# Networks and Hierarchies: How Amorphous Materials Learn to Remember

## TL;DR

This paper models the deformation of amorphous solids as a directed network, revealing hierarchical structures and memory effects that explain reversible and irreversible behaviors.

## Contribution

It introduces a network-based framework to analyze plastic rearrangements and memory in amorphous materials, linking topology to dynamics.

## Key findings

- Highly connected regions form hierarchical hysteresis cycles
- Near-perfect return point memory observed at small to moderate strains
- Transitions are driven by localized particle rearrangements and deformation fields

## 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.