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

Ahmed Boughammoura; Yousra Braham

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 45-73
  • ISSN: 0011-4642

Abstract

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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 ε β ( ε > 0 and β > 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 ε 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 ε β with 0 < β ≤ 1 .

How to cite

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Boughammoura, Ahmed, and Braham, Yousra. "Homogenization of a three-phase composites of double-porosity type." Czechoslovak Mathematical Journal (2021): 45-73. <http://eudml.org/doc/297363>.

@article{Boughammoura2021,
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 $0<\beta \le 1$.},
author = {Boughammoura, Ahmed, Braham, Yousra},
journal = {Czechoslovak Mathematical Journal},
keywords = {homogenization; three-phase composite; unfolding operator; double-porosity type},
language = {eng},
number = {1},
pages = {45-73},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homogenization of a three-phase composites of double-porosity type},
url = {http://eudml.org/doc/297363},
year = {2021},
}

TY - JOUR
AU - Boughammoura, Ahmed
AU - Braham, Yousra
TI - Homogenization of a three-phase composites of double-porosity type
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 45
EP - 73
AB - 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 $0<\beta \le 1$.
LA - eng
KW - homogenization; three-phase composite; unfolding operator; double-porosity type
UR - http://eudml.org/doc/297363
ER -

References

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