References
- B. Straughan, Mathematical Aspects of Multi-Porosity Continua. Advances in Mechanics and Mathematics, vol. 38. Cham, Switzerland: Springer Int. Publ. AG, 2017.
- M. Svanadze, Potential Method in Mathematical Theories of Multi-Porosity Media. Interdisciplinary Applied Mathematics, vol. 51. Cham, Switzerland: Springer Nature Switzerland AG, 2019.
- O. Kolditz, T. Nagel, H. Shao, W. Wang, S. Bauer (eds), Thermo-Hydro-Mechanical-Chemical Processes in Fractured Porous Media: Modelling and Benchmarking. From Benchmarking to Tutoring. Cham, Switzerland: Springer Int. Publ. AG, 2018.
- M. Svanadze, “Potential Method in the coupled linear theory of porous elastic solids,” Math. Mech. Solids, vol. 25, no. 3, pp. 768–790, 2020. DOI: https://doi.org/10.1177/1081286519888970.
- M. Svanadze, “Boundary integral equations method in the coupled theory of thermoelasticity for porous materials,” Proceedings of ASME, IMECE2019, Vol. 9: Mechanics of Solids, Structures, and Fluids, V009T11A033, November 11–14, 2019. DOI: https://doi.org/10.1115/IMECE2019-10367.
- M. M. Svanadze, “Potential method in the coupled theory of viscoelasticity of porous materials,” J. Elast., vol. 144, no. 2, pp. 119–140, 2021. DOI: https://doi.org/10.1007/s10659-021-09830-y.
- M. Svanadze, “Potential Method in the coupled theory of elastic double-porosity materials,” Acta Mech., vol. 232, no. 6, pp. 2307–2329, 2021. DOI: https://doi.org/10.1007/s00707-020-02921-2.
- M. M. Svanadze, “Problems of steady vibrations in the coupled linear theory of double-porosity viscoelastic materials,” Arch. Mech., vol. 73, no. 4, pp. 365–390, 2021.
- L. Bitsadze, “Explicit solution of the Dirichlet boundary value problem of elasticity for porous infinite strip,” Zeit. Angew. Math. Phys., vol. 71, no. 5, pp. 145, 2020. DOI: https://doi.org/10.1007/s00033-020-01379-5.
- L. Bitsadze, “Explicit solutions of quasi-static problems in the coupled theory of poroelasticity,” Continuum Mech. Thermodyn., vol. 33, no. 6, pp. 2481–2492, 2021. DOI: https://doi.org/10.1007/s00161-021-01029-9.
- M. Mikelashvili, “Quasi-static problems in the coupled linear theory of elasticity for porous materials,” Acta. Mech., vol. 231, no. 3, pp. 877–897, 2020. DOI: https://doi.org/10.1007/s00707-019-02565-x.
- M. Mikelashvili, “Quasi-static problems in the coupled linear theory of thermoporoelasticity,” J. Thermal Stress, vol. 44, no. 2, pp. 236–259, 2021. DOI: https://doi.org/10.1080/01495739.2020.1814178.
- M. A. Biot, “General theory of three-dimensional consolidation,” J. Appl. Phys., vol. 12, no. 2, pp. 155–164, 1941. DOI: https://doi.org/10.1063/1.1712886.
- J. Bear, Modeling Phenomena of Flow and Transport in Porous Media. Switzerland: Springer Int. Publ. AG, 2018.
- A. H. D. Cheng, Poroelasticity. Theory and Applications of Transport in Porous Media, vol. 27. Switzerland: Springer Int. Publ., 2016.
- O. Coussy, Mechanics and Physics of Porous Solids. Chichester, U.K: Wiley, 2010.
- Y. Ichikawa and A. P. S. Selvadurai, Transport Phenomena in Porous Media: Aspects of Micro/Macro Behaviour. Berlin, Heidelberg: Springer-Verlag, 2012.
- H. F. Wang, Theory of Linear Poro-Elasticity with Applications to Geomechanics and Hydrogeology. Princeton: Princeton Univ. Press, 2000.
- S. Chiriţă and A. Arusoaie, “Thermoelastic waves in double porosity materials,” Europ. J. Mech. - A/Solids, vol. 86, pp. 104177, 2021. DOI: https://doi.org/10.1016/j.euromechsol.2020.104177.
- I. Masters, W. K. S. Pao, and R. W. Lewis, “Coupling temperature to a double-porosity model of deformable porous media,” Int. J. Numer. Meth. Engng, vol. 49, no. 3, pp. 421–438, 2000. DOI: https://doi.org/10.1002/1097-0207(20000930)49:3<421::AID-NME48>3.0.CO;2-6.
