Asymptotic expansion homogenization for heterogeneous media: computationalissues and applications

Developments in asymptotic expansion homogenization (AEH) are overviewed in the context of engineering multi-scale problems. The problems of multi-sca les presently considered are those linking continuum level descriptions at two different length scales. Concurrent research in the literature is first described. A recipe of the AEH approach is then presented that can be used for future developments in many areas of material and geometric non-linear continuum mechanics. Then, a derivation is outlined using the finite eleme nt method that is useful for engineering applications that leads to coupled hierarchical partial differential equations in elasticity. The approach pr ovides causal relationships between macro and micro scales wherein procedur es for homogenization of properties and localization of small-scale respons e are built-in. A brief discussion of a physical paradox is introduced in t he estimation of micro-stresses that tends to be a barrier in the understan ding of the method. Computational issues are highlighted and illustrative a pplications in linear elasticity are then presented for composites containi ng microstructures with complex geometries. (C) 2001 Elsevier Science Ltd. Ail rights reserved.