10.24423/EngTrans.3102.20231017
Fundamental Solutions in the Generalized Theory of Thermoelastic Diffusion with Triple Porosity
The main aim of this paper is to derive the basic governing equations for an anisotropic thermoelastic medium with mass diffusion and triple porosity. Additionally, the fundamental solutions of a system of equations for steady, pseudo-, quasi-static oscillations and equilibrium are also constructed.
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References
Nowacki W., Dynamical problems of thermodiffusion in solids – I, Bulletin of the Polish Academy of Sciences: Technical Sciences, 22: 55–64, 1974.
Nowacki W., Dynamical problems of thermodiffusion in solids – II, Bulletin of the Polish Academy of Sciences: Technical Sciences, 22: 205–211, 1974.
Nowacki W., Dynamical problems of thermodiffusion in solids – III, Bulletin of the Polish Academy of Sciences: Technical Sciences, 22: 257–266, 1974.
Nowacki W., Dynamical problems of thermodiffusion in solids, Engineering Fracture Mechanics, 8(1): 261–266, 1976, doi: 10.1016/0013-7944(76)90091-6.
Sherief H.H., Hamza F.A., Saleh H.A., The theory of generalized thermoelastic diffusion, International Journal of Engineering Science, 42(5–6): 591–608, 2004, doi: 10.1016/j.ijengsci.2003.05.001.
Biot M.A., General theory of three-dimensional consolidation, Journal of Applied Physics, 12(2): 155–164, 1941, doi: 10.1063/1.1712886.
Wilson R.K., Aifantis E.C., On the theory of consolidation with double porosity – I, International Journal of Engineering Science 20(9): 1009–1035, 1982, doi: 10.1016/0020-7225(82)90036-2.
Khaled M.Y., Beskos D.E., Aifantis E.C., On the theory of consolidation with double porosity – III, A finite element formulation, International Journal for Numerical and Analytical Methods in Geomechanics, 8(2): 101–123, 1984, doi: 10.1002/nag.1610080202.
Beskos D.E., Aifantis E.C., On the theory of consolidation with double porosity — II, International Journal of Engineering Science, 24(11): 1697–1716, 1986, doi: 10.1016/0020-7225(86)90076-5.
Khalili N., Selvadurai A.P.S., A fully coupled constitutive model for thermo-hydro-mechanical analysis in elastic media with double porosity, Geophysical Research Letters, 30(24): 22–68, 2003, doi: 10.1029/2003GL018838.
Khalili N., Selvadurai A.P.S., On the constitutive modelling of thermo- hydromechanical coupling in elastic media with double porosity, Elsevier Geo Engineering Book Series, 2: 559–564, 2004, doi: 10.1016/S1571-9960(04)80099-5.
Gelet R., Loret B., Khalili N., A thermo-hydro-mechanical coupled model in local thermal non-equilibrium for fractured HDR reservoir with double porosity, Journal of Geophysical Research: Solid Earth, 117(B7): 1–23, 2012, doi: 10.1029/2012JB009161.
Ieşan D., Quintanilla R., On a theory of thermoelastic materials with a double porosity structure, Journal of Thermal Stresses, 37(9): 1017–1036, 2014, doi: 10.1080/01495739.2014.914776.
Kansal T., Generalized theory of thermoelastic diffusion with double porosity, Archives of Mechanics, 70(3): 241–268, 2018.
Svanadze M., Boundary value problems of steady vibrations in the theory of thermoelasticity for materials with a double porosity structure, Archives of Mechanics, 69(4–5): 347–370, 2017.
Marin M., O¨ chsner A., Craciun E.M., A generalization of the Saint-Venant’s principle for an elastic body with dipolar structure, Continuum Mechanics and Thermodynamics, 32(1): 269–278, 2020, doi: 10.1007/s00161-019-00827-6.
Amin A.N. , Florea O., Cr˘aciun E.M., Some uniqueness results for thermoelastic materials with double porosity structure, Continuum Mechanics and Thermodynamics, 33(4): 1083–1106, 2021, doi: 10.1007/s00161-020-00952-7.
Svanadze M., Fundamental solutions in the theory of elasticity for triple porosity materials, Meccanica, 51(8): 1825–1837, 2016, doi: 10.1007/s11012-015-0334-6.
Straughan B., Uniqueness and stability in triple porosity thermoelasticity, Rendiconti Lincei-Matematica e Applicazioni, 28(2): 191–208, 2017, doi: 10.4171/RLM/758.
Svanadze M., External boundary value problems in the quasi static the- ory of elasticity for triple porosity materials, PAMM, 16(1): 495–496, 2016, doi: 10.1002/pamm.201610236.
Svanadze M., Boundary value problems in the theory of thermoelasticity for triple porosity materials, [in:] Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition, Vol. 9: Mechanics of Solids, Structures and Fluids; NDE, Diagnosis, and Prognosis, Paper No: IMECE2016-65046, V009T12A079, 10 pages, 2016, doi: 10.1115/IMECE2016-65046.
Svanadze M., External boundary value problems in the quasi static theory of triple porosity thermoelasticity, PAMM, 17(1): 471–472, 2017, doi: 10.1002/pamm.201710205.
Svanadze M., Potential method in the theory of elasticity for triple porosity materials, Journal of Elasticity, 130(1): 1–24, 2018, doi: 10.1007/s10659-017-9629-2.
Svanadze M., Potential method in the linear theory of triple porosity ther- moelasticity, Journal of Mathematical Analysis and Applications, 461(2): 1585– 1605, 2018, doi: 10.1016/j.jmaa.2017.12.022.
Svanadze M., On the linear equilibrium theory of elasticity for materials with triple voids, The Quarterly Journal of Mechanics and Applied Mathematics, 71(3): 329–348, 2018, doi: 10.1093/qjmam/hby008.
Straughan B., Mathematical Aspects of Multi-Porosity Continua. Advances in Mechanics and Mathematics, Vol. 38, Springer Cham, 2017, doi: 10.1007/978-3-319-70172-1.
Svanadze M., Fundamental solution in the theory of consolidation with double porosity, Journal of the Mechanical Behavior of Materials, 16(1–2): 123– 130, 2005, doi: 10.1515/JMBM.2005.16.1-2.123.
Svanadze M., De Cicco S., Fundamental solutions in the full coupled linear theory of elasticity for solid with double porosity, Archives of Mechanics, 65(5): 367–390, 2013.
Svanadze M., Fundamental solution in the linear theory of consolidation for elastic solids with double porosity, Journal of Mathematical Sciences, 195(2): 258–268, 2013, doi: 10.1007/s10958-013-1578-0.
Scarpetta E., Svanadze M., Zampoli V., Fundamental solutions in the theory of thermoelasticity for solids with double porosity, Journal of Thermal Stresses, 37(6): 727–748, 2014, doi: 10.1080/01495739.2014.885337.
Kumar R., Vohra R., Gorla M.G., Some considerations of fundamental solution in micropolar thermoelastic materials with double porosity, Archives of Mechanics, 68(4): 263–284, 2016.
Kansal T., Fundamental solution in the theory of thermoelastic diffusion materials with double porosity, Journal of Solid Mechanics, 11(2): 281–296, 2019, doi: 10.22034/jsm.2019.665384.
Svanadze M., Fundamental solutions in the linear theory of thermoelas- ticity for solids with triple porosity, Mathematics and Mechanics of Solids, 24(4): 919–938, 2019, doi: 10.1177/1081286518761183.
Nowacki W., Theory of Asymmetric Elasticity, Polish Scientific Publishers, Warsaw, 1986.
DOI: 10.24423/EngTrans.3102.20231017