  Multiscale techniques have been widely shown to potentially overcome the
limitation of homogenization schemes in representing the microscopic failure
mechanisms in heterogeneous media as well as their influence on their
structural response at the macroscopic level. Such techniques allow the use of
fully detailed models to be avoided, thus resulting in a notable decrease in
the overall computational cost at fixed numerical accuracy compared to the
so-called direct numerical simulations. In the present work, two different
multiscale modeling approaches are presented for the analysis of
microstructural instability-induced failure in locally periodic
fiber-reinforced composite materials subjected to general loading conditions
involving large deformations. The first approach, which is of a semi-concurrent
kind, consists in the on-the-fly derivation of the macroscopic constitutive
response of the composite structure together with its microscopic stability
properties through a two-way computational homogenization scheme. The latter
one is a novel hybrid hierarchical-concurrent multiscale approach relying on a
two-level domain decomposition scheme used in conjunction with a nonlinear
homogenization scheme performed at the preprocessing stage. Both multiscale
approaches have been suitably validated through comparisons with reference
direct numerical simulations, by which the ability of the latter approach in
capturing boundary layer effects has been demonstrated.

Numerical Analysis;Numerical Analysis