Generalized thermal microstretch elastic solid with harmonic wave for mode-I crack problem

• Autorzy: Lotfy Khaled , El-Bary Alaa Abd , Allan Mohamed , Ahmed Marwa H.

Identyfikatory

DOI

10.24425/ather.2020.133626

• Języki publikacji: EN

Abstrakty

EN

A general model of the equations of generalized thermo-microstretch for an infinite space weakened by a finite linear opening mode-I crack is solved. Considered material is the homogeneous isotropic elastic half space. The crack is subjected to a prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, using mathematical analysis with the purview of the Lord-Şhulman (involving one relaxation time) and Green-Lindsay (includes two relaxation times) theories with respect to the classical dynamical coupled theory (CD). The harmonic wave method has been used to obtain the exact expression for normal displacement, normal stress force, coupled stresses, microstress and temperature distribution. Variations of the considered fields with the horizontal distance are explained graphically. A comparison is also made between the three theories and for different depths for the case of copper crystal.

Słowa kluczowe

EN

mode-I crack; L-S theory; GL theory; thermoelasticity; microrotation; microstretch

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2020
• Tom: Vol. 41, no 2
• Strony: 147--168
• Opis fizyczny: Bibliogr. 31 poz., rys., wykr., wz.

Twórcy

autor

Lotfy Khaled

• Department of Mathematics, Faculty of Science, P.O. Box 44519, Zagazig University, Zagazig, Egypt
• Department of Mathematics, Faculty of Science, Taibah University, Madinah, Saudi Arabia

autor

El-Bary Alaa Abd

• Arab Academy for Science,Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt

autor

Allan Mohamed

• Arab Academy for Science,Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt

autor

Ahmed Marwa H.

• Department of Mathematics, Faculty of Science, P.O. Box 44519, Zagazig University, Zagazig, Egypt
• Department of Mathematics, Faculty of Science, Taibah University, Madinah, Saudi Arabia

Bibliografia

• [1] Eringen A.C., Suhubi E.S.: Non linear theory of simple micropolar solids. Int. J. Engng. Sci. 2(1964), 1–18.
• [2] Eringen A.C.: Linear theory of micropolar elasticity. J. Math. Mech. 15(1966), 909–923.
• [3] Othman M.I.A.: Relaxation effects on thermal shock problems in an elastic half-space of generalized magneto-thermoelastic waves. Mechanics Mechanical Eng. 7(2004), 165–178.
• [4] Othman M.I.A, Lotfy Kh. and Farouk R.M.: Transient disturbance in a halfspace under generalized magneto-thermoelasticity with internal heat source. Acta Phys. Pol. A 116(2009), 2, 185–192.
• [5] Eringen A.C.: Micropolar elastic solids with stretch. Ari Kitabevi Matbassi, Istanbul 24(1971), 1–18.
• [6] Eringen A.C.: Theory of micropolar elasticity. In: , Fracture, Vol. II, (H. Liebowitz, Ed.) Academic Press, New York 1968.
• [7] Eringen A.C.: Theory of thermo-microstretch elastic solids. Int. J. Engng. Sci. 28(1990), 291–1301.
• [8] Eringen A.C.: Microcontinuum Field Theories I: Foundation and Solids. SpringerVerlag, New York, Berlin, Heidelberg 1999.
• [9] Iesau D., Nappa L.: On the plane strain of microstretch elastic solids. Int. J. Engng. Sci. 39(2001), 1815–1835.
• [10] Iesau D., Pompei A.: On the equilibrium theory of microstretch elastic solids. Int. J. Engng. Sci. 33(1995), 399–410.
• [11] De Cicco S.: Stress concentration effects in microstretch elastic bodies. Int. J. Engng. Sci. 41(2003), 187–199.
• [12] Bofill F., Quintanilla R.: Some qualitative results for the linear theory of thermo-microstretcli elastic solids. Int. J. Engng. Sci. 33(1995), 2115–2125.
• [13] De Cicco S., Nappa L.: Some results in the linear theory of thermo-microstretch elastic solids. J. Math. Mech. 5(2000), 467–482.
• [14] De Cicco S., Nappa L.: On the theory of thermomicrostretch elastic solids. J. Therm. Stresses 22(1999), 565–580.
• [15] Green A.E., Laws N.: On the entropy production inequality. Arch. Ration. Mech. Anal. 45(1972), 47–59.
• [16] Lord H.W., Şhulman Y.: A generalized dynamical theory of thennoelasticity. J. Mech. Phys. Solid 15(1967), 299–306.
• [17] Green A.E., Lindsay K.A.: Thermoelasticity. J. Elasticity 2(1972), 1–7.
• [18] Lotfy Kh.: A novel solution of fractional order heat equation for photothermal waves in a semiconductor medium with a spherical cavity. Chaos Soliton Fract. 99(2017), 233–242.
• [19] Lotfy Kh., Gabr M.E.: Response of a semiconducting infinite medium under two temperature theory with photothermal excitation due to laser pulses. Opt. Laser Technol. 97(2017), 198–208.
• [20] Othman M.I.A., Lotfy Kh.: On the plane waves in generalized thermo- microstretch elastic half-space. Int. Commun. Heat Mass 37(2010), 192–200.
• [21] Othman M.I.A.., Lotfy Kh.: Effect of magnetic field and inclined in micropolar thermoelastic medium possessing cubic symmetry. Int. J. Industrial Math. 1(2009), 2, 87–104.
• [22] Othman M.I.A., Lotfy Kh.: Generalized thermo-microstretch elastic medium with temperature dependent properties for different theories. Eng. Anal. Bound. Elem. 34(2010), 229–237.
• [23] Dhaliwal R.: External Crack due to Thermal Effects in an Infinite Elastic Solid with a Cylindrical Inclusion. In: Thermal Stresses in Server Environments, SpringerVerlag, 1980, 665–692.
• [24] Lotfy Kh., Abo-Dahb S.: Two-dimensional problem of two temperature generalized thermoelasticity with normal mode analysis under thermal shock problem. J. Comput. Theor. Nanos. 12(2015), 8, 1709–1719.
• [25] Abo-Dahb S., 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.
• [26] Lotfy Kh., Abo-Dah S.: Generalized Magneto-thermoelasticity with fractional derivative heat transfer for a rotation of a fibre-reinforced thermoelastic. J. Comput. Theor. Nanos. 12(2015), 8, 1869–1881.
• [27] Lotfy Kh.: The elastic wave motions for a photothermal medium of a dual-phaselag model with an internal heat source and gravitational field. Can. J. Phys. 94(2016), 400–409.
• [28] Lotfy Kh.: Mode-I crack in a two-dimensional fibre-reinforced generalized thermoelastic problem. Chin. Phys. B. 2(2012), 1, 014209.
• [29] Lotfy Kh.: The effect of a magnetic field on a 2D problem of fibre-reinforced thermoelasticity rotation under three theories. Chin. Phys. B. 21(2012), 064214.
• [30] Sarkar N., Lahiri A.: A three-dimensional thermoelastic problem for a half-space without energy dissipation. Int. J. Eng. Sci. 51(2012), 310–325.
• [31] Abd-alla A.M.: Influences of rotation, magnetic field, initial stress and gravity on Rayleigh waves in a homogeneous orthotropic elastic half-space. Appl. Math. Sci. 4(2010), 2, 91–108.