How Geometry Tames Disorder in Lattice Fracture

TL;DR

This paper explores how geometric parameters influence the impact of disorder on fracture behavior in beam-lattices, revealing three regimes of failure and challenging previous notions of disorder-induced toughening.

Contribution

It introduces a model linking geometry and disorder in lattice fracture, identifying failure regimes and demonstrating non-monotonic disorder effects on toughness.

Findings

Disorder effects vary with Weibull modulus and Slenderness Ratio.

Disorder-induced toughening depends non-monotonically on disorder.

Geometry controls how disorder influences fracture behavior.

Abstract

We investigate the fracture behavior of pre-cracked triangular beam-lattices whose elements have failure stresses drawn from a Weibull distribution. Through a statistical analysis and numerical simulations, we identify and verify the existence of three distinct failure regimes: (i) disorder is effectively suppressed, (ii) disorder manifests locally near the crack tip, modifying the crack morphology, and (iii) disorder manifests globally, leading to initially diffuse failure. Our model naturally reveals the key parameters governing this behavior: the Weibull modulus, quantifying the spread in failure thresholds, and a geometric quantity termed the Slenderness Ratio. We also reproduce the disorder-induced toughening reported in previous experimental and numerical studies, further demonstrating that its manifestation depends non-monotonically on disorder. Crucially, our results indicate that this toughening cannot be simply connected to the amount of damage in the lattice, challenging interpretations that attribute increased fracture energy solely to enhanced crack tortuosity or diffuse failure. Overall, our results establish geometry as a powerful control parameter for regulating how disorder is expressed during fracture in beam-lattices, with broader implications for the disorder-induced toughening in engineered materials.