Quasi-static problems in the coupled linear theory of thermoporoelasticity

References

• M. A. Biot, “General theory of three-dimensional consolidation,” J. Appl. Phys., vol. 12, no. 2, pp. 155–164, 1941. DOI: 10.1063/1.1712886.
   Google Scholar
• 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: 10.1007/BF00249363.
   Web of Science ®Google Scholar
• S. C. Cowin and J. W. Nunziato, “Linear elastic materials with voids,” J Elasticity, vol. 13, no. 2, pp. 125–147, 1983. DOI: 10.1007/BF00041230.
   Web of Science ®Google Scholar
• R. L. Schiffman, “A thermoelastic theory of consolidation,” in Environmental and Geophysical Heat Transfer, C. J. Cremers, F. Kreith, and J. A. Clark, Eds, New York: ASME, 1971, pp. 78–84.
   Google Scholar
• J. R. Booker and C. Savvidou, “Consolidation around a spherical heat source,” Int. J. Solids Struct., vol. 20, no. 11-12, pp. 1079–1090, 1984. DOI: 10.1016/0020-7683(84)90091-X.
   Web of Science ®Google Scholar
• W. Derski and S. Kowalski, “Equations of linear thermoconsolidation,” Arch. Mech., vol. 31, pp. 303–316, 1979.
   Web of Science ®Google Scholar
• D. F. McTigue, “Thermoelastic response of fluid-saturated porous rock,” J. Geophys. Res., vol. 91, no. B9, pp. 9533–9542, 1986. DOI: 10.1029/JB091iB09p09533.
   Web of Science ®Google Scholar
• M. Kurashige, “A thermoelastic theory of fluid-filled porous materials,” Int. J. Solids Struct., vol. 25, no. 9, pp. 1039–1052, 1989. DOI: 10.1016/0020-7683(89)90020-6.
   Web of Science ®Google Scholar
• T. S. Nguyen and A. P. S. Selvadurai, “Coupled thermal-mechanical-hydrological behaviour of sparsely fractured rock: Implications for nuclear fuel waste disposal,” Int. J. Rock Mech. Min. Sci., vol. 32, no. 5, pp. 465–479, 1995. DOI: 10.1016/0148-9062(95)00036-G.
   Web of Science ®Google Scholar
• A. P. S. Selvadurai, “The analytical method in geomechanics,” Appl. Mech. Rev. ASME, vol. 60, no. 3, pp. 87–106, 2007. DOI: 10.1115/1.2730845.
   Web of Science ®Google Scholar
• A. H. D. Cheng, Poroelasticity. Switzerland: Springer Int. Publ., 2016
   Google Scholar
• Z. Liu, Multiphysics in Porous Materials. Switzerland: Springer Int. Publ. AG, 2018
   Google Scholar
• A. P. S. Selvadurai and A. Suvorov, Thermo-Poroelasticity and Geomechanics. Cambridge: Cambridge University Press, 2017
   Google Scholar
• D. Ieşan, “A theory of thermoelastic materials with voids,” Acta Mech., vol. 60, no. 1-2, pp. 67–89, 1986. DOI: 10.1007/BF01302942.
   Web of Science ®Google Scholar
• M. Ciarletta and D. Ieşan, “Non-classical elastic solids,” Longman Scientific and Technical, New York, NY: John Wiley & Sons, Inc., 1993
   Google Scholar
• D. Ieşan, Thermoelastic Models of Continua. Dordrecht: Springer Science + Business Media, 2004
   Google Scholar
• B. Straughan, Stability and Wave Motion in Porous Media. New York, NY: Springer, 2008
   Google Scholar
• B. Straughan, Convection with Local Thermal Non-Equilibrium and Microfluidic Effects. Advances in Mechanics and Mathematics, vol. 32, New York, NY: Springer, 2015
   Google Scholar
• B. Straughan, Mathematical Aspects of Multi-Porosity Continua. Advances in Mechanics and Mathematics, vol. 38. Switzerland: Springer Inter. Publ. AG, 2017
   Google Scholar
• M. Svanadze, “Steady vibration problems in the coupled linear theory of porous elastic solids,” Math. Mech. Solids, vol. 25, no. 3, pp. 768–790, 2020. DOI: 10.1177/1081286519888970.
   Web of Science ®Google Scholar
• 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: 10.1007/s00707-019-02565-x.
   Web of Science ®Google Scholar
• M. Svanadze, “Boundary integral equations method in the coupled theory of thermoelasticity for porous materials,” Proceedings of ASME, IMECE2019, Volume 9: Mechanics of Solids, Structures, and Fluids, V009T11A033, November 11-14, 2019. DOI: 10.1115/IMECE2019-10367.
   Google Scholar
• 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: North-Holland, 1979
   Google Scholar
• S. G. Mikhlin, Multidimensional Singular Integrals and Integral Equations. Oxford: Pergamon Press, 1965
   Google Scholar
• M. Svanadze, Potential Method in Mathematical Theories of Multi-Porosity Media. Interdisciplinary Applied Mathematics, vol. 51, Switzerland: Springer Nature AG, 2019
   Google Scholar