A multi‐scale modeling method for heterogeneous structures without scale separation using a filter‐based homogenization scheme

Abstract

SummaryA method is proposed to compute the response of highly heterogeneous structures by constructing homogenized models when no scale separation can be assumed. The technique is based on an extended homogenization scheme where the averaging operators are replaced by linear filters to cut off fine scale fluctuations, while maintaining locally varying mechanical fields with larger wavelength. As a result, the constitutive law at an intermediate scale, called mesoscale, arises to be naturally nonlocal by construction, where the kernel operator is fully constructed by computations on the unit cell associated with the microstructure. A displacement‐based numerical strategy is developed to implement the technique in a classical finite element framework and does not require higher‐order elements. The methodology is applied to construct simplified models of heterogeneous structures subjected to loads, which have a characteristic wavelength comparable with the dimensions of the heterogeneities or in presence of strong strain localization as in cracked heterogeneous structures. Copyright © 2016 John Wiley & Sons, Ltd.