Multiscale failure analysis with coarse-grained micro cracks and damage

A multiscale aggregating discontinuities method for treating unit cells which undergo material failure is further described; the method can also be used when the material response predicted by the unit cell loses rank-one stability. Its notable features are the decomposition of the unit cell response into a continuous and a discontinuous response, and the extraction of the equivalent discontinuities by coarse-graining procedures. In this study, the method is further combined with the extended finite element method for macro model and the cracking nodes method for micro model so that arbitrary discontinuities in the macro and the micro models can be treated free from the initial mesh topologies. The examples that are studied include a composite with circular inclusions and a micro cracking solid with an emerging macro failure.