Skip to main content
SpringerLink
Log in

Two-dimensional problem of a fiber-reinforced thermo-diffusive half-space with four relaxation times

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

The present manuscript is aimed at studying the propagation of plane waves in a fiber-reinforced, anisotropic, thermoelastic half-space with diffusion. The formulation is applied to generalized thermoelasticity based on the Green–Lindsay (G–L) theory. A thermal shock is applied on the surface of the half-space, which is taken to be traction free. The analytical expressions for the displacement components, stresses, concentration and temperature field are obtained in the physical domain by using normal mode analysis. Moreover, the derived expressions are computed numerically, and corresponding graphs are plotted to illustrate and compare theoretical results. Comparisons are made within the theory in the presence and absence of fiber-reinforcement and diffusion. The effect of time on the physical fields is also observed. Some particular cases of interest have been deduced from the present investigation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Abbas, I.A.: A two-dimensional problem for a fiber-reinforced anisotropic thermoelastic half-space with energy dissipation. Sadhana 36, 411–423 (2011)

    Article  Google Scholar 

  • Abo-Dahab, S.M., Lotfy, Kh., Gohaly, A.: Rotation and magnetic field effect on surface waves propagation in an elastic layer lying over a generalized thermoelastic diffusive half-space with imperfect boundary. Math. Probl. Eng. 2015, 1–12 (2015)

    Article  MathSciNet  Google Scholar 

  • Bayones, F.S.: Effect of rotation and initial magnetic field in fiber-reinforced anisotropic elastic media. Appl. Math. 6, 877–898 (2015)

    Article  Google Scholar 

  • Belfield, A.J., Rogers, T.G., Spencer, A.J.M.: Stress in elastic plates reinforced by fiber lying in concentric circles. J. Mech. Phys. Solids 31, 25–54 (1983)

    Article  Google Scholar 

  • Chattopadhyay, A., Choudhury, S.: Propagation, reflection and transmission of magnetoelastic shear waves in a self-reinforced medium. Int. J. Eng. Sci. 28, 485–495 (1990)

    Article  Google Scholar 

  • Deswal, S., Choudhary, S.: Impulsive effect on an elastic solid with generalized thermodiffusion. J. Eng. Math. 63, 79–94 (2009)

    Article  MathSciNet  Google Scholar 

  • Deswal, S., Kalkal, K.K.: A two-dimensional generalized electromagneto-thermoviscoelastic problem for a half-space with diffusion. Int. J. Therm. Sci. 50, 749–759 (2011)

    Article  Google Scholar 

  • Deswal, S., Kalkal, K.K., Sheoran, S.S.: Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction. Physica B 496, 57–68 (2016)

    Article  Google Scholar 

  • Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2, 1–7 (1972)

    Article  Google Scholar 

  • Hashin, Z., Rosen, W.B.: The elastic moduli of fiber-reinforced materials. J. Appl. Mech. 31, 223–232 (1964)

    Article  Google Scholar 

  • Kalkal, K.K., Deswal, S.: Analysis of vibrations in fractional order magneto-thermo-viscoelasticity with diffusion. J. Mech. 30, 383–394 (2014)

    Article  Google Scholar 

  • Kumar, R., Kansal, T.: Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. Int. J. Solids Struct. 45, 5890–5913 (2008)

    Article  Google Scholar 

  • Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299–309 (1967)

    Article  Google Scholar 

  • Lotfy, Kh.: Two temperature generalized magneto-thermoelastic interactions in an elastic medium under three theories. Appl. Math. Comput. 227, 871–888 (2014)

    MathSciNet  MATH  Google Scholar 

  • Lotfy, Kh.: The elastic wave motions for a photothermal medium of a dual-phase-lag model with an internal heat source and gravitational field. Can. J. Phys. 94, 400–409 (2016)

    Article  Google Scholar 

  • Lotfy, Kh., Allan, M.: Two temperature theory in a rotating semiconducting medium under photothermal theory with hydrostatic initial stress. J. Comput. Theor. Nanosci. 14, 899–909 (2017)

    Article  Google Scholar 

  • Lotfy, Kh., Hassan, W.: Normal mode method for two-temperature generalized thermoelasticity under thermal shock problem. J. Therm. Stresses 37, 545–560 (2014)

    Article  Google Scholar 

  • Lotfy, Kh., Sarkar, N.: Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature. Mech. Time-Depend. Mater. 21, 519–534 (2017)

    Article  Google Scholar 

  • Lotfy, Kh., Hassan, W., Gabr, M.E.: Thermomagnetic effect with two temperature theory for photothermal process under hydrostatic initial stress. Results Phys. 7, 3918–3927 (2017)

    Article  Google Scholar 

  • Nowacki, W.: Dynamical problems of thermodiffusion in solids I. Bull. Acad. Pol. Sci., Sér. Sci. Tech. 22, 55–64 (1974a)

    MathSciNet  MATH  Google Scholar 

  • Nowacki, W.: Dynamical problems of thermodiffusion in solids II. Bull. Acad. Pol. Sci., Sér. Sci. Tech. 22, 129–135 (1974b)

