Higher-order asymptotic homogenization of periodic materials with low scale separation

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Abstract

In this work, we investigate the limits of classical homogenization theories pertaining to homogenization of periodic linear elastic composite materials at low scale separations and demonstrate the effectiveness of higher-order periodic homogenization in alleviating this limitation. Classical homogenization techniques are known to be very effective for materials with large scale separation between the scale of the heterogeneity and the macro-scale dimension, but inaccurate at low scale separations. Literature suggests that asymptotic homogenization is capable of pushing the limit to smaller scale separation by taking on board higher-order terms of the asymptotic expansion. We studied infinite two-dimensional elastic two-phase composite materials consisting of stiff inclusions in a soft matrix, subjected to a periodic body force, for various scale ratios between the period of the body force and that of the inclusions. We created reference solution using direct numerical simulation and used ensemble averaging for the complete family of all possible microstructures to obtain the reference homogenized solution. We show that the response predicted using zeroth order classical homogenization deviates from this reference homogenized solution for scale ratios below 10. The higher-order asymptotic homogenization solution still gives a very good approximation even in the low scale separation regime and it becomes better as more higher-order terms are included. The higher-order theory results in a size-dependent macroscopic model, which indeed allows one to push the limitations of homogenization in the direction of less scale separation.

Original languageEnglish
Title of host publicationECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
PublisherNational Technical University of Athens
Pages2346-2352
Number of pages7
ISBN (Electronic)9786188284401
DOIs
Publication statusPublished - 2016
Event7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016, 5-10 June 2016, Hersonissos, Crete, Greece - Creta Maris Conference Centre, Hersonissos, Crete, Greece
Duration: 5 Jun 201610 Jun 2016
Conference number: 7
https://www.eccomas2016.org/

Publication series

NameEccomas Proceedia
Volume1964

Conference

Conference7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016, 5-10 June 2016, Hersonissos, Crete, Greece
Abbreviated titleECCOMAS2016
CountryGreece
CityHersonissos, Crete
Period5/06/1610/06/16
Internet address

Keywords

  • Higher-order periodic homogenization
  • Homogenization methods
  • Linear elastic composites
  • Size effects

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