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Homogenization of a 1D nonlinear dynamical problem for periodic composites
Author(s) -
Andrianov I.V.,
Danishevs'kyy V.V.,
Topol H.,
Weichert D.
Publication year - 2011
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201000176
Subject(s) - homogenization (climate) , asymptotic homogenization , nonlinear system , imperfect , cauchy distribution , materials science , mathematical analysis , composite material , composite number , mathematics , physics , biodiversity , ecology , linguistics , philosophy , quantum mechanics , biology
In this paper we study wave propagation through a composite material built up of a periodically repeated one‐dimensional structure of coated inclusions and matrix material by the application of the asymptotic homogenization method. We take into account geometrical nonlinearity, which is described by the Cauchy‐Green strain tensor and physical nonlinearity by the Murnaghan elastic potential. We take into account structural nonlinearity by considering the bonding between two materials to be imperfect. As a result we obtain homogenized equations for the low‐frequency range.