Networks and Hierarchies: How Amorphous Materials Learn to Remember

Abstract

We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions joined by occasional one-way transitions. The highly connected regions include hierarchically organized hysteresis cycles and sub-cycles. At small to moderate strains this organization leads to near-perfect return point memory. The transitions in the network can be traced back to localized particle rearrangements (soft-spots) that interact via Eshelby-type deformation fields. By linking topology to dynamics, the network representations provides new insights into the mechanisms that lead to reversible and irreversible behavior in amorphous solids.

5 pages, 4 figures. Minor changes, addition of of ancillary file providing numerical implementation details and supporting evidence