Microstructure Features that Most Influence the Mori–Tanaka Scheme Breakdown in 2D Solids with Crack-Like Flat Cavities

This study aims to detect in which microstructure conditions the Mori–Tanaka scheme is inappropriate to calculate the effective stiffness of a two-phase matrix-inclusion system. We analyze the discrepancy between numerical and Mori–Tanaka stiffness estimates in two-dimensional (2D) solids with crack-like flat cavities. The maximum transfer entropy that occurs between a microstructure feature and a stiffness component discrepancy cannot only detect the phase change between a Mori–Tanaka-like cracked solid to a non-Mori–Tanaka-like cracked solid, but also reveal at which load step that phase change first occurs and which microstructure features most affect that phase change. Further analysis with a binary classifier based on a support vector machine (SVM) algorithm shows that the systematic calculation of nine microstructure features based on six statistical crack network descriptors at each step of a loading path can inform the detection of a microstructure transition. The microstructure features identified here could thus be used to trigger the transition from one homogenization scheme to another during incremental stiffness updates, for example, during the simulation of a load path.