- E. Scarpetta, M. Svanadze and V. Zampoli, “Fundamental solutions in the theory of thermoelasticity for solids with double porosity,” J. Thermal Stress, vol. 37, no. 6, pp. 727–748, 2014. DOI: https://doi.org/10.1080/01495739.2014.885337.
- E. Scarpetta and M. Svanadze, “Uniqueness theorems in the quasi-static theory of thermoelasticity for solids with double porosity,” J. Elast., vol. 120, no. 1, pp. 67–86, 2015. DOI: https://doi.org/10.1007/s10659-014-9505-2.
- M. Svanadze, “Uniqueness theorems in the theory of thermoelasticity for solids with double porosity,” Meccanica, vol. 49, no. 9, pp. 2099–2108, 2014. DOI: https://doi.org/10.1007/s11012-014-9876-2.
- M. Svanadze, “Boundary value problems in the theory of thermoporoelasticity for materials with double porosity,” Proc. Appl. Math. Mech., vol. 14, no. 1, pp. 327–328, 2014. DOI: https://doi.org/10.1002/pamm.201410151.
- M. Bai and J. C. Roegiers, “Fluid flow and heat flow in deformable fractured porous media,” Int. J. Eng. Sci., vol. 32, no. 10, pp. 1615–1633, 1994. DOI: https://doi.org/10.1016/0020-7225(94)90169-4.
- N. Khalili and A. P. S. Selvadurai, “A fully coupled constitutive model for thermo-hydro-mechanical analysis in elastic media with double porosity,” Geophys. Res. Lett, vol. 30, no. 24, pp. 2268, 2003. DOI: https://doi.org/10.1029/2003GL018838.
- R. Gelet, “Thermo-hydro-mechanical study of deformable porous media with double porosity in local thermal nonequilibrium,” Ph.D. thesis, Institute National Polytechnique de Grenoble, France, and The University of New South Wales, Sydney, Australia, 2011.
- R. Gelet, B. Loret and N. Khalili, “A thermo-hydromechanical model in local thermal non-equilibrium for fractured HDR reservoirs with double porosity,” J. Geophys. Res., vol. 117, pp. B07205, 2012.
- R. Gelet, B. Loret and N. Khalili, “Thermal recovery from a fractured medium in local thermal non-equilibrium,” Int. J. Numer. Anal. Meth. Geomech, vol. 37, no. 15, pp. 2471–2501, 2013. DOI: https://doi.org/10.1002/nag.2145.
- F. Franchi, B. Lazzari, R. Nibbi and B. Straughan, “Uniqueness and decay in local thermal non-equilibrium double porosity thermoelasticity,” Math Meth Appl Sci, vol. 41, no. 16, pp. 6763–6771, 2018. DOI: https://doi.org/10.1002/mma.5190.
- M. Svanadze, “On the linear theory of double porosity thermoelasticity under local thermal non-equilibrium,” J. Thermal Stress, vol. 42, no. 7, pp. 890–913, 2019. DOI: https://doi.org/10.1080/01495739.2019.1571973.
- B. Straughan, Convection with Local Thermal Non-Equilibrium and Microfluidic Effects. Adv. Mech. Appl. Math., vol. 32. New York: Springer, 2015.
- J. W. Nunziato and S. C. Cowin, “A nonlinear theory of elastic materials with voids,” Arch. Rational Mech. Anal., vol. 72, no. 2, pp. 175–201, 1979. DOI: https://doi.org/10.1007/BF00249363.
- S. C. Cowin and J. W. Nunziato, “Linear elastic materials with voids,” J. Elasticity, vol. 13, no. 2, pp. 125–147, 1983. DOI: https://doi.org/10.1007/BF00041230.
- D. Ieşan, Thermoelastic Models of Continua. Dordrecht: Springer Science + Business Media, 2004.
- M. Ciarletta and D. Ieşan, Non-Classical Elastic Solids. New York, NY, Harlow, Essex, UK: Longman Scientific and Technical, John Wiley & Sons, Inc., 1993.
- M. Aouadi, “A theory of thermoelastic diffusion materials with voids,” Z. Angew. Math. Phys., vol. 61, no. 2, pp. 357–379, 2010. DOI: https://doi.org/10.1007/s00033-009-0016-0.
- M. Aouadi, I. Mahfoudhi and T. Moulahi, “Spectral and numerical analysis for a thermoelastic problem with double porosity and second sound,” Asymp. Anal., pp. 1–38, 2021. (in press). DOI: https://doi.org/10.3233/ASY-211745.
