Representative area element for double porosity materials with random microstructures
Email:
tbthao.tran@utc.edu.vn
Keywords:
RVE, RAE, unit cell, effective permeability, double porosity, Monte-Carlo
Abstract
Porous materials constitute an important class of natural or artificial materials in many engineering branches and industrial sectors. In general, a porous multiphase medium can be considered as a heterogeneous material. Note that, the representative volume element (RVE) or representative area element (RAE) play an important role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties. Therefore, the present work aims to apply the homogenization theory for determining the minimum size of the RAE for a two-dimensional (2D) porous materials consisting of an isotropic permeable solid matrix in which fluid-filled pores are embedded. To achieve the objective, the microstructure of the RAE is randomly generated first with identical elips. The Monte-Carlo method is proposed to determine the ensemble average of the effective permeability of the porous media for many independent realizations on each area size. The minimum size of the RAE will be derived from a required precision on the average value and variance of the effective permeabilityReferences
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[4]. C. Boutin, P. Royer, J. Auriault, Acoustic absorption of porous surfacing with dual porosity, Int. J. Solids Struct., 35 (1998) 4709–4737. https://doi.org/10.1016/S0020-7683(98)00091-2
[5]. X. Haller, Y. Monerie, S. Pagano, P. -G. Vincent, Elastic behavior of porous media with spherical nanovoids, Int. J. Solids Struct., 84 (2016) 99–109. https://doi.org/10.1016/j.ijsolstr.2016.01.018
[6]. K. Sab, On the homogenization and the simulation of random materials, Euro J. Mech. A/Solids, 11 (1992) 585–607.
[7]. A. A. Gusev, Representative volume element size for elastic: A numerical study, J. Mech. Phys. Solids, 45 (1997) 1449–1459. https://doi.org/10.1016/S0022-5096(97)00016-1
[8]. A. Lachihab, K. Sab, Aggregate composites: a contact based modeling, Comput. Mater. Sci., 33 (2005) 467–490. https://doi.org/10.1016/j.commatsci.2004.10.003
[9]. A. Lachihab, K. Sab, Does a representative volume element exist for fatigue life prediction? The case of aggregate composites, Int. J. Numer. Anal. Methods Geomech., 32 (2008) 1005–1021. https://doi.org/10.1002/nag.655
[10]. G. S. Beavers, D. D. Joseph, Boundary conditions at a naturally permeable wall, J.Fluid. Mech., 30 (1967) 197–207. https://doi.org/10.1017/S0022112067001375
[11]. P. G. Saffman, On the boundary condition at the surface of a porous medium, Stud. Appl. Math., L2 (1971) 93–101. https://doi.org/10.1002/sapm197150293
[12]. C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge University Press, Cambridge, 1992.
[13]. C. Pozrikidis, A practical guide to boundary element methods with the software library BEMLIB, Chapman & Hall/CRC, 2002.
[14]. C. A. Brebbia, J. Dominguez, Boundary elements An introductory course, WIT Press/Computational Mechanics Publications, Southamton, 1992.
[15]. J. T. Katsikadelis, Boundary elements: Theory and applications, Elsevier, Amsterdam, 2002.
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Received
15/10/2023
Revised
16/11/2023
Accepted
08/12/2023
Published
15/12/2023
Type
Research Article
How to Cite
Trần Thị Bích, T. (3200). Representative area element for double porosity materials with random microstructures . Transport and Communications Science Journal, 74(9), 1088-1099. https://doi.org/10.47869/tcsj.74.9.6
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