Internal heat source in a temperature dependent thermoelastic half space with microtemperatures

[1]           A. C. Eringen, E. Suhubi, Nonlinear theory of simple micro-elastic solids—I, International Journal of Engineering Science, Vol. 2, No. 2, pp. 189-203, 1964.

[2]           E. Suhubl, A. C. Eringen, Nonlinear theory of micro-elastic solids—II, International Journal of Engineering Science, Vol. 2, No. 4, pp. 389-404, 1964.

[3]           A. Eringen, Linear theory of micropolar elasticity", ONR Technical Report No. 29, School of Aeronautics, Aeronautics and Engineering Science, Purdue University, West Lafayette, IN, Purdue University, 1965.

[4]           A. C. Eringen, A unified theory of thermomechanical materials, International Journal of Engineering Science, Vol. 4, No. 2, pp. 179-202, 1966.

[5]           A. C. Eringen, Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics, pp. 909-923, 1966.

[6]           R. A. Grot, Thermodynamics of a continuum with microstructure, International Journal of Engineering Science, Vol. 7, No. 8, pp. 801-814, 1969.

[7]           P. Říha, On the microcontinuum model of heat conduction in materials with inner structure, International Journal of Engineering Science, Vol. 14, No. 6, pp. 529-535, 1976.

[8]           D. I. Quintanilla, R, On a theory of thermoelasticity with microtemperatures, Journal of Thermal Stresses, Vol. 23, No. 3, pp. 199-215, 2000.

[9]           D. Ieşan, On a theory of micromorphic elastic solids with microtemperatures, Journal of Thermal Stresses, Vol. 24, No. 8, pp. 737-752, 2001.

[10]         M. Ezzat, M. Othman, A. El-Karamany, The dependence of the modulus of elasticity on the reference temperature in generalized thermoelasticity, Journal of thermal stresses, Vol. 24, No. 12, pp. 1159-1176, 2001.

[11]         P. S. Casas, R. Quintanilla, Exponential stability in thermoelasticity with microtemperatures, International Journal of Engineering Science, Vol. 43, No. 1-2, pp. 33-47, 2005.

[12]         A. Scalia, M. Svanadze, On the representations of solutions of the theory of thermoelasticity with microtemperatures, Journal of Thermal Stresses, Vol. 29, No. 9, pp. 849-863, 2006.

[13]         D. Ieşan, Thermoelasticity of bodies with microstructure and microtemperatures, International Journal of Solids and Structures, Vol. 44, No. 25-26, pp. 8648-8662, 2007.

[14]         M. Aouadi, Some theorems in the isotropic theory of microstretch thermoelasticity with microtemperatures, Journal of Thermal Stresses, Vol. 31, No. 7, pp. 649-662, 2008.

[15]         D. Ie? an, R. Quintanilla, On thermoelastic bodies with inner structure and microtemperatures, Journal of Mathematical Analysis and Applications, Vol. 354, No. 1, pp. 12-23, 2009.

[16]         A. Scalia, M. Svanadze, R. Tracinà, Basic theorems in the equilibrium theory of thermoelasticity with microtemperatures, Journal of Thermal Stresses, Vol. 33, No. 8, pp. 721-753, 2010.

[17]         R. Quintanilla, On growth and continuous dependence in thermoelasticity with microtemperatures, Journal of Thermal Stresses, Vol. 34, No. 9, pp. 911-922, 2011.

[18]         H. Steeb, J. Singh, S. K. Tomar, Time harmonic waves in thermoelastic material with microtemperatures, Mechanics Research Communications, Vol. 48, pp. 8-18, 2013.

[19]         S. Chiriţă, M. Ciarletta, C. D’Apice, On the theory of thermoelasticity with microtemperatures, Journal of Mathematical Analysis and Applications, Vol. 397, No. 1, pp. 349-361, 2013.

[20]         R. Kumar, M. Kaur, Reflection and refraction of plane waves at the interface of an elastic solid and microstretch thermoelastic solid with microtemperatures, Archive of Applied Mechanics, Vol. 84, No. 4, pp. 571-590, 2014.

[21]         N. Noda, Thermal stresses in materials with temperature-dependent properties, Applied Mechanics Reviews, Vol. 44, No. 9, pp. 383-397, 1991.

[22]         H. M. Youssef, Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity, Applied Mathematics and Mechanics, Vol. 26, No. 4, pp. 470-475, 2005.

[23]         M. I. Othman, K. Lotfy, Two-dimensional problem of generalized magneto-thermoelasticity with temperature dependent elastic moduli for different theories, Multidiscipline Modeling in Materials and Structures, Vol. 5, No. 3, pp. 235-242, 2009.

[24]         M. A. Biot, 1964, Mechanics of incremental deformations,

[25]         R. Kumar, S. Devi, Thermomechanical intereactions in porous generalized thermoelastic material permeated with heat sources, Multidiscipline Modeling in Materials and Structures, Vol. 4, No. 3, pp. 237-254, 2008.

[26]         K. Lotfy, Transient disturbance in a half-space under generalized magneto-thermoelasticity with a stable internal heat source under three theories, Multidiscipline Modeling in Materials and Structures, Vol. 7, No. 1, pp. 73-90, 2011.

[27]         K. Lotfy, Transient thermo-elastic disturbances in a visco-elastic semi-space due to moving internal heat source, International Journal of Structural integrity, Vol. 2, No. 3, pp. 264-280, 2011.

[28]         M. Othman, State space approach to the generalized thermoelastic problem with temperature-dependent elastic moduli and internal heat sources, Journal of applied mechanics and technical physics, Vol. 52, No. 4, pp. 644, 2011.

[29]         R. Kumar, S. Devi, Deformation in porous thermoelastic material with temperature dependent properties, Applied Mathematics & Information Sciences, Vol. 5, No. 1, pp. 132-147, 2011.

[30]         P. Ailawalia, S. Budhiraja, Internal Heat Source in Temperature Rate Dependent Thermoelastic Medium with Hydrostatic Initial Stress, Mechanics and Mechanical Engineering, Vol. 20, No. 3, pp. 263-277, 2016.

[31]         M. I. Othman, M. E. Zidan, M. I. Hilal, Effect of gravitational field and temperature dependent properties on two-temperature thermoelastic medium with voids under GN theory, Computers, Materials & Continua, Vol. 40, No. 3, pp. 179-201, 2014.

[32]         R. Kumar, M. Kaur, S. Rajvanshi, Plane wave propagation in microstretch thermoelastic medium with microtemperatures, Journal of Vibration and Control, Vol. 21, No. 16, pp. 3403-3416, 2015.

[33]         P. Ailawalia, S. K. Sachdeva, D. Pathania, Two dimensional deformation in microstretch thermoelastic half space with microtemperatures and internal heat source, Cogent Mathematics, Vol. 2, No. 1, pp. 1086293, 2015.

[34]         P. Ailawalia, S. K. Sachdeva, D. S. Pathania, Plane strain problem in a rotating microstretch thermoelastic solid with microtemperatures, Theoretical and Applied Mechanics, Vol. 44, No. 1, pp. 51-82, 2017.

[35]         A. C. Eringen, Plane waves in nonlocal micropolar elasticity, International Journal of Engineering Science, Vol. 22, No. 8-10, pp. 1113-1121, 1984.

[36]         R. Dhaliwal, A. Singh, Dynamic coupled thermoelasticity Hindustan Publ, Corp., New Delhi, 1980.