Modeling of imperfect contacts in determining the effective diffusion permeability
DOI:
https://doi.org/10.21638/spbu01.2023.405Abstract
The work develops a universal approach to acounting for imperfect contacts in determining the effective properties of various nature, namely, effective diffusivity, thermal and electrical conductivity. Imperfect contacts take place when fields at the microlevel are not continuous. The possibility of creating a unified approach is due to the similarity of the governing equations. At the same time, the appearance of imperfect contacts can be caused by microstructural features and by the specifics of the process itself. For concreteness, the effective diffusion permeability is determined, since various reasons for the appearance of imperfect contacts can be considered. The reasons can be associated both with the formation of structural defects and with the presence of the specific segregation effect. The paper generalizes and compares two approaches to accounting for imperfect contacts. In the first case, a field jump is set. In the second case, an inhomogeneity with a thin coating possessing extreme properties is introduced. A comprehensive analysis is carried out on the example of a material with spherical inhomogeneities. Analytical expressions for contribution tensor of the equivalent inhomogeneity are obtained, which results in simplification of generalization of various homogenization methods.
Keywords:
effective properties, inhomogeneity, imperfect contacts, segregation, diffusivity
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References
Литература
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7. Belova I. V., Murch G. E. Calculation of the effective conductivity and diffusivity in composite solid electrolytes. Journal of Physics and Chemistry of Solids 66 (5), 722-728 (2005). https://doi.org/10.1016/j.jpcs.2004.09.009
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11. Duan H. L., Karihaloo B. L. Effective thermal conductivities of heterogeneous media containing multiple imperfectly bonded inclusions. Physical Review B. 75 (6), 064206 (2007). https://doi.org/10.1103/PhysRevB.75.064206
12. Kushch V. I., Sevostianov I., Belyaev A. S. Effective conductivity of spheroidal particle composite with imperfect interfaces: Complete solutions for periodic and random micro structures. Mechanics of Materials 89, 1-11 (2015). https://doi.org/10.1016/j.mechmat.2015.05.010
13. Endres A. L., Knight R. J. A model for incorporating surface phenomena into the dielectric response of a heterogeneous medium. Journal of colloid and interface science 157 (2), 418-425 (1993). https://doi.org/10.1006/jcis.1993.1204
14. Levin V., Markov M. Effective thermal conductivity of micro-inhomogeneous media containing imperfectly bonded ellipsoidal inclusions. International Journal of Engineering Science 109, 202-215 (2016). https://doi.org/10.1016/j.ijengsci.2016.09.012
15. Hill R. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids 11 (5), 357-372 (1963). https://doi.org/10.1016/0022-5096(63)90036-X
16. Fricke H. Mathematical treatment of the electric conductivity and capacity of disperse systems I. The electric conductivity of a suspension of homogeneous spheroids. Physical Review 24 (5), 575 (1924). https://doi.org/10.1103/PhysRev.24.575
17. Markov K. Z. Elementary micromechanics of heterogeneous media. Birkhauser, Boston (2000).
References
1. Kanaun S.K., Levin V.M. Effective field method in mechanics of matrix composite materials. Advances in mathematical modelling of composite materials 1 (58) (1994). https://doi.org/10.1142/9789814354219_0001
2. Kachanov M., Sevostianov I. Micromechanics of materials, with applications. Cham, Springer (2018).
3. Zhang Y., Liu L. On diffusion in heterogeneous media American Journal of Science 312 (9), 1028-1047 (2012). https://doi.org/10.2475/09.2012.03
4. Bokstein B. S., Magidson I.A., Svetlov I. L. On diffusion in volume and along grain boundaries. Physics of metals and metallography 6 (6), 1040-1052 (1958). (In Russian)
5. Kaur I., Mishin Y., Gust W. Fundamentals of grain and interphase boundary diffusion. John Wiley (1995).
6. Kalnin J. R., Kotomin E. A., Maier J. Calculations of the effective diffusion coefficient for inhomogeneous media. Journal of physics and chemistry of solids 63 (3), 449-456 (2002). https://doi.org/10.1016/S0022-3697(01)00159-7
7. Belova I.V., Murch G. E. Calculation of the effective conductivity and diffusivity in composite solid electrolytes. Journal of Physics and Chemistry of Solids 66 (5), 722-728 (2005). https://doi.org/10.1016/j.jpcs.2004.09.009
8. Knyazeva A.G., Grabovetskaya G. P., Mishin I.P., Sevostianov I. On the micromechanical modelling of the effective diffusion coefficient of a polycrystalline material. Philosophical Magazine 95 (19), 2046-2066 (2015). https://doi.org/10.1080/14786435.2015.1046965
9. Frolova K.P., Vilchevskaya E. N. Effective diffusivity of transversely isotropic material with embedded pores. Materials Physics & Mechanics 47 (6), 937-950 (2021). https://doi.org/10.18149/MPM.4762021_12
10. Miloh T., Benveniste Y. On the effective conductivity of composites with ellipsoidal inhomogeneities and highly conducting interfaces. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 455 (1987), 2687-2706 (1999). https://doi.org/10.1098/rspa.1999.0422
11. Duan H. L., Karihaloo B. L. Effective thermal conductivities of heterogeneous media containing multiple imperfectly bonded inclusions. Physical Review B. 75 (6), 064206 (2007). https://doi.org/10.1103/PhysRevB.75.064206
12. Kushch V. I., Sevostianov I., Belyaev A. S. Effective conductivity of spheroidal particle composite with imperfect interfaces: Complete solutions for periodic and random micro structures. Mechanics of Materials 89, 1-11 (2015). https://doi.org/10.1016/j.mechmat.2015.05.010
13. Endres A. L., Knight R. J. A model for incorporating surface phenomena into the dielectric response of a heterogeneous medium. Journal of colloid and interface science 157 (2), 418-425 (1993). https://doi.org/10.1006/jcis.1993.1204
14. Levin V., Markov M. Effective thermal conductivity of micro-inhomogeneous media containing imperfectly bonded ellipsoidal inclusions. International Journal of Engineering Science 109, 202-215 (2016). https://doi.org/10.1016/j.ijengsci.2016.09.012
15. Hill R. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids 11 (5), 357-372 (1963). https://doi.org/10.1016/0022-5096(63)90036-X
16. Fricke H. A mathematical treatment of the electric conductivity and capacity of disperse systems I. The electric conductivity of a suspension of homogeneous spheroids. Physical Review 24 (5) 575 (1924). https://doi.org/10.1103/PhysRev.24.575
17. Markov K. Z. Elementary micromechanics of heterogeneous media. Birkhauser, Boston (2000).
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Published
2023-12-23
How to Cite
Frolova, K. P., Vilchevskaya, E. N., & Polyanskiy, V. A. (2023). Modeling of imperfect contacts in determining the effective diffusion permeability. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(4), 650–664. https://doi.org/10.21638/spbu01.2023.405
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Section
On the anniversary of A. K. Belyaev
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
