MULTI-SCALE SECOND-ORDER COMPUTATIONAL HOMOGENIZATION OF HETEROGENEOUS MATERIALS

摘要

A novel second-order computational homogenization scheme suitable for a multi-scale modelling of macroscopic localization and size effects is proposed. The second-order scheme is an extension of the classical first-order computational homogenization framework and is based on a proper incorporation of the gradient of the macroscopic deformation gradient tensor and the associated higher-order stress measure into the macro-micro scale transition. The applicability of the approach is illustrated by several examples.