A general finite element based non-local theory for the medium-long-range correlation of metallic glasses

Abstract

Mean-field theory is extensively used in statistical physics, solid-state physics, and biophysics to compress a large number of interacting multi-body problems into an effective single-body problem, providing some insight into the system’s behavior at a lower computing cost. Nonetheless, the mean-field approximation always suppresses the non-local effects, hence obscuring the underlying mechanisms involving unit interactions between microscopic events, such as competition, co-evolution, and self-organized criticality. This paper presents a general, non-local mean-field approximation for the medium-long-range correlation of materials based on the finite element method, which has excellent compatibility and scalability with existing theories. It ties the evolution of a deformation unit to the status of other spatial domain elements, which is analogous to the fundamental principle of cellular automata. When applied to metallic glasses, the model demonstrates excellent spatial–temporal agreement between the shear band evolution measurements and simulation findings. Excitingly, the self-organized criticality of amorphous systems and the self-adaptive evolution mechanism of shear bands are realized in both two and three dimensions for the first time. Without restriction to amorphous systems, this work explores the application of mean-field theories to non-local phenomena. Future research into new mathematical types of medium-long range interaction is conceivable through multiscale simulation techniques.