I know the computational homogenisation(CH) by which we can get the macro response from micro sample RVE. but when RVE contains the crack then CH has limited use. Can anybody suggest me some method for analysing cracked RVE
the article: On multi-scale approaches to composites and heterogeneous solids with damage by R. Talreja (2010) gives some useful suggestions about how to solve this problem.
In particular, two strategies are proposed. One is the discrete microstructure (DM), where an RVE with explicitly modelled cracks is homogenized, obtaining an equivalent material where the information about damage topology is lost. Another strategy is the homogenized microstructure (HM), where the damage is embedded in a previously homogenized RVE. The choice of the appropriate modelling strategy depends on the damage you expect to have; matrix cracks and fibre-matrix debondings lead to different behaviours using DM strategy, while using HM strategy they would behave similarly.
In case you want to deal with bigger cracks, spanning over the entire thickness and width of a ply, I would like to recommend a model that allows prediction of stiffness for cracked laminates: A representative volume element based on translational symmetries for FE analysis of cracked laminates with two arrays of cracks by S. Li, C.V. Singh and R. Talreja (2009).