Homogenization of a 1D nonlinear dynamical problem for periodic composites

Abstract

Abstract 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.