Czechoslovak Mathematical Journal, first online, pp. 1-29

Homogenization of a three-phase composites of double-porosity type

Ahmed Boughammoura, Yousra Braham

Received April 1, 2019.   Published online July 1, 2020.

Abstract:  In this work we consider a diffusion problem in a periodic composite having three phases: matrix, fibers and interphase. The heat conductivities of the medium vary periodically with a period of size $\varepsilon^\beta$ ($\varepsilon>0$ and $\beta>0$) in the transverse directions of the fibers. In addition, we assume that the conductivity of the interphase material and the anisotropy contrast of the material in the fibers are of the same order $\varepsilon^2$ (the so-called double-porosity type scaling) while the matrix material has a conductivity of order $1$. By introducing a partial unfolding operator for anisotropic domains we identify the limit problem. In particular, we prove that the effect of the interphase properties on the homogenized models is captured only when the microstructural length scale is of order $\varepsilon^\beta$ with $0<\beta\leq1$.
Keywords:  homogenization; three-phase composite; unfolding operator; double-porosity type
Classification MSC:  35B27, 35B45, 35K55, 35K65, 76S05
DOI:  10.21136/CMJ.2020.0151-19

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Affiliations:   Ahmed Boughammoura, University of Monastir, Higher Institute of Computer Sciences and Mathematics of Monastir, Corniche Avenue, BP 223, Monastir 5000, Tunisia, e-mail:; Yousra Braham, University of Monastir, Faculty of Sciences of Monastir, Avenue of the environment, 5019 Monastir, Tunisia, e-mail:

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