Green-Lindsay thermoelasticity for double porous materials

Emin, Anamaria N.; Florea, Olivia A.

doi:10.2478/auom-2023-0005

Abstract

The main purpose of this paper is to obtain new results in the thermoelasticity for double porous materials, starting from the classical theory of Green-Lindsay’s elasticity. The novelty of the proposed method consists in proving a reciprocal theorem and obtaining the energy equation in the context of Green-Lindsay’s thermoelasticity for double porous materials. The added value in this article is the result regarding the uniqueness of the solution of the problem with mixed data for bodies with double porosity.

References

[Green(1972)] Green A.E., Lindsay K.A. (1972) Thermoelasticity, J. Elast., 2, 17.
Search in Google Scholar Back to article
[Aouadi(2019)] Aouadi M., Campo M., Copetti M.I.M. and Fernndez J.R. (2019) Analysis of a multidimensional thermoviscoelastic contact problem under the GreenLindsay theory, J. Comput. Appl. Math., 1, 224246.
Search in Google Scholar Back to article
[Nieto(2018)] Nieto M., Rivera J.E.M., Naso M.G. and Quintanilla R.(2018) Qualitative results for a mixture of GreenLindsay thermoelastic solids, Chaotic Mod. Simul., 3, 285294.
Search in Google Scholar Back to article
[Marin and Craciun(2020)] Marin M., Craciun E.M. and Pop N. (2020), Some Results in GreenLindsay Thermoelasticity of Bodies with Dipolar Structure, Mathematics, 8, 497.
Search in Google Scholar Back to article
[Barenblatt(1960)] Barenblatt G.I., Zheltov Iu. and Kochina I.N. (1960), Basic concept in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech., 24, 12861303.
Search in Google Scholar Back to article
[Barenblatt(1963)] Barenblatt G.I. (1963), On certain boundary-value-problems for the equations of seepage of liquid in fissured rocks, Prikl. Mat. Mekh., 27, 513518.
Search in Google Scholar Back to article
[Svanadze(2013)] Svanadze M., Scalia A. (2013), Mathematical problems in the coupled linear theory of bone poroelasticity, Comput. Math. Appl., vol. 662, 15541566.
Search in Google Scholar Back to article
[Scarpetta(2014)] Scarpetta E., Svanadze M. and Zampoli V. (2014), Fundamental solutions in the theory of thermoelasticity for solids with double porosity, J. Therm. Stresses, vol. 37, no. 6, 727748.
Search in Google Scholar Back to article
[Wilson(1982)] Wilson R., Aifantis E. (1982), On the theory of consolidation with double porosity, Int. J. Eng. Sci., vol. 20, 10091035.
Search in Google Scholar Back to article
[Kumar(2016)] Kumar R., Vohra R. and Gorla M.G. (2016), Some considerations of fundamental solution in micropolar thermoelastic materials with double porosity, Arch. Mech., vol. 68, no. 4, 263284.
Search in Google Scholar Back to article
[Bai(1994)] Bai M., Roegiers J. C. (1994), Fluid flow and heat flow in deformable fractured porous media, Internat. J. Engrg. Sci., 32, 16151633.
Search in Google Scholar Back to article
[Masters(2000)] Masters I., Pao W.K.S. and Lewis R. W. (2000), Coupling temperature to a double-porosity model of deformable porous media,Int. J. Numer. Methods Eng., 49, 42138.
Search in Google Scholar Back to article
[Florea(2019)] Florea O. (2019), The backward in time problem of double porosity material with microtemperature, Symmetry, 11(4), 552.
Search in Google Scholar Back to article
[Bazarra(2019)] Bazarra N., Fernndez J.R., Leseduarte M.C., Magaa A. and Quintanilla R. (2019), On the thermoelasticity with two porosities: asymptotic behaviour, Math. Mech. Solids, 24(9), 2713-2725.10.1177/1081286518783219
Search in Google Scholar Back to article
[Florea(2021)] Florea O.A., Bobe A. (2021), MooreGibsonThompson thermoelasticity in the context of double porous materials, Continuum Mech. Thermodyn., 33, 22432252.
Search in Google Scholar Back to article
[Florea(2019)] Florea O. (2019), Harmonic vibrations in thermoelastic dynamics with double porosity structure, Math. Mech. Solids, 24(8), 24102424.
Search in Google Scholar Back to article
[Emin(2020)] Emin A.N., Florea O.A. and Craciun E.M. (2020), Some uniqueness results for thermoelastic materials with double porosity structure, Continuum Mech. Thermodyn., 33, 10831106.
Search in Google Scholar Back to article
[Svanadze(2020)] Svanadze M. (2020), Steady vibration problems in the coupled linear theory of porous elastic solids, Math. Mech. Solids, 25, 768790.
Search in Google Scholar Back to article
[Svanadze(2014)] Svanadze M. (2014), Uniqueness theorems in the theory of thermoelasticity for solids with double porosity, Meccanica 49, 20992108.
Search in Google Scholar Back to article

Green-Lindsay thermoelasticity for double porous materials

Abstract

Paradigm

My account