Asymptotic expansion homogenization for heterogeneous media: Computational issues and applications

Peter W. Chung, Kumar K. Tamma, Raju R. Namburu

Research output: Contribution to journalArticlepeer-review

156 Scopus citations


Developments in asymptotic expansion homogenization (AEH) are overviewed in the context of engineering multi-scale problems. The problems of multi-scales 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 element method that is useful for engineering applications that leads to coupled hierarchical partial differential equations in elasticity. The approach provides causal relationships between macro and micro scales wherein procedures for homogenization of properties and localization of small-scale response are built-in. A brief discussion of a physical paradox is introduced in the estimation of micro-stresses that tends to be a barrier in the understanding of the method. Computational issues are highlighted and illustrative applications in linear elasticity are then presented for composites containing microstructures with complex geometries.

Original languageEnglish (US)
Pages (from-to)1291-1301
Number of pages11
JournalComposites - Part A: Applied Science and Manufacturing
Issue number9
StatePublished - Sep 2001

Bibliographical note

Funding Information:
The authors are very pleased to acknowledge support in part by Battelle/US Army Research Office (ARO) Research Triangle Park, North Carolina, under grant number DAAH04-96-C-0086, and by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory Cooperative agreement number DAAH04-95-2-0003/contract number DAAH04-95-C-0008. The content does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred. Support in part by Dr Andrew Mark of the IMT Computational Technology Activity and the ARL/MSRC facilities is also gratefully acknowledged. Special thanks are also due to the CICD at the US Army Research Laboratory, Aberdeen Proving Grounds, Maryland. Other related support in form of computer grants from the Minnesota Supercomputer Institute (MSI), Minneapolis, Minnesota and the Doctoral Dissertation Fellowship from the University of Minnesota are also gratefully acknowledged.


  • A. glass fibers
  • A. resins
  • B. elasticity
  • B. microstructure
  • Homogenization


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