Consolidation Around a Heat Source in an Isotropic Fully Saturated Rock with Porous Structure in Quasi-Static State

Subject Areas : Engineering

N Das Gupta ¹ , N.C Das ²

1 - Department of Mathematics, Jadavpur University, Kolkata, India
2 - Department of Mathematics, Brainware Group of Institutions, Barasat, India

Received: 2015-12-25 Accepted : 2016-02-28 Published : 2016-03-30

Keywords:

References:

[1] Nunziato J.W., Cowin S.C., 1979, A nonlinear theory of elastic materials with voids, Archive for Rational Mechanics and Analysis 72: 175-201.
[2] Iesan D., 2006, Nonlinear plane strain of elastic materials with voids, Mathematics and Mechanics of solids 11:361-384.
[3] Cowin S.C., Nunziato J.W., 1983, Linear elastic materials with voids, Journal of Elasticity 13: 125-147.
[4] Iesan D., 1986, A theory of thermoelastic materials with voids, Acta Mechanica 60: 67-89.
[5] Dhaliwal R.S., Wang J., 1995, A heat-flux dependent theory of thermoelasticity with voids, Acta Mechanica 110:33-39.
[6] Puri P., Cowin S.C., 1985, Plane waves in linear elastic materials with voids, Journal of Elasticity 15:167-183.
[7] Ciarletta M., Chirita S., 2006, On some growth-decay results in thermoelasticity of porous media, Journal of Thermal Stresses 29: 905-924.
[8] Cicco S.D., Diaco M., 2002, A theory of thermoelastic materials with voids without energy dissipation, Journal of Thermal Stresses 25: 493-503.
[9] Chirita S., Scalia A., 2001, On the spatial and temporal behaviour in linear thermoelasticity of potentials with voids, Journal of Thermal Stresses 24: 433- 455.
[10] Scalia A., Pompei A., Chirita S., 2004, On the behaviour of steady time harmonic oscillations thermoelastic materials with voids, Journal of Thermal Stresses 27: 209-226.
[11] Chirita S., Ciarletta M., 2008, On the structural stability of thermoelastic model of porous media, Mathematical Methods in the Applied Sciences 31:19-34.
[12] Giraud A., Rousset G., 1995, Consolidation around a volumic spherical decaying heat source, Journal of Thermal Stresses 18:513-527.
[13] Booker J.R., Savvidou C., 1984, Consolidation around a spherical heat source, International Journal of Solids and Structures 20:1079-1090.
[14] Sharma J.N., Grover D., 2012, Thermoelastic vibration analysis of Mems/Nems plate resonators with voids, Acta mechanica 223: 167-187.
[15] Kumar R., Rani L., 2004, Response of generalized thermoelastic half-space with voids to mechanical and thermal sources, Meccanica 39: 563-584.
[16] Kumar R., Devi S., 2011, Deformation in porousthermoelastic material with temperature dependent properties, An International Journal Applied Mathematics and Information Sciences 5:132-147.
[17] Lord H.W., Shulman Y., 1967, A generalized dynamic theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15:299-309.
[18] Rice J.R., Cleary M.P., 1976, Some basic stress diffusion solutions for fluid saturated elastic porous media with compressible constituents, Reviews of Geophysics and Space Physics 14:227-241.
[19] Coussy O., 1991, Mecanique des Milieux Preux, Technip Paris.
[20] Biot MA., 1955, Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics 26:182-185.
[21] Lahiri A., Das N.C., Sarkar S., Das M., 2009, Matrix method of solution of coupled differential equations and its applications in generalized thermoelasticity, Bulletin of Calcutta Mathematical Society 101: 571-590.
[22] Zakian V., 1969, Numerical inversion of Laplace transforms, Electronic Letters 5: 120-121.