Fundamental solution in the coupled theory of thermoelastic nanoporous materials with triple porosity
Corresponding Author
Merab Svanadze
Institute for Fundamental and interdisciplinary Mathematical Research, Ilia State University, Tbilisi, Georgia
Correspondence
Merab Svanadze, Institute for Fundamental and interdisciplinary Mathematical Research, Ilia State University, 0162 Tbilisi, Georgia. Email:[email protected]
Search for more papers by this authorCorresponding Author
Merab Svanadze
Institute for Fundamental and interdisciplinary Mathematical Research, Ilia State University, Tbilisi, Georgia
Correspondence
Merab Svanadze, Institute for Fundamental and interdisciplinary Mathematical Research, Ilia State University, 0162 Tbilisi, Georgia. Email:[email protected]
Search for more papers by this authorAbstract
In this paper, the linear coupled theory of thermoelasticity for nanoporous materials with a triple porosity structure based on Darcy's law and the volume fraction concept is considered. The fundamental solution of the system of steady vibration equations is constructed by means of elementary functions. Finally, some basic properties of this solution are established.
REFERENCES
- 1 A. Uthaman, S. Thomas, T. Li, H. Maria (Eds.). (2022). Advanced functional porous materials. From macro to nano scale lengths (p. 688). Springer Nature Switzerland AG, Cham, Switzerland.
10.1007/978-3-030-85397-6 Google Scholar
- 2Biot, M. A. (1941). General theory of three-dimensional consolidation. Journal of Applied Physics, 12, 155–164.
- 3Straughan, B. (2017). Mathematical aspects of multi-porosity continua (p. 208). Springer Int. Publ. AG, Cham, Switzerland.
- 4Svanadze, M. (2019). Potential method in mathematical theories of multi-porosity media (p. 302). Springer Nature Switzerland AG, Cham, Switzerland.
- 5Nunziato, J. W., & Cowin, S. C. (1979). A nonlinear theory of elastic materials with voids. Archive for Rational Mechanics and Analysis, 72, 175–201.
- 6Cowin, S. C., & Nunziato, J. W. (1983). Linear elastic materials with voids. Journal of Elasticity, 13, 125–147.
- 7Ieşan, D., & Quintanilla, R. (2014). On a theory of thermoelastic materials with a double porosity structure. Journal of Thermal Stresses, 37, 1017–1036.
- 8Svanadze, M. (2018). On the linear equilibrium theory of elasticity for materials with triple voids. The Quarterly Journal of Mechanics and Applied Mathematics, 71, 329–348.
- 9Svanadze, M. (2019). Potential method in the theory of thermoelasticity for materials with triple voids. Archives of Mechanics, 71, 113–136.
- 10Svanadze, M. (2020). Steady vibration problems in the coupled linear theory of porous elastic solids. Mathematics and Mechanics of Solids, 25, 768–790.
- 11Svanadze, M. (2019). Boundary integral equations method in the coupled theory of thermoelasticity for porous materials, Proc. of ASME, IMECE2019, Vol. 9: Mechanics of solids, structures, and fluids, V009T11A033, November 11–14, 2019. DOI: https://doi.org/10.1115/IMECE2019-10367
10.1115/IMECE2019?10367 Google Scholar
- 12Svanadze, M. M. (2021). Potential method in the coupled theory of viscoelasticity of porous materials. Journal of Elasticity, 144, 119–140.
- 13Bitsadze, L. (2020). Explicit solution of the Dirichlet boundary value problem of elasticity for porous infinite strip. Zeitschrift für angewandte Mathematik und Physik, 71, 145.
- 14Bitsadze, L. (2021). Explicit solutions of quasi-static problems in the coupled theory of poroelasticity. Continuum Mechanics and Thermodynamics, 33, 2481–2492.
- 15Mikelashvili, M. (2020). Quasi-static problems in the coupled linear theory of elasticity for porous materials. Acta Mechanica, 231, 877–897.
- 16Mikelashvili, M. (2021). Quasi-static problems in the coupled linear theory of thermoporoelasticity. Journal of Thermal Stresses, 44, 236–259.
- 17Svanadze, M. (2021). Potential method in the coupled theory of elastic double-porosity materials. Acta Mechanica, 232, 2307–2329.
- 18Svanadze, M. (2022). On the coupled theory of thermoelastic double-porosity materials. Journal of Thermal Stresses, 45, 576–596.
- 19Svanadze, M. M. (2021). Problems of steady vibrations in the coupled linear theory of double-porosity viscoelastic materials. Archieves of Mechanics, 73, 365–390.
- 20Svanadze, M. (2022). Steady vibration problems in the coupled theory of elastic triple-porosity materials. Transactions of A. Razmadze Mathematical Institute, 176, 83–98.
- 21Svanadze, M. M. (2023). Steady vibration problems in the coupled theory of viscoelasticity for materials with triple porosity. Transactions of A. Razmadze Mathematical Institute, 177, 289–302.
- 22Svanadze, M. (2023). On the coupled linear theory of thermoelasticity for nanomaterials which triple porosity. Mechanics Research Communications, 132, 104161. DOI: https://doi.org/10.1016/j.mechrescom.2023.104161
- 23Hörmander, L. (2005). The analysis of linear partial differential operators, II: Differential operators with constant coefficients (p. 392). Springer.
- 24Kupradze, V. D., Gegelia, T. G., Basheleishvili, M. O., & Burchuladze, T. V. (1979). Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity (p. 929). North-Holland Publishing Company.
- 25de Boer, R., & Svanadze, M. (2004). Fundamental solution of the system of equations of steady oscillations in the theory of fluid-saturated porous media. Transport in Porous Media, 56, 39–50.
- 26Svanadze, M. (2005). Fundamental solution in the theory of consolidation with double porosity. Journal of Mathematical Sciences, 16, 123–130.
- 27Svanadze, M. (2013). Fundamental solutions in the linear theory of consolidation for elastic solids with double porosity. Journal of Mathematical Sciences, 195, 258–268.
10.1007/s10958-013-1578-0 Google Scholar
- 28Svanadze, M. (2016). Fundamental solutions in the theory of elasticity for triple porosity materials. Meccanica, 51, 1825–1837.
- 29Svanadze, M. M. (2017). Fundamental solution and uniqueness theorems in the linear theory of thermoviscoelasticity for solids with double porosity. Journal of Thermal Stresses, 40, 1339–1352.
- 30Svanadze, M. M. (2018). On the solutions of quasi-static and steady vibrations equations in the theory of viscoelasticity for materials with double porosity. Transactions of A. Razmadze Mathematical Institute, 172, 276–292.
- 31Svanadze, M., & De Cicco, S. (2013). Fundamental solutions in the full coupled theory of elasticity for solid with double porosity. Archives of Mechanics, 65, 367–390.