Higher-order asymptotic homogenization of periodic materials at low scale separations

Abstract eng:
In 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.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket