The cross-scale rheology of amorphous system and the resultant Turing-like patterns

The cross-scale rheology of amorphous systems raises a number of problems in the fields of materials science and soft condensed matter physics about their fundamental physical principles. Nevertheless, a clear and concise theoretical framework is still lacking to elucidate the process from microscopic plastic events to the coalescence of shear transformation zones, and subsequently from mesoscopic slip line networks to the emergence of multi-level shear bands. This paper proposes an approach for tracking the activation of plastic events and the growth of plastic zones in amorphous alloys using clustering algorithms. The role of the plastic zone affected zones in the system’s percolation process is described using the Eshelby’s equivalent inclusion theory and the Grady–Kipp momentum diffusion theory, which offers a novel perspective on the mechanism of spontaneous symmetry breaking in amorphous systems with external force. Meanwhile, our research suggests that the cross-scale amorphous rheology is consistent with the fundamental characteristics of Turing patterns to some extent and can be abstracted as a reaction–diffusion system. The stress concentration and stress relaxation caused by plastic zone affected zones function as the activator and the inhibitor in Turing’s framework, respectively. We advocate for additional in-depth research and conceptual innovation to achieve disordered material design in multiple scales.