Variational Principle and Plane Wave Propagation in Thermoelastic Medium with Double Porosity Under Lord-Shulman Theory
Subject Areas : EngineeringR Kumar 1 , R Vohra 2 , M.G Gorla 3
1 - Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India
2 - Department of Mathematics& Statistics, H.P.University, Shimla, HP, India
3 - Department of Mathematics& Statistics, H.P.University, Shimla, HP, India
Keywords:
Abstract :
[1] Biot M. A., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[2] Lord H., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics of Physics of Solids 15: 299-309.
[3] Hetnarski R. B., Ignaczak J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451-476.
[4] Biot M. A., 1941, General theory of three-dimensional consolidation, Journal of Applied Physics 12: 155-164.
[5] Bowen R.M.,1980, Incompressible porous media models by use of the theory of mixtures, International Journal of Engineering Science 18: 1129-1148.
[6] De Boer R., Ehlers W., 1990, Uplift, friction and capillarity-Three fundamental effects for liquid saturated porous solids, International Journal of Solids and Structures 26: 43-57.
[7] Barenblatt G.I., Zheltov I.P., Kochina I.N., 1960, Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), Journal of Applied Mathematics and Mechanics 24: 1286-1303.
[8] Wilson R. K., Aifantis E. C.,1982, On the theory of consolidation with double porosity, International Journal of Engineering Science 20(9): 1009-1035.
[9] Khaled M.Y., Beskos D. E., Aifantis E. C.,1984, On the theory of consolidation with double porosity-III, International Journal for Numerical and Analytical Methods in Geomechanics 8: 101-123.
[10] Wilson R. K., Aifantis E. C., 1984, A double porosity model for acoustic wave propagation in fractured porous rock, International Journal of Engineering Science 22(8-10): 1209-1227.
[11] Beskos D. E., Aifantis E. C.,1986., On the theory of consolidation with double porosity-II, International Journal of Engineering Science 24(111): 1697-1716.
[12] Khalili N., Valliappan S., 1996, Unified theory of flow and deformation in double porous media, European Journal of Mechanics - A/Solids 15: 321-336.
[13] Aifantis E. C., 1977, Introducing a multi –porous medium, Developments in Mechanics 8: 209-211.
[14] Aifantis E. C.,1979, On the response of fissured rocks, Developments in Mechanics 10: 249-253.
[15] Aifantis E.C., 1980, On the problem of diffusion in solids, Acta Mechanica 37: 265-296.
[16] Aifantis E.C., 1980, The Mechanics of Diffusion in Solids, T.A.M. Report No. 440, Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, Illinois.
[17] Moutsopoulos K. N., Eleftheriadis I. E., Aifantis E. C.,1996, Numerical simulation of transport phenomena by using the double porosity/ diffusivity continuum model, Mechanics Research Communications 23(6): 577-582.
[18] Khalili N., SelvaduraiA. P. S.,2003, A fully coupled constitutive model for thermo-hydro -mechanical analysis in elastic media with double porosity, Geophysical Research Letters 30: 2268-2271.
[19] Pride S. R., Berryman J. G., 2003, Linear dynamics of double–porosity dual-permeability materials-I, Physical Review E 68: 036603.
[20] Straughan B., 2013, Stability and uniqueness in double porosity elasticity, International Journal of Engineering Science 65:1-8.
[21] Svanadze M., 2005, Fundamental solution in the theory of consolidation with double porosity, Journal of the Mechanical Behavior of Biomedical Materials 16: 123-130.
[22] Svanadze M., 2010, Dynamical problems on the theory of elasticity for solids with double porosity, Proceedings in Applied Mathematics and Mechanics 10: 209-310.
[23] Svanadze M., 2012, Plane waves and boundary value problems in the theory of elasticity for solids with double porosity, Acta Applicandae Mathematicae 122: 461-470.
[24] Svanadze M., 2014, On the theory of viscoelasticity for materials with double porosity, Discrete and Continuous Dynamical Systems - Series B 19(7): 2335-2352.
[25] Svanadze M., 2014, Uniqueness theorems in the theory of thermoelasticity for solids with double porosity, Meccanica 49: 2099-2108.
[26] Scarpetta E., Svanadze M., Zampoli V., 2014, Fundamental solutions in the theory of thermoelasticity for solids with double porosity, Journal of Thermal Stresses 37(6): 727-748.
[27] Scarpetta E., Svanadze M., 2015 ,Uniqueness theorems in the quasi-static theory of thermo elasticity for solids with double porosity, Journal of Elasticity 120: 67-86.
[28] Kumar R., Kansal T., 2014, Propagation of plane waves and fundamental solution in the theories of thermoelastic diffusive materials with voids, International Journal of Applied Mathematics and Mechanics 8(13): 84-103.
[29] Kumar R., Singh M., 2007, Propagation of plane waves in thermoelastic cubic crystal material with two relaxation times, Applied Mathematics and Mechanics 28(5): 627-641.
[30] Kumar R., Kumar R., 2010, Propagation of wave at the boundary surface of transversely isotropic thermoelastic material with voids and isotropic elastic half-space, Applied Mathematics and Mechanics 31(9): 1153-1172.
[31] Kumar R., Kaur M., Rajvanshi S.C., 2014, Plane wave propagation in microstretch thermoelastic medium with microtemperatures, Journal of Vibration and Control 21: 2678.
[32] Iesan D., Quintanilla R, 2014, On a theory of thermoelastic materials with a double porosity structure, Journal of Thermal Stresses 37: 1017-1036.
[33] Sherief H., Saleh H., 2005, A half space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 42: 4484-4493.
[34] Khalili N., 2003, Coupling effects in double porosity media with deformable matrix, Geophysical Research Letters 30(22): 2153.