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Generalized Thermo-Microstretch Elastic Solid for Different Theories with Finite Element Method under the Influence of Gravity Field

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Abstract

The present paper is aimed at studying the influence of gravity field on the general model of the generalized thermo-microstretch equations for a homogeneous isotropic elastic half-space solid. The problem is in the context of the Lord-Şhulman and Green-Lindsay theories, as well as the coupled theory. The Finite Element Method is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and microstress distribution. The variations of the considered variables perpendicular to the axis of rotation are illustrated graphically using MATLAB software. Comparisons are made with the results in the presence and absence of gravity field of a particular case for the generalized micropolar thermoelasticity medium (without microstretch constants) between the three theories. The results obtained are agreement with the previous results obtained with neglecting the new external parameters that predict new results applicable and useful for the related topics as geophysics, biology, acoustics, …, etc.

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REFERENCES

  1. S. Bhattacharyya and S. N. De, “Surface waves in viscoelastic media under the influence of gravity,” Aust. J. Phys. 30 (3), 347–353 (1977). https://doi.org/10.1071/PH770347

    Article  ADS  Google Scholar 

  2. S. N. De and P. R. Sengupta, “Plane influence of gravity on wave propagation in elastic layer,” J. Acoust. Soc. Am. 55, 919-921 (1974).

    Article  ADS  Google Scholar 

  3. V. K. Agarwal, “On electromagneto-thermoelastic plane waves,” Acta Mech. 34, 181–191 (1979). https://doi.org/10.1007/BF01227983

    Article  MathSciNet  Google Scholar 

  4. P. Ailawalia, G. Khurana, and S. Kumar, “Effect of rotation in a generalized thermoelastic medium with two temperature under the influence of gravity,” Int. J. Appl. Math. Mech. 5 (5), 99–116 (2009).

    Google Scholar 

  5. M. Sethi and K. C. Gupta, “Surface waves in non-homogeneous, general thermos visco-elastic media of higher order under influence of gravity and couple-stress,” Int. J. Appl. Math. Mech. 7, 1–20 (2011).

    Google Scholar 

  6. A. C. Eringen, “Theory of thermo-microstretch elastic solids,” Int. J. Eng. Sci. 28 (12), 1291–1301 (1990). https://doi.org/10.1016/0020-7225(90)90076-U

    Article  Google Scholar 

  7. F. Bofill and R. Quintanilla, “Some qualitative results for the linear theory of thermo-microstretch elastic solids,” Int. J. Eng. Sci. 33 (14), 2115–2125 (1995). https://doi.org/10.1016/0020-7225(95)00048-3

    Article  MathSciNet  Google Scholar 

  8. S. De Cicco and L. Nappa, “On the theory of thermo-microstretch elastic solids,” J. Therm. Stress. 22 (6), 565–580 (1999). https://doi.org/10.1080/014957399280751

    Article  Google Scholar 

  9. S. De Cicco and L. Nappa, “Some results in the linear theory of thermo-micro-stretch elastic solids,” J. Math. Mech. 5 (4), 467–482 (2000). https://doi.org/10.1177/108128650000500405

    Article  Google Scholar 

  10. D. Ieşan and L. Nappa, “On the plane strain of microstretch elastic solids,” Int. J. Eng. Sci. 39 (16), 1815–1835 (2001). https://doi.org/10.1016/S0020-7225(01)00017-9

    Article  MathSciNet  Google Scholar 

  11. A. C. Eringen, Micro-Continuum Field Theories: I. Foundation and Solids (Springer, New York, 1999).

    Book  Google Scholar 

  12. M. Biot, “Thermoelasticity and irreversible thermodynamics,” J. Appl. Phys. 27, 240–253 (1956). https://doi.org/10.1063/1.1722351

    Article  ADS  MathSciNet  Google Scholar 

  13. H. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solids 15 (5), 299–309 (1967). https://doi.org/10.1016/0022-5096(67)90024-5

    Article  ADS  Google Scholar 

  14. M. I. A. Othman, “Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermo- elasticity,” J. Therm. Stress. 25 (11), 1027–1045 (2002). https://doi.org/10.1080/01495730290074621