- A. Arusoaie, “Spatial and temporal behavior in the theory of thermoelasticity for solids with double porosity,” J. Thermal Stress, vol. 41, no. 4, pp. 500–521, 2018. DOI: https://doi.org/10.1080/01495739.2017.1387882.
- L. Bitsadze, “Explicit solutions of boundary value problems of elasticity for circle with a double-voids structure,” J. Brazil. Soc. Mech. Sci, vol. 41, no. 9, pp. 383, 2019. DOI: https://doi.org/10.1007/s40430-019-1888-3.
- M. Ciarletta and A. Scalia, “On uniqueness and reciprocity in linear thermoelasticity of materials with voids,” J. Elasticity, vol. 32, no. 1, pp. 1–17, 1993. DOI: https://doi.org/10.1007/BF00042245.
- S. Chiriţă and M. Ciarletta, “On the structural stability of thermoelastic model of porous media,” Math. Meth. Appl. Sci., vol. 31, no. 1, pp. 19–34, 2008. DOI: https://doi.org/10.1002/mma.894.
- S. Chiriţă and V. Zampoli, “Wave propagation in porous thermoelasticity with two delay times,” Math. Methods App. Sci., vol. 45, no. 3, pp. 1498–1512, 2022. DOI: https://doi.org/10.1002/mma.7869.
- S. De Cicco and D. Ieşan, “On the theory of thermoelastic materials with a double porosity structure,” J. Thermal Stress, vol. 44, no. 12, pp. 1514–1533, 2021. DOI: https://doi.org/10.1080/01495739.2021.1994493.
- O. Florea, “Spatial behavior in thermoelastodynamics with double porosity structure,” Int. J. Appl. Mech., vol. 9, no. 7, pp. 1750097, 2017. [14 pages] DOI: https://doi.org/10.1142/S1758825117500971.
- D. Ieşan, “A theory of thermoelastic materials with voids,” Acta Mech., vol. 60, no. 1–2, pp. 67–89, 1986. DOI: https://doi.org/10.1007/BF01302942.
- D. Ieşan and R. Quintanilla, “On a theory of thermoelastic materials with a double porosity structure,” J. Thermal Stress, vol. 37, no. 9, pp. 1017–1036, 2014. DOI: https://doi.org/10.1080/01495739.2014.914776.
- R. Kumar, R. Vohra and M. G. Gorla, “Thermomechanical response in thermoelastic medium with double porosity,” J. Solid Mech., vol. 9, no. 1, pp. 24–38, 2017.
- A. Magan˜ A and R. Quintanilla, “Decay of quasi-static porous-thermo-elastic waves,” Zeit. Angew. Math. Phys., vol. 72, no. 3, pp. 125, 2021. DOI: https://doi.org/10.1007/s00033-021-01557-z.
- M. Marin, “Some basic theorems in elastostatics of micropolar materials with voids,” J. Comp. Appl. Math., vol. 70, no. 1, pp. 115–126, 1996. DOI: https://doi.org/10.1016/0377-0427(95)00137-9.
- R. Quintanilla, “Impossibility of localization in linear thermoelasticity with voids,” Mech. Res. Comm., vol. 34, no. 7–8, pp. 522–527, 2007. DOI: https://doi.org/10.1016/j.mechrescom.2007.08.004.
- M. Svanadze, “Boundary value problems of steady vibrations in the theory of thermoelasticity for materials with a double porosity structure,” Arch. Mech., vol. 69, no. 4/5, pp. 347–370, 2017.
- I. Tsagareli, “Solution of boundary value problems of thermoelasticity for a porous disk with voids,” J. Por. Media, vol. 23, no. 2, pp. 177–185, 2020. DOI: https://doi.org/10.1615/JPorMedia.2020025807.
- I. N. Vekua, “On metaharmonic functions,” Proc. Tbilisi Math. Inst. Academy Sci. Georgian SSR, vol. 12, pp. 105–174, 1943. (Russian). Eng Trans: Lecture Notes of TICMI, vol. 14, pp. 1–62, 2013.
- V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili and T. V. Burchuladze, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. Amsterdam, New York, Oxford: North-Holland Publishing Company, 1979.
- C. M. Dafermos, “On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity,” Arch. Rational Mech. Anal., vol. 29, no. 4, pp. 241–271, 1968. DOI: https://doi.org/10.1007/BF00276727.
- S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations. Oxford: Pergamon Press, 1965.