# Athermal Fracture of Elastic Networks: How Rigidity Challenges the Unavoidable Size-Induced Brittleness

## TL;DR

This study uses large-scale simulations to explore how rigidity affects fracture behavior in disordered elastic networks, revealing size-induced brittleness and universal damage trends near the isostatic point.

## Contribution

It uncovers the universal non-monotonic size dependence of brittleness and identifies a characteristic size where brittleness emerges, considering disorder and thermal effects.

## Key findings

- Maximum damage occurs near the isostatic point and with small rupture thresholds.
- Brittleness increases with system size regardless of network properties.
- A universal non-monotonic trend of stress drop with system size is observed.

## Abstract

By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. We observe the largest damage in networks with connectivity close to the isostatic point and when the rupture thresholds are small. However, regardless of network and spring properties, a more brittle fracture is observed upon increasing system size. Differently from most of the fracture descriptors, the maximum stress drop, a proxy for brittleness, displays a universal non-monotonic dependence on system size. Based on this uncommon trend it is possible to identify the characteristic system size $L^*$ at which brittleness kicks in. The more the disorder in network connectivity or in spring thresholds, the larger $L^*$. Finally, we speculate how this size-induced brittleness is influenced by thermal fluctuations.