    Article  Google Scholar 

  15. I. A. Abbas and M. I. A. Othman, “Plane waves in generalized thermo-micro- stretch elastic solid with thermal relaxation using finite element method,” Int. J. Thermophys. 33 (12), 2407–2423 (2012). https://doi.org/10.1007/s10765-012-1340-8

    Article  ADS  Google Scholar 

  16. I. Müller, “The Coldness, a universal function in thermoelastic bodies,” Arch. Rat. Mech. Anal. 41, 319–332 (1971). https://doi.org/10.1007/BF00281870

    Article  MathSciNet  Google Scholar 

  17. A. E. Green and N. Laws, “On the entropy production inequality,” Arch. Rat. Mech. Anal. 45, 45–47 (1972). https://doi.org/10.1007/BF00253395

    Article  MathSciNet  Google Scholar 

  18. A. E. Green and K. A. Lindsay, “Thermoelasticity,” J. Elasticity 2, 1–7 (1972).

    Google Scholar 

  19. M. I. A. Othman, A. Khan, R. Jahangir, and A. Jahangir, “Analysis on plane waves through magneto-thermoelastic microstretch rotating medium with temperature dependent elastic properties,” Appl. Math. Model. 65, 535–548 (2019). https://doi.org/10.1016/j.apm.2018.08.032

    Article  MathSciNet  Google Scholar 

  20. B. K. Datta, “Some observation on interactions of Rayleigh waves in an elastic solid medium with the gravity field,” Roman. J. Techn. Sci. Appl. Mech. 31 (4), 369–374 (1986).

    Google Scholar 

  21. S. C. Das, D.P. Acharya, and P. R. Sengupta, “Surface waves in an inhomogeneous elastic medium under the influence of gravity,” Roman. J. Techn. Sci. Appl. Mech. 37 (5), 539–552 (1992).

    MathSciNet  Google Scholar 

  22. A. M. Zenkour, “Two-temperature generalized thermoelastic interaction in an infinite fiber-reinforced anisotropic plate containing a circular cavity with two relaxation times,” J. Comput. Theor. Nanosci. 11 (1), 1–7 (2014). https://doi.org/10.1166/jctn.2014.3309

    Article  Google Scholar 

  23. I. A. Abbas and H. M. Yossef, “A non-linear generalized thermoelasticity of temperature dependent materials using finite element method,” Int. J. Thermophys. 33 (7), 1302–1312 (2012). https://doi.org/10.1007/s10765-012-1272-3

    Article  ADS  Google Scholar 

  24. I. A. Abbas and H. M. Yossef, “Two-temperature generalized thermoelasticity under ramp-type heating by finite element method,” Meccanica 48 (2), 331–339 (2013). https://doi.org/10.1007/s11012-012-9604-8

    Article  MathSciNet  Google Scholar 

  25. S. M. Abo-Dahab, Kh. Lotfy, M. E. Gabr, et al., “Study on the effect of relaxation time and mode-I crack on the wave through the magneto-thermoelasticity medium with two temperatures,” Mech. Solids 58 (5), 1–17 (2023). https://doi.org/10.3103/S0025654423600708

    Article  Google Scholar 

  26. P. Wriggers, Nonlinear Finite Element Methods (Springer, Berlin Heidelberg, 2008).

    Google Scholar 

  27. M. I. A. Othman and B. Singh, “The effect of rotation on generalized micropolar thermoelasticity for a half-space under five theories,” Int. J. Solids Struct. 44, 2748–2762 (2007). https://doi.org/10.1016/j.ijsolstr.2006.08.016

    Article  Google Scholar 

  28. A. M. S. Mahdy, Kh. Lotfy, A. El-Bary, and I. M. Tayel, “Variable thermal conductivity and hyperbolic two-temperature theory during magneto-photothermal theory of semiconductor induced by laser pulses,” Eur. Phys. J. Plus. 136 (6), 651, (2021). https://doi.org/10.1140/epjp/s13360-021-01633-3

    Article  Google Scholar 

  29. M. Yasein, N. Mabrouk, Kh. Lotfy, and A.A. EL-Bary, “The influence of variable thermal conductivity of semiconductor elastic medium during photothermal excitation subjected to thermal ramp type,” Results Phys. 15, 102766 (2019). https://doi.org/10.1016/j.rinp.2019.102766

  30. Kh. Lotfy and R. S. Tantawi, “Photo-thermal-elastic interaction in a functionally graded material (FGM) and magnetic field,” Silicon 12 (2), 295–303 (2020).https://doi.org/10.1007/s12633-019-00125-5

