantawi
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  4. Nehal T Mansour
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Correspondence to Nehal T Mansour.

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Abdou, M.A., Othman, M.I.A., Tantawi, R.S. et al. Exact solutions of generalized thermoelastic medium with double porosity under L–S theory. Indian J Phys 94, 725–736 (2020). https://doi.org/10.1007/s12648-019-01505-8

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  • DOI: https://doi.org/10.1007/s12648-019-01505-8

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