Lotfy, K. (2019). On Plane Waves for Mode-I Crack Problem in Generalized Thermoelasticity. Journal of Solid Mechanics, (), -. doi: 10.22034/jsm.2019.666687

kh Lotfy. "On Plane Waves for Mode-I Crack Problem in Generalized Thermoelasticity". Journal of Solid Mechanics, , , 2019, -. doi: 10.22034/jsm.2019.666687

Lotfy, K. (2019). 'On Plane Waves for Mode-I Crack Problem in Generalized Thermoelasticity', Journal of Solid Mechanics, (), pp. -. doi: 10.22034/jsm.2019.666687

Lotfy, K. On Plane Waves for Mode-I Crack Problem in Generalized Thermoelasticity. Journal of Solid Mechanics, 2019; (): -. doi: 10.22034/jsm.2019.666687

On Plane Waves for Mode-I Crack Problem in Generalized Thermoelasticity

Articles in Press, Corrected Proof , Available Online from 31 July 2019

^{}Department of Mathematics, Faculty of Science, Taibah University, Madina, Kingdom of Saudi Arabia--- Department of Mathematics, Faculty of Science, Zagazig University, Egypt

Abstract

A general model of the equations of generalized thermoelasticity for an infinite space weakened by a finite linear opening Mode-I crack is solving. The material is homogeneous and has isotropic properties of elastic half space. The crack is subjected to prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, the Lord-Şhulman and Green-Lindsay theories, as well as the classical dynamical coupled theory. The normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, temperature, couple stresses and micro-stress distribution. The variations of the considered variables through the horizontal distance are illustrated graphically. Comparisons are made with the results between the three theories.

Nowacki W.,1958, Thermoelasticity, Addison-Wesley, London. [2] Nowinski J.,1978, Theory of Thermoelasticity with Applications, Setoff and Noord-Hoff, International Publishers, Alphenaan den Rijn. [3] Biot M.,1956, Thermoelasticity and irreversible thermo-dynamics, Journal of Applied Physics 27: 240-253. [4] Lord H., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309. [5] Dhaliwal R., Sherief H. H., 1980, Generalized thermoelasticity for an isotropic Media, Quarterly of Applied Mathematics 33: 1-8. [6] Sherief H. H., Dhaliwal R., 1981, Generalized one-dimensional hermal-shock problem for small times, Journal of Thermal Stresses 4: 407. [7] Othman M. I. A., 2002, Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized Thermoelasticity, Journal of Thermal Stresses 25: 1027-1045. [8] Müller I., 1971, The Coldness, A universal function in thermo-elastic solids, Archive for Rational Mechanics and Analysis 41: 319. [9] Green A. E., Laws N., 1972, On the entropy production inequality, Archive for Rational Mechanics and Analysis 45: 45-47. [10] Lord H. W., Şhulman Y., 1967, A generalized dynamical theory of thennoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-306. [11] Green A. E., Lindsay K. A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7. [12] Şuhubi E. S., 1975, Themoelastic Solids in Continuum Physics II, Academic, Press, New York. [13] Ignaczak J., 1985, A strong discontinuity wave in thermoelasticity with relaxation times, Journal of Thermal Stresses 8: 25-40. [14] Ignaczak J., 1978, Decomposition theorem for thermoelasticity with finite wave speeds, Journal of Thermal Stresses 1: 41. [15] Dhaliwal R., 1989, Thermal shock problem in generalized thermoelastic, Journal of Thermal Stresses 12: 259-278. [16] Lotfy Kh., Hassan W., 2014, Normal mode method for two-temperature generalized thermoelasticity under thermal shock problem, Journal of Thermal Stresses 37(5): 545-560. [17] Othman M. I. A., Lotfy Kh., Farouk R. M., 2009, Transient disturbance in a half-space under generalized magneto-thermoelasticity due to moving internal heat source, Acta Physica Polonica A 116: 186-192. [18] Lotfy Kh., 2017, A novel solution of fractional order heat equation for photothermal waves in a semiconductor medium with a spherical cavity, Chaos, Solitons and Fractals 99: 233-242, [19] Lotfy Kh., Gabr M.E., 2017, Response of a semiconducting infinite medium under two temperature theory with photothermal excitation due to laser pulses, Optics and Laser Technology 97: 198-208. [20] Dhaliwal R., 1980, External Crack due to Thermal Effects in an Infinite Elastic Solid with a Cylindrical Inclusion, Thermal Stresses in Server Environments Plenum Press, New York and London. [21] Hasanyan D., Librescu L., Qin Z., Young R., 2005, Thermoelastic cracked plates carrying nonstationary electrical current, Journal of Thermal Stresses 28: 729-745. [22] Ueda S., 2003, Thermally induced fracture of a piezoelectric laminate with a crack normal to interfaces, Journal of Thermal Stresses 26: 311-323. [23] Elfalaky A., Abdel-Halim A. A., 2006, A mode-I crack problem for an infinite space in thermoelasticity, Journal of Applied Sciences 6: 598-606. [24] Abouelregal A. S., Abo-Dahab S. M., 2018, A two-dimensional problem of a mode I crack in a rotating fibre-reinforced isotropic thermoelastic medium under Dual Phase Lags model, Sadhana 43(1): 1-11. [25] Lotfy Kh., Abo-Dahab S. M., Hobiny A. D., 2018, Plane waves on a gravitational rotating fibre-reinforced rhermoelastic medium with thermal shock problem, Journal of Advanced Physics 7: 58-69. [26] El-Naggar A. M., Kishka Z., Abd-Alla A. M., Abbas I. A., Abo-Dahab S. M., Elsagheer M., 2018, On the initial stress, magnetic field, voids and rotation effects on plane waves in generalized thermoelasticity, Journal of Computational and Theoretical Nanoscience 10(6): 1408-1417.