A Universal Scaling Law for Intrinsic Fracture Energy of Networks

TL;DR

This paper introduces a universal scaling law that predicts the intrinsic fracture energy of various networks by linking strand mechanics and connectivity, validated through simulations and experiments across diverse conditions.

Contribution

It presents a novel physical model that connects local strand rupture mechanics with global network fracture energy, applicable across different network types and scales.

Findings

The scaling law accurately predicts fracture energy in diverse networks.

Intrinsic fracture energy depends on rupture force, breaking length, and connectivity.

The model is validated through extensive simulations and experiments.

Abstract

Networks of interconnected materials permeate throughout nature, biology, and technology due to exceptional mechanical performance. Despite the importance of failure resistance in network design and utility, no existing physical model effectively links strand mechanics and connectivity to predict bulk fracture. Here, we reveal a universal scaling law that bridges these levels to predict the intrinsic fracture energy of diverse networks. Simulations and experiments demonstrate its remarkable applicability to a breadth of strand constitutive behaviors, topologies, dimensionalities, and length scales. We show that local strand rupture and nonlocal energy release contribute synergistically to the measured intrinsic fracture energy in networks. These effects coordinate such that the intrinsic fracture energy scales independent of the energy to rupture a strand; it instead depends on the strand rupture force, breaking length, and connectivity. Our scaling law establishes a physical basis for understanding network fracture and a framework for fabricating tough materials from networks across multiple length scales.