A review of concurrent multiscale methods for the analysis of fine scale discontinuity problems

Modeling of crack and discontinuity related problems has had a great influence on numerous industries for a long time. Simulation of discontinuity behavior in different scales, especially in atomistic scales, can lead to better insight of the crack/discontinuity initiation and propagation phenomena and prediction of its behavior in larger scales. On the other hand, modeling based on fully refined scales requires huge computational effort compared to other methods due to the higher number of degrees of freedom. Concurrent multiscale methods have been developed to overcome the high computational cost issues of refined models, while preserving sufficient accuracy. Studies have shown that concurrent multiscale methods are capable of simulating all atomic behaviors in order to establish a compatible solution with larger scales, and to accurately resemble the laboratory results. In the present review, concurrent multiscale methods, which could be categorized into homogenization and partitioned-domain methods, are briefly investigated and compared. These methods have been widely used for modelling of cracks, discontinuities and impurities in different types of problems in the past two decades. To create a suitable basis for comparing the main concurrent methods, the problem of edge crack propagation is redesigned and modeled, and the simulation results and their computational accuracy are compared.