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  4. Homogenization of the Helmholtz problem in the presence of a row of viscoelastic inclusions

Homogenization of the Helmholtz problem in the presence of a row of viscoelastic inclusions

MMC.
2023;
Volume 10, Number 3
: pp. 899–917
https://doi.org/10.23939/mmc2023.03.899
Received: April 15, 2023
Revised: June 19, 2023
Accepted: June 22, 2023

Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 899–917 (2023)

Authors:
  1. R. Belemou
  2. A. Sbitti
  3. M. Jaouahri
  4. J.-J. Marigo
1
University Hassan II, Ens
2
University Mohammed V, Ensam
3
University Hassan II, Ens
4
Solid Mechanics Laboratory, Ecole Polytechnique

We propose a homogenization method based on a matched asymptotic expansion technique to obtain the effective behavior of a periodic array of linear viscoelastic inclusions embedded in a linear viscoelastic matrix.  The problem is considered for shear waves and the wave equation in the harmonic regime is considered.  The obtained effective behavior is that of an equivalent interface associated to jump conditions, for the displacement and the normal stress at the interface.  The transmission coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of a rectangular inclusions.

homogenization
matched asymptotic expansion
subwavelength scale
transmission of waves
viscoelastic
interface homogenization
effective jump conditions
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