Fundamental Solutions in the Theory of Micromorphic Thermoelastic Diffusion Materials with Microtemperatures and Microconcentrations
Markanda National College
Department of Mathematics
Shahabad Markanda, 136135, IndiaE-mail: tarun1_kansal@yahoo.co.in
Received:
Received: 17 November 2021; revised: 29 December 2021; accepted: 22 January 2022; published online: 3 February 2022
DOI: 10.12921/cmst.2021.0000029
Abstract:
The main purpose of this paper is to construct the fundamental solutions of a system of equations of isotropic micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations in case of steady oscillations in terms of elementary functions. In a particular case, the fundamental solutions of the system of equations of equilibrium theory of isotropic micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations are also established.
Key words:
diffusion, microconcentrations, microstretch, microtemperatures, thermoelasticity
References:
[1] W. Nowacki, Dynamical problems of thermodiffusion in solids – I, Bull. Pol. Acad. Sci. Tech. Sci. 22, 55–64 (1974).
[2] W. Nowacki, Dynamical problems of thermodiffusion in solids – II, Bull. Pol. Acad. Sci. Tech. Sci. 22, 205–211 (1974).
[3] W. Nowacki, Dynamical problems of thermodiffusion in solids – III, Bull. Pol. Acad. Sci. Tech. Sci. 22, 257–266 (1974).
[4] W. Nowacki, Dynamical problems of thermodiffusion in solids, Eng. Fract. Mech. 8, 261–266 (1976).
[5] H.H. Sherief, F.A. Hamza, H.A. Saleh, The theory of generalized thermoelastic diffusion, Int. J. Eng. Sci. 42, 591–608 (2004).
[6] M. Aouadi, Generalized theory of thermoelastic diffusion for anisotropic media, J. Therm. Stresses 31, 270–285 (2008).
[7] T. Kansal, R. Kumar, Variational Principle, Uniqueness and Reciprocity theorems in the theory of generalized thermoelastic diffusion material, QScience Connect 2013, 1–18 (2013).
[8] R.A. Grot, Thermodynamics of a continuum with microstructure, Int. J. Eng. Sci. 7, 801–814 (1969).
[9] D. Iesan, R. Quintanilla, On a theory of thermoelasticity with microtemperatures, J. Therm. Stresses 23, 199–215 (2000).
[10] D. Iesan, On a theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses 24, 737–752 (2001).
[11] D. Iesan, Thermoelasticity of bodies with microstructure and microtemperatures, Int. J. Solids Struct. 44, 8648–8662 (2007).
[12] M. Svanadze, Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures, J. Therm. Stresses 27, 151–170 (2004).
[13] M. Svanadze, Fundamental solution in the theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses 27, 345–366 (2004).
[14] M. Aouadi, M. Ciarletta, V. Tibullo, A thermoelastic diffusion theory with microtemperatures and microconcentrations, J. Therm. Stresses 40, 486–501 (2017).
[15] A. Chirila, M. Marin, Diffusion in microstretch thermoelasticity with microtemperatures and microconcentrations, [In:] Models and Theories in Social Systems, 149–164 (2019).
[16] A.C. Eringen, Theory of thermo-microstretch elastic solids, Int. J. Eng. Sci. 28, 1291–1301 (1990).
The main purpose of this paper is to construct the fundamental solutions of a system of equations of isotropic micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations in case of steady oscillations in terms of elementary functions. In a particular case, the fundamental solutions of the system of equations of equilibrium theory of isotropic micromorphic thermoelastic diffusion materials with microtemperatures and microconcentrations are also established.
Key words:
diffusion, microconcentrations, microstretch, microtemperatures, thermoelasticity
References:
[1] W. Nowacki, Dynamical problems of thermodiffusion in solids – I, Bull. Pol. Acad. Sci. Tech. Sci. 22, 55–64 (1974).
[2] W. Nowacki, Dynamical problems of thermodiffusion in solids – II, Bull. Pol. Acad. Sci. Tech. Sci. 22, 205–211 (1974).
[3] W. Nowacki, Dynamical problems of thermodiffusion in solids – III, Bull. Pol. Acad. Sci. Tech. Sci. 22, 257–266 (1974).
[4] W. Nowacki, Dynamical problems of thermodiffusion in solids, Eng. Fract. Mech. 8, 261–266 (1976).
[5] H.H. Sherief, F.A. Hamza, H.A. Saleh, The theory of generalized thermoelastic diffusion, Int. J. Eng. Sci. 42, 591–608 (2004).
[6] M. Aouadi, Generalized theory of thermoelastic diffusion for anisotropic media, J. Therm. Stresses 31, 270–285 (2008).
[7] T. Kansal, R. Kumar, Variational Principle, Uniqueness and Reciprocity theorems in the theory of generalized thermoelastic diffusion material, QScience Connect 2013, 1–18 (2013).
[8] R.A. Grot, Thermodynamics of a continuum with microstructure, Int. J. Eng. Sci. 7, 801–814 (1969).
[9] D. Iesan, R. Quintanilla, On a theory of thermoelasticity with microtemperatures, J. Therm. Stresses 23, 199–215 (2000).
[10] D. Iesan, On a theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses 24, 737–752 (2001).
[11] D. Iesan, Thermoelasticity of bodies with microstructure and microtemperatures, Int. J. Solids Struct. 44, 8648–8662 (2007).
[12] M. Svanadze, Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures, J. Therm. Stresses 27, 151–170 (2004).
[13] M. Svanadze, Fundamental solution in the theory of micromorphic elastic solids with microtemperatures, J. Therm. Stresses 27, 345–366 (2004).
[14] M. Aouadi, M. Ciarletta, V. Tibullo, A thermoelastic diffusion theory with microtemperatures and microconcentrations, J. Therm. Stresses 40, 486–501 (2017).
[15] A. Chirila, M. Marin, Diffusion in microstretch thermoelasticity with microtemperatures and microconcentrations, [In:] Models and Theories in Social Systems, 149–164 (2019).
[16] A.C. Eringen, Theory of thermo-microstretch elastic solids, Int. J. Eng. Sci. 28, 1291–1301 (1990).
