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: Consolidation, Isotropic, Thermoelasticity, Porous, Quasi-Static,

Abstract :

The titled problem of coupled thermoelasticity for porous structure has been solved with an instantaneous heat source acting on a plane area in an unbounded medium. The basic equations of thermoelasticity, after being converted into a one-dimensional form, have been written in the form of a vector-matrix differential equation and solved by the eigenvalue approach for the field variables in the Laplace transform domain in closed form. The deformation, temperature and pore pressure have been determined for the space time domain by numerical inversion from the Laplace transform domain. Finally the results are analyzed by depicting several graphs for the field variables.

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.