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Homogenization of microstructures in dynamics using periodic boundary conditions
Author(s) -
Stadler Michael,
Schanz Martin
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910192
Subject(s) - homogenization (climate) , periodic boundary conditions , boundary value problem , mathematical analysis , microstructure , homogeneous , mathematics , lagrangian , physics , materials science , composite material , biodiversity , ecology , combinatorics , biology
Abstract A homogenization method is used to calculate effective material properties of periodic microstructures subjected to small, time‐harmonic strain fields. The method is based on the equivalence of averaged micro‐field quantities in dispersive heterogeneous media and those in effective homogeneous media with frequency dependent elastic constants. Solutions to the elastodynamic boundary value problem (BVP) are obtained from a boundary element method where periodic boundary conditions on the unit‐cell are incorporated using Lagrangian multipliers. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)