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  • Open Access

How geometry tames disorder in lattice fracture

Matthaios Chouzouris1,*, Leo de Waal1,2, Antoine Sanner3, Alessandra Lingua3, David S. Kammer3, and Marcelo A. Dias1,†

  • 1Institute for Infrastructure and Environment, School of Engineering, University of Edinburgh, Edinburgh EH9 3FG, United Kingdom
  • 2Faculty of Engineering Sciences, University College London, London WC1E 7JE, United Kingdom
  • 3Institute for Building Materials, ETH Zurich, 8093 Zurich, Switzerland

  • *Contact author: m.chouzouris@sms.ed.ac.uk
  • †Contact author: mdias@ed.ac.uk
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Phys. Rev. Applied 26, 014011 – Published 6 July, 2026

DOI: https://doi.org/10.1103/634w-nkwl

Abstract

We investigate the fracture behavior of precracked 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 nonmonotonically 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.

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Outline

Information

Phys. Rev. Applied 26, 014011– Published 6 July, 2026
  • Received 10 February 2026
  • Revised 8 May 2026
  • Accepted 5 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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