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Analysis of Effective Properties of Poroelastic Composites with Surface Effects Depending on Boundary Conditions in Homogenization Problems

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Numerical Methods and Applications (NMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13858))

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Abstract

The paper considers the homogenization problems for two-component poroelastic composites with a random structure of nanosized inclusions. The nanoscale nature of the inclusions was taken into account according to the generalized Gurtin–Murdoch theory by specifying surface elastic and porous stresses at the interface boundaries, the scale factor of which was related to the size of the inclusions. The formulation of homogenization problems was based on the theory of effective moduli, considering Hill’s energy relations. The problems of static poroelasticity were solved in accordance with the Biot and filtration models. A feature of this investigation was the comparison of solutions of four types of homogenization problems with different boundary conditions. Modeling of representative volumes and solving problems of determining the effective material moduli were carried out in the ANSYS finite element package. Representative volumes were built in the form of a cubic grid of hexahedral finite elements with poroelastic properties of materials of one of the two phases and with a random arrangement of elements of the second phase. To consider interface effects, the interfaces were covered with shell elements with options for membrane stresses. The results of computational experiments made it possible to study the effective moduli depending on the boundary conditions, on the percentage of inclusions, their characteristic nanosizes, and areas of interface boundaries.

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Acknowledgements

The financial support of the Russian Foundation for Basic Research according to the research project No 19-58-18011 Bulg_a (M.C., A.N., A.N.), the National Science Fund of Bulgaria (project KP-06-Russia-1/27.09.2019) and by the Science and Education for Smart Growth Operational Program (2014-2020) and the ESIF through grant BG05M2OP001-1.001-0003 (M.D.) is gratefully acknowledged.

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Authors and Affiliations

  1. Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, 344090, Rostov-on-Don, Russia

    Mikhail Chebakov, Andrey Nasedkin & Anna Nasedkina

  2. Institute of Mechanics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Maria Datcheva & Roumen Iankov

Authors
  1. Mikhail Chebakov
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  2. Maria Datcheva
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  3. Andrey Nasedkin
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  4. Anna Nasedkina
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  5. Roumen Iankov
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Correspondence to Maria Datcheva .

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Editors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Georgiev

  2. Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Maria Datcheva

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir Georgiev

  4. Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    Geno Nikolov

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Chebakov, M., Datcheva, M., Nasedkin, A., Nasedkina, A., Iankov, R. (2023). Analysis of Effective Properties of Poroelastic Composites with Surface Effects Depending on Boundary Conditions in Homogenization Problems. In: Georgiev, I., Datcheva, M., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2022. Lecture Notes in Computer Science, vol 13858. Springer, Cham. https://doi.org/10.1007/978-3-031-32412-3_10

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  • DOI: https://doi.org/10.1007/978-3-031-32412-3_10

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  • Online ISBN: 978-3-031-32412-3

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