Fundamental Solutions in the Theory of Micromorphic Thermoelastic Diffusion for Triple Porosity Materials with Microtemperature and Microconcentration Effects
Markanda National College
Department of Mathematics
Shahabad Markanda, 136135, India
E-mail: tarun1_kansal@yahoo.co.in
Received:
Received: 12 January 2025; revised: 2 March 2025; accepted: 4 March 2025
DOI: 10.12921/cmst.2025.0000001
Abstract:
The main goal of this article is to derive the basic governing equations for the linearized theory of a micromorphic thermoelastic diffusion medium. This encompasses the analysis of microtemperatures, microconcentrations, and triple porosity. Moreover, the objective is to establish the fundamental solution for these equations in situations involving steady oscillations and equilibrium, presented in elementary functions.
Key words:
steady oscillations, thermoelastic diffusion, triple porosity
References:
[1] A.C. Eringen, Simple Microfluids, Int. J. Eng. Sci. 2, 205–217 (1964).
[2] A.C. Eringen, E.S. Suhubi, Nonlinear Theory of Simple Microelastic Solids, I and II, Int. J. Eng. Sci. 2, 189–203, 389–403 (1964).
[3] A.C. Eringen, Mechanics of Micromorphic Continua, [In:] Mechanics of Generalized Continua, Ed. E. Kröner, Springer-Verlag, Berlin (1967).
[4] A.C. Eringen, Balance Laws of Micromorphic Mechanics, Int. J. Eng. Sci. 8, 819–828 (1970).
[5] A.C. Eringen, Microcontinuum field theory I: Foundations and solids, Springer-Verlag, Berlin (1999).
[6] R.A. Grot, Thermodynamics of a continuum with microstructure, Int. J. Eng. Sci. 7, 801–814 (1969).
[7] D. Iesan, On a theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses 24, 737–752 (2001).
[8] D. Iesan, Thermoelasticity of bodies with microstructure and microtemperatures, Int. J. Solids Struct. 44, 8648–8662 (2007).
[9] M. Aouadi, M. Ciarletta, V. Tibullo, A thermoelastic diffusion theory with microtemperatures and microconcentrations, J. Therm. Stresses 40, 486–501 (2017).
[10] A. Chirila˘, M. Marin, Diffusion in Microstretch Thermoelasticity with Microtemperatures and Microconcentrations, [In:] Models and Theories in Social Systems. Studies in Systems, Decision and Control 179, Eds. C. Flaut, Š. Hošková-Mayerová, D. Flaut, Springer, Cham (2019).
[11] T. Kansal, Fundamental solutions in the theory of micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations, CMST 28, 11–25 (2022).
[12] M. Svanadze, Fundamental solutions in the theory of elasticity for triple porosity materials, Meccanica 51, 1825–1837 (2016).
[13] B. Straughan, Uniqueness and stability in triple porosity thermoelasticity, Rend. Lincei-Mat. Appl. 28, 191–208 (2017).
[14] T. Kansal, Fundamental solutions in generalized theory of thermoelastic diffusion with triple porosity, Eng. Trans. 71, 473–505 (2023).
[15] M. Svanadze, Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity, Math. Mech. Solids 24, 919–938 (2019).
[16] M. Svanadze, Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures, J. Therm. Stresses 27, 151–170 (2004).
[17] M. Svanadze, Fundamental solution in the theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses 27, 345–366 (2004).
[18] A.C. Eringen, Theory of thermo-microstretch elastic solids, Int. J. Eng. Sci. 28, 1291–1301 (1990).
The main goal of this article is to derive the basic governing equations for the linearized theory of a micromorphic thermoelastic diffusion medium. This encompasses the analysis of microtemperatures, microconcentrations, and triple porosity. Moreover, the objective is to establish the fundamental solution for these equations in situations involving steady oscillations and equilibrium, presented in elementary functions.
Key words:
steady oscillations, thermoelastic diffusion, triple porosity
References:
[1] A.C. Eringen, Simple Microfluids, Int. J. Eng. Sci. 2, 205–217 (1964).
[2] A.C. Eringen, E.S. Suhubi, Nonlinear Theory of Simple Microelastic Solids, I and II, Int. J. Eng. Sci. 2, 189–203, 389–403 (1964).
[3] A.C. Eringen, Mechanics of Micromorphic Continua, [In:] Mechanics of Generalized Continua, Ed. E. Kröner, Springer-Verlag, Berlin (1967).
[4] A.C. Eringen, Balance Laws of Micromorphic Mechanics, Int. J. Eng. Sci. 8, 819–828 (1970).
[5] A.C. Eringen, Microcontinuum field theory I: Foundations and solids, Springer-Verlag, Berlin (1999).
[6] R.A. Grot, Thermodynamics of a continuum with microstructure, Int. J. Eng. Sci. 7, 801–814 (1969).
[7] D. Iesan, On a theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses 24, 737–752 (2001).
[8] D. Iesan, Thermoelasticity of bodies with microstructure and microtemperatures, Int. J. Solids Struct. 44, 8648–8662 (2007).
[9] M. Aouadi, M. Ciarletta, V. Tibullo, A thermoelastic diffusion theory with microtemperatures and microconcentrations, J. Therm. Stresses 40, 486–501 (2017).
[10] A. Chirila˘, M. Marin, Diffusion in Microstretch Thermoelasticity with Microtemperatures and Microconcentrations, [In:] Models and Theories in Social Systems. Studies in Systems, Decision and Control 179, Eds. C. Flaut, Š. Hošková-Mayerová, D. Flaut, Springer, Cham (2019).
[11] T. Kansal, Fundamental solutions in the theory of micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations, CMST 28, 11–25 (2022).
[12] M. Svanadze, Fundamental solutions in the theory of elasticity for triple porosity materials, Meccanica 51, 1825–1837 (2016).
[13] B. Straughan, Uniqueness and stability in triple porosity thermoelasticity, Rend. Lincei-Mat. Appl. 28, 191–208 (2017).
[14] T. Kansal, Fundamental solutions in generalized theory of thermoelastic diffusion with triple porosity, Eng. Trans. 71, 473–505 (2023).
[15] M. Svanadze, Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity, Math. Mech. Solids 24, 919–938 (2019).
[16] M. Svanadze, Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures, J. Therm. Stresses 27, 151–170 (2004).
[17] M. Svanadze, Fundamental solution in the theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses 27, 345–366 (2004).
[18] A.C. Eringen, Theory of thermo-microstretch elastic solids, Int. J. Eng. Sci. 28, 1291–1301 (1990).
