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Composites: Mechanics, Computations, Applications: An International Journal
ESCI SJR: 0.354 SNIP: 0.655 CiteScore™: 1.2

ISSN 印刷: 2152-2057
ISSN オンライン: 2152-2073

Composites: Mechanics, Computations, Applications: An International Journal

DOI: 10.1615/CompMechComputApplIntJ.v8.i4.50
pages 339-354

HIGH-FREQUENCY APPROXIMATION OF PLANE WAVE PROPAGATION IN AN ELASTIC MEDIUM WITH PERIODIC DISTRIBUTION OF CRACKS

Alexey Talonov
UNLV, MEPhI
Viktoria L. Savatorova
Central Connecticut State University, New Britain, CT
A. N. Vlasov
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russian Federation

要約

In this work, we consider the propagation of plane waves in elastic media weakened by isolated open cracks with periodic distribution of their concentration. The problem under study is essentially multiscale. One can distinguish several space scales such as the characteristic size of a crack, a period of crack distribution l, wavelength λ, and the characteristic size of the sample as a whole L. We are interested in the high-frequency approximation, by which we mean the case where the wavelength is small in comparison with the macroscopic size of the problem (λ << L). In this situation, the classical multiscale homogenization does not work. However, for the case where the wavelength exceeds the characteristic size of a crack, but is of the same order of magnitude as the period of distribution of cracks concentration (λ ~ l), it is possible to perform perturbations with respect to the small parameter ε = l/L << 1 and get displacements and frequencies of oscillations in cracked media in the form of two-scale asymptotic expansions.


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