# Rigidity percolation control of the brittle-ductile transition in disordered networks

## TL;DR

This study demonstrates how controlling the mean coordination number in disordered 2D networks influences the brittle-ductile failure transition, revealing a critical point at the isostatic value where failure mode changes.

## Contribution

It introduces an experimental approach to tune failure modes in disordered networks via mean coordination number and elucidates the underlying cooperative mechanisms using a pebble game algorithm.

## Key findings

- Transition occurs at mean coordination number $rac{z}{7} = 3$ in large-friction limit.
- Brittle failure associated with rigid, spanning clusters.
- Ductile failure occurs in floppy networks with nonspanning rigid clusters.

## Abstract

In ordinary solids, material disorder is known to increase the size of the process zone in which stress concentrates at the crack tip, causing a transition from localized to diffuse failure. Here, we report experiments on disordered 2D lattices, derived from frictional particle packings, in which the mean coordination number $\langle z \rangle$ of the underlying network provides a similar control. Our experiments show that tuning the connectivity of the network provides access to a range of behaviors from brittle to ductile failure. We elucidate the cooperative origins of this transition using a frictional pebble game algorithm on the original, intact lattices. We find that the transition corresponds to the isostatic value $\langle z \rangle = 3$ in the large-friction limit, with brittle failure occurring for structures vertically spanned by a rigid cluster, and ductile failure for floppy networks containing nonspanning rigid clusters. Furthermore, we find that individual failure events typically occur within the floppy regions separated by the rigid clusters.