We present an analysis of fractal geometry of extensive and complex shear band patterns in a severely deformed metallic glass. We show that the shear band patterns have fractal characteristics, and the fractal dimensions are determined by the stress noise induced by the interaction between shear bands. A theoretical model of the spatial evolution of multiple shear bands is proposed in which the collective shear bands slide is considered as a stochastic process far from thermodynamic equilibrium.

The structural geometry and size distribution of the local atomic rearrangements induced by external stress in amorphous solids are investigated by molecular dynamics studies. We find that the size distribution exhibits a generic power-law behavior and their structural geometry shows fractal feature. This indicates that the local atomic rearrangements in amorphous solids are self-organized during deformation. A simple theoretical model based on the interaction of the heterogeneous elastic field sources is proposed which predicts the power-law scaling and characterizes the properties of the local atomic rearrangements in amorphous solids.