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Fracture toughness and auxeticity in disordered metamaterials

Hannes Holey1, Andrea Lorenzo Henri Sergio Detry1, Silvia Bonfanti1,2, Roberto Guerra1, Anshul D.S. Parmar2, Jacopo Fiocchi3, Ausonio Tuissi3, Michael Zaiser4, and Stefano Zapperi1,5,*

  • *Contact author: stefano.zapperi@unimi.it
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Phys. Rev. Applied 25, 024075 – Published 24 February, 2026

DOI: https://doi.org/10.1103/r66g-hyxx

Abstract

Auxetic metamaterials are commonly thought to exhibit favorable mechanical properties, notably high-energy absorption. Here we investigate disordered metamaterials obtained from random beam networks by optimizing simultaneously auxeticity and the energy absorbed before fracture. By giving different weights to these optimization targets, we demonstrate that the optimal configurations are connected along a Pareto front where high auxeticity implies comparatively low-energy absorption and vice versa. We study the mechanical properties of the resulting metamaterials and characterize the different deformation modes obtained for distinct optimization targets. The simulation and optimization results are validated by comparison with the deformation behavior of additively manufactured samples. Our work provides an illustration of the potentials and limitations of multiobjective optimization in the design of disordered mechanical metamaterials.

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References (34)

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Phys. Rev. Applied 25, 024075– Published 24 February, 2026
  • Received 25 July 2025
  • Revised 10 November 2025
  • Accepted 3 December 2025
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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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