    MathSciNet  MATH  Google Scholar 

  • Nowacki, W.: Dynamical problems of thermodiffusion in solids III. Bull. Acad. Pol. Sci., Sér. Sci. Tech. 22, 257–266 (1974c)

    MathSciNet  MATH  Google Scholar 

  • Othman, M.I.A., Atwa, S.Y.: Two-dimensional problem of a fiber-reinforced anisotropic thermoelastic medium, comparison with the Green–Naghdi theory. Comput. Math. Model. 24, 307–325 (2013)

    Article  MathSciNet  Google Scholar 

  • Othman, M.I.A., Said, S.M.: Wave propagation in a two-temperature fiber-reinforced magneto-thermoelastic medium with three-phase-lag model. Struct. Eng. Mech. 57, 201–220 (2016)

    Article  Google Scholar 

  • Othman, M.I.A., Sarkar, N., Atwa, S.Y.: Effect of fractional parameter on plane waves of generalized magneto-thermoelastic diffusion with reference temperature-dependent elastic medium. Comput. Math. Appl. 65, 1103–1118 (2013)

    Article  MathSciNet  Google Scholar 

  • Pipkin, A.C.: Finite deformations of ideal fiber-reinforced composites. In: Sendeckyj, G.P. (ed.) Composites Materials, vol. 2, pp. 251–308. Academic, New York (1973)

    Google Scholar 

  • Podstrigach, Y.S.: Differential equations of the problem of thermodiffusion in isotropic deformable solids. Dokl. Acad. Sci. Ukr. SSR 2, 169–172 (1961)

    Google Scholar 

  • Podstrigach, Y.S., Pavlina, V.S.: Fundamental equations of the plane thermodiffusion problems. Appl. Mech. (Prikl. Mech.) 1, 101–106 (1965)

    Google Scholar 

  • Podstrigach, Y.S., Pavlina, V.S.: Differential equations of thermodynamic processes in n-component solid solutions. Sov. Mater. Sci. 1, 259–264 (1966)

    Article  Google Scholar 

  • Rogers, T.G.: Anisotropic elastic and plastic materials. In: Thoft-Christensen, P. (ed.) Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics, pp. 177–200. Reidel, Dordrecht (1975)

    Google Scholar 

  • Said, S.M.: Deformation of a rotating two-temperature generalized magneto thermoelastic medium with internal heat source due to hydrostatic initial stress. Meccanica 50, 2077–2091 (2015)

    Article  MathSciNet  Google Scholar 

  • Said, S.M.: Wave propagation in a magneto-micropolar thermoelastic medium with two temperatures for three-phase-lag model. Comput. Mater. Continua 52, 1–24 (2016)

    Google Scholar 

  • Said, S.M.: A fiber-reinforced thermoelastic medium with an internal heat source due to hydrostatic initial stress and gravity for the three-phase-lag model. Multid. Model. Material. Struct. 13, 83–99 (2017)

    Article  Google Scholar 

  • Said, S.M., Othman, M.I.A.: Effects of gravitational and hydrostatic initial stress on a two-temperature fiber-reinforced thermoelastic medium for three-phase-lag. J. Solid Mech. 8, 806–822 (2016)

    Google Scholar 

  • Said, S.M., Othman, M.I.A.: Effect of mechanical force, rotation and moving internal heat source on a two-temperature fiber-reinforced thermoelastic medium with two theories. Mech. Time-Depend. Mater. 21, 245–261 (2017)

    Article  Google Scholar 

  • Sengupta, P.R., Nath, S.: Surface waves in fiber-reinforced anisotropic elastic media. Sadhana 26, 363–370 (2001)

    Article  Google Scholar 

  • Sherief, H.H., Hamza, F., Saleh, H.: The theory of generalized thermoelastic diffusion. Int. J. Eng. Sci. 42, 591–608 (2004)

    Article  MathSciNet  Google Scholar 

  • Singh, B.: Wave propagation in thermally conducting linear fiber-reinforced composite materials. Arch. Appl. Mech. 75, 513–520 (2006)

    Article  Google Scholar 

Download references

Acknowledgements

One of the authors, Suresh Kumar Sheokand, is thankful to University Grants Commission, New Delhi, for the financial support Vide Letter no. F. 17-11/2008 (SA-1).

Author information

Authors and Affiliations

  1. Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, 125001, Haryana, India

    Kapil Kumar Kalkal, Suresh Kumar Sheokand & Sunita Deswal

Authors
  1. Kapil Kumar Kalkal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suresh Kumar Sheokand
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sunita Deswal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sunita Deswal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalkal, K.K., Sheokand, S.K. & Deswal, S. Two-dimensional problem of a fiber-reinforced thermo-diffusive half-space with four relaxation times. Mech Time-Depend Mater 23, 443–463 (2019). https://doi.org/10.1007/s11043-018-9399-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-018-9399-7

Keywords

Search

Navigation