    Article  Google Scholar 

  31. Kh. Lotfy, A. A. El-Bary, and R. S. Tantawi, “Effects of variable thermal conductivity of a small semiconductor cavity through the fractional order heat-magneto-photothermal theory,” Eur. Phys. J. Plus. 134 (6), 280 (2019). https://doi.org/10.1140/epjp/i2019-12631-1

    Article  Google Scholar 

  32. Kh. Lotfy, E. S. Elidy, and R. S. Tantawi, “Piezo-photo-thermoelasticity transport process for hyperbolic two-temperature theory of semiconductor material,” Int. J. Modern Phys. C 32 (7), 2150088 (2021). https://doi.org/10.1142/S0129183121500881

  33. M. I. A. Othman, I. A. Abbas, and S. M. Abo-Dahab, “Generalized magneto-thermo-microstretch elastic solid with finite element method under the effect of gravity via different theories,” Geomech. Eng. 27 (1), 45–54 (2021). https://doi.org/10.12989/gae.2021.27.1.000

    Article  Google Scholar 

  34. S. M. Abo-Dahab, A. Kumar, and P. Ailawalia, “Mechanical changes due to pulse heating in a microstretch thermoelastic half-space with two-temperatures,” J. Appl. Sci. Eng. 23 (1), 153–161 (2020). https://doi.org/10.6180/jase.202003_23(1).0016

    Article  Google Scholar 

  35. S. M. Abo-Dahab, A. Jahangir, and A. N. Abd-Alla, “Reflection of plane waves in thermoelastic microstructured materials under the influence of gravitation,” Contin. Mech. Thermody. 32, 803–815 (2020). https://doi.org/10.1007/s00161-018-0739-2

    Article  ADS  MathSciNet  Google Scholar 

  36. S. M. Abo-Dahab and A. E. Abouelregal, “On a two-dimensional problem in thermoelasticity half-space with microstructure subjected to a uniform thermal shock,” Phys. Wave Phen. 27 (1), 56–66 (2019). https://doi.org/10.3103/S1541308X19010102

    Article  ADS  Google Scholar 

  37. A. Kumar, S. M. Abo-Dahab, and P. Ailawalia, “Mathematical study of Rayleigh waves in peizoelectric microstretch thermoelastic medium,” Mech. Mech. Eng. 23, 86–93 (2019). https://doi.org/10.2478/mme-2019-0012

    Article  Google Scholar 

  38. S. M. Abo-Dahab, A. M. Abd-Alla, M. Elsagheer, and A. A. Kilany, “Effect of rotation and gravity on the reflection of P-waves from thermo-magneto-micro-stretch medium in the context of three phase lag model with initial stress,” Microsyst. Technol. 24, 3357–3369 (2018). https://doi.org/10.1007/s00542-017-3697-x

    Article  Google Scholar 

  39. A. Kumar1, R. Kumar, and S. M. Abo-Dahab, “Mathematical model for Rayleigh waves in microstretch thermoelastic medium with microtemperatures,” J. Appl. Sci. and Eng. 20 (2), 149–156 (2017). https://doi.org/10.6180/jase.2017.20.2.02

  40. M. I. A. Othman, S. M. Abo-Dahab, and Kh. Lotfy, “Gravitational effect and initial stress on generalized magneto-thermo-microstretch elastic solid for different theories,” Appl. Math. Comput. 230, 597–615 (2014). https://doi.org/10.1016/j.amc.2013.12.148

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, South Valley University, 83523, Qena, Egypt

    S. M. Abo-Dahab

  2. Mathematics Department, Faculty of Science, Sohag University, Egypt

    Ibrahim A. Abbas

  3. Mathematics Department, Faculty of Science, Zagazig University, 44519, Zagazig, Egypt

    Mohamed I. A. Othman

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  1. S. M. Abo-Dahab
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  2. Ibrahim A. Abbas
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Abo-Dahab, S.M., Abbas, I.A. & Othman, M.I. Generalized Thermo-Microstretch Elastic Solid for Different Theories with Finite Element Method under the Influence of Gravity Field. Mech. Solids 58, 3346–3359 (2023). https://doi.org/10.3103/S0025654423601489

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