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Coarse-grained equivalent stiffness: A structure-plasticity indicator across the order-disorder spectrum

Chen-Wei Bian1, Lin-Li Cao2, Rong-Hao Shi1,3,*, Daniel Şopu3,4,†, and Yun-Jiang Wang2,‡

  • *Contact author: smartsrh@hnas.ac.cn
  • †Contact author: daniel.sopu@oeaw.ac.at
  • ‡Contact author: yjwang@imech.ac.cn
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Phys. Rev. B 113, 224103 – Published 1 June, 2026

DOI: https://doi.org/10.1103/qbmm-s8n5

Abstract

Predicting plastic deformation across the spectrum of structural order, from crystalline to amorphous solids, remains a grand challenge. Coarse-grained equivalent stiffness (CGES), derived from the local dynamical matrix, is introduced as a broadly applicable parameter for mechanical stability. Its spatial variation effectively pinpoints “soft zones” susceptible to plastic rearrangements. Across six systems ranging from single crystals with dislocations to disordered polycrystals, quasicrystals, and amorphous solids, CGES spatially correlate with local plastic rearrangements, accurately capturing dislocation cores, grain boundaries, and shear transformation zones. In single crystals, CGES gradients deterministically pinpoint dislocation cores where plasticity is fully localized. For the four disordered systems, quantitative analysis shows that plastic events are statistically concentrated within CGES-identified soft zones, with occurrence probabilities 3–7 times higher than in the bulk. Moreover, local eigenvectors align with plastic rearrangements' directions, elucidating microscopic deformation pathways. Within the athermal quasistatic regime studied here, CGES offers an efficient structural descriptor for identifying plasticity-prone regions without prior loading, thereby helping to clarify the microscopic origins of localized failure in diverse solids.

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Phys. Rev. B 113, 224103– Published 1 June, 2026
  • Received 24 December 2025
  • Revised 29 April 2026
  • Accepted 12 May 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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