期刊
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 467, 期 2130, 页码 1749-1769出版社
ROYAL SOC
DOI: 10.1098/rspa.2010.0389
关键词
homogenization; periodic media; effective medium
资金
- ANR (Agence Nationale de la Recherche) [ANR-08-BLAN-0101-01]
- cluster AMA (Advanced Materials in Aquitaine)
- Agence Nationale de la Recherche (ANR) [ANR-08-BLAN-0101] Funding Source: Agence Nationale de la Recherche (ANR)
A method to derive homogeneous effective constitutive equations for periodically layered elastic media is proposed. The crucial and novel idea underlying the procedure is that the coefficients of the dynamic effective medium can be associated with the matrix logarithm of the propagator over a unit period. The effective homogeneous equations are shown to have the structure of a Willis material, characterized by anisotropic inertia and coupling between momentum and strain, in addition to effective elastic constants. Expressions are presented for the Willis material parameters which are formally valid at any frequency and horizontal wavenumber as long as the matrix logarithm is well defined. The general theory is exemplified for scalar SH motion. Low frequency, long wavelength expansions of the effective material parameters are also developed using a Magnus series, and explicit estimates are derived for the rate of convergence.
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