The Theory of Thermoelasticity with Double Porosity and Microtemperatures
Markanda National College
Department of Mathematics
Shahabad Markanda, 136135, IndiaE-mail: tarun1_kansal@yahoo.co.in
Received:
Received: 16 June 2022; revised: 16 July 2022; accepted: 28 July 2022; published online: 27 August 2022
DOI: 10.12921/cmst.2022.0000016
Abstract:
The aim of the paper is to establish the basic governing equations for anisotropic thermoelastic medium with double porosity and microtemperatures and to construct the fundamental solution of a system of equations in cases of steady, pseudo-, quasi-static oscillations and equilibrium.
Key words:
References:
[1] R.A. Grot, Thermodynamics of a continuum with microstructure, Int. J. Engg. Sci. 7, 801–814 (1969).
[2] D. Iesan, R. Quintanilla, On a theory of thermoelasticity with microtemperatures, J. Ther. Stress. 23, 199–215 (2000).
[3] D. Iesan, On a theory of micromorphic elastic solids with microtemperatures, J. Ther. Stress. 24, 737–752 (2001).
[4] D. Iesan, Thermoelasticity of bodies with microstructure and microtemperatures, Int. J. Solids Struct. 44, 8648–8662 (2007).
[5] R.K. Wilson, E.C. Aifantis, On the theory of consolidation with double porosity-I, Int. J. Engg. Sci. 20, 1009–1035 (1982).
[6] D. Iesan, R. Quintanilla, On a theory of thermoelastic materials with a double porosity structure, J. Ther. Stress. 37, 1017–1036 (2014).
[7] T. Kansal, Generalized theory of thermoelastic diffusion with double porosity, Arch. Mech. 70, 241–268 (2018).
[8] T. Kansal, Fundamental solution of the system of equations of pseudo oscillations in the theory of thermoelastic diffusion materials with double porosity, MMMS 15, 317–336 (2019).
[9] T. Kansal, The theory of generalized micropolar thermoelastic diffusion with double porosity, Theo. and Appl. Mech. 49, 85–109 (2022).
[10] M. Svanadze, Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures, J. Ther. Stress. 27, 151–170 (2004).
[11] M. Svanadze, Fundamental solution in the theory of micromorphic elastic solids with microtemperatures, J. Ther. Stress. 27, 345–366 (2004).
[12] M. Svanadze, Fundamental solution in the theory of consolidation with double porosity, J. Mech. Beh. Mat. 16, 123–130 (2005).
[13] M. Svanadze, S.D. Cicco, Fundamental solutions in the full coupled linear theory of elasticity for solid with double porosity, Arch. Mech. 65, 367–390 (2013).
[14] M. Svanadze, Fundamental Solution in the linear theory of consolidation for elastic solids with double porosity, J. Math. Sci. 195, 258–268 (2013).
[15] E. Scarpetta, M. Svanadze, V. Zampoli, Fundamental solutions in the theory of thermoelasticity for solids with double porosity, J. Ther. Stress. 37, 727–748 (2014).
[16] T. Kansal, Fundamental solutions in the theory of micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations, CMST 28, 11–25 (2022).
The aim of the paper is to establish the basic governing equations for anisotropic thermoelastic medium with double porosity and microtemperatures and to construct the fundamental solution of a system of equations in cases of steady, pseudo-, quasi-static oscillations and equilibrium.
Key words:
References:
[1] R.A. Grot, Thermodynamics of a continuum with microstructure, Int. J. Engg. Sci. 7, 801–814 (1969).
[2] D. Iesan, R. Quintanilla, On a theory of thermoelasticity with microtemperatures, J. Ther. Stress. 23, 199–215 (2000).
[3] D. Iesan, On a theory of micromorphic elastic solids with microtemperatures, J. Ther. Stress. 24, 737–752 (2001).
[4] D. Iesan, Thermoelasticity of bodies with microstructure and microtemperatures, Int. J. Solids Struct. 44, 8648–8662 (2007).
[5] R.K. Wilson, E.C. Aifantis, On the theory of consolidation with double porosity-I, Int. J. Engg. Sci. 20, 1009–1035 (1982).
[6] D. Iesan, R. Quintanilla, On a theory of thermoelastic materials with a double porosity structure, J. Ther. Stress. 37, 1017–1036 (2014).
[7] T. Kansal, Generalized theory of thermoelastic diffusion with double porosity, Arch. Mech. 70, 241–268 (2018).
[8] T. Kansal, Fundamental solution of the system of equations of pseudo oscillations in the theory of thermoelastic diffusion materials with double porosity, MMMS 15, 317–336 (2019).
[9] T. Kansal, The theory of generalized micropolar thermoelastic diffusion with double porosity, Theo. and Appl. Mech. 49, 85–109 (2022).
[10] M. Svanadze, Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures, J. Ther. Stress. 27, 151–170 (2004).
[11] M. Svanadze, Fundamental solution in the theory of micromorphic elastic solids with microtemperatures, J. Ther. Stress. 27, 345–366 (2004).
[12] M. Svanadze, Fundamental solution in the theory of consolidation with double porosity, J. Mech. Beh. Mat. 16, 123–130 (2005).
[13] M. Svanadze, S.D. Cicco, Fundamental solutions in the full coupled linear theory of elasticity for solid with double porosity, Arch. Mech. 65, 367–390 (2013).
[14] M. Svanadze, Fundamental Solution in the linear theory of consolidation for elastic solids with double porosity, J. Math. Sci. 195, 258–268 (2013).
[15] E. Scarpetta, M. Svanadze, V. Zampoli, Fundamental solutions in the theory of thermoelasticity for solids with double porosity, J. Ther. Stress. 37, 727–748 (2014).
[16] T. Kansal, Fundamental solutions in the theory of micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations, CMST 28, 11–25 (2022).
