000014294 001__ 14294
000014294 005__ 20161115100147.0
000014294 04107 $$aeng
000014294 046__ $$k2016-08-21
000014294 100__ $$aMohammed Ameen, Maqsood
000014294 24500 $$aHigher-order asymptotic homogenization of periodic materials at low scale separations

000014294 24630 $$n24.$$p24th International Congress of Theoretical and Applied Mechanics - Book of Papers
000014294 260__ $$bInternational Union of Theoretical and Applied Mechanics, 2016
000014294 506__ $$arestricted
000014294 520__ $$2eng$$aIn this work, we investigate the limits of classical homogenization theories pertaining to homogenization of periodic composite materials at low scale separations and demonstrate the effectiveness of higher-order periodic homogenization in alleviating this limitation. Classical homogenization techniques are 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 show that the classical homogenization deviates from the actual solution for scale ratios below 10. Beyond this limit, the higher-order asymptotic homogenization solution still gives a very good approximation which becomes better as more higher-order terms are included. This results in a size-dependent macroscopic model, which indeed allows one to push the limitations of homogenization in the direction of less scale separation.

000014294 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000014294 653__ $$a

000014294 7112_ $$a24th International Congress of Theoretical and Applied Mechanics$$cMontreal (CA)$$d2016-08-21 / 2016-08-26$$gICTAM2016
000014294 720__ $$aMohammed Ameen, Maqsood
000014294 8560_ $$ffischerc@itam.cas.cz
000014294 8564_ $$s73374$$uhttps://invenio.itam.cas.cz/record/14294/files/PO.SM10-1.07.297.pdf$$yOriginal version of the author's contribution as presented on CD,  page 2544, code PO.SM10-1.07.297
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000014294 962__ $$r13812
000014294 980__ $$aPAPER