- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Resolving Structural Avalanches in Amorphous Carbon with Arclength Continuation

Fraser Birks1,*, Ibrahim Ghanem2, Lars Pastewka2, James Kermode1, and Maciej Buze3

  • 1Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 2Department of Microsystems Engineering, University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany
  • 3MARS: Mathematics for AI in Real-world Systems, School of Mathematical Sciences, Lancaster University, Lancaster LA1 4YF, United Kingdom

  • *Contact author: fraser.birks@warwick.ac.uk
PDF

Phys. Rev. Lett. 136, 206101 – Published 20 May, 2026

DOI: https://doi.org/10.1103/6n5m-rxc1

Abstract

Plastic deformation in amorphous solids is carried by localized shear transformations that self-organize into avalanches. In amorphous carbon modeled with a machine-learned interatomic potential, we find that the energetics and organization of these avalanches can be resolved by systematically following the underlying energy landscape. With a pseudoarclength numerical continuation framework, we decompose avalanches into constituent shear transformations and determine their strain-dependent energetics. Our analysis shows that, prior to onset, avalanches have a latent structure that consists of well-separated local minima. We further demonstrate that arclength continuation yields an event driven framework for following avalanche dynamics, eliminating time-step effects on statistical avalanche properties such as distributions of stress drops.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (40)

  1. P. M. Anderson, J. P. Hirth, and J. Lothe, Theory of Dislocations, 3rd ed. (Cambridge University Press, Cambridge, 2017), ISBN [Amazon][WorldCat].
  2. A. S. Argon, Acta Metall. 27, 47 (1979).
  3. F. Spaepen, Acta Metall. 25, 407 (1977).
  4. M. L. Falk and J. S. Langer, Phys. Rev. E 57, 7192 (1998).
  5. D. Richard, M. Ozawa, S. Patinet, E. Stanifer, B. Shang, S. A. Ridout, B. Xu, G. Zhang, P. K. Morse, J.-L. Barrat, L. Berthier, M. L. Falk, P. Guan, A. J. Liu, K. Martens, S. Sastry, D. Vandembroucq, E. Lerner, and M. L. Manning, Phys. Rev. Mater. 4, 113609 (2020).
  6. C. Maloney and A. Lemaître, Phys. Rev. Lett. 93, 016001 (2004).
  7. J. P. Sethna, K. A. Dahmen, and C. R. Myers, Nature (London) 410, 242 (2001).
  8. C. E. Maloney and A. Lemaître, Phys. Rev. E 74, 016118 (2006).
  9. A. Lemaître and C. Caroli, Phys. Rev. Lett. 103, 065501 (2009).
  10. S. Karmakar, E. Lerner, I. Procaccia, and J. Zylberg, Phys. Rev. E 82, 031301 (2010).
  11. C. Liu, E. E. Ferrero, F. Puosi, J. L. Barrat, and K. Martens, Phys. Rev. Lett. 116, 065501 (2016).
  12. D. Korchinski and J. Rottler, Phys. Rev. E 106, 034103 (2022).
  13. M. Qamar, M. Mrovec, Y. Lysogorskiy, A. Bochkarev, and R. Drautz, J. Chem. Theory Comput. 19, 5151 (2023).

  14. Note that a prereleased version of this potential was used to avoid a known problem with numerical instabilities affecting relaxations due to the explicit pairwise dispersion correction added to the published potential.

  15. T. Kunze, M. Posselt, S. Gemming, G. Seifert, A. R. Konicek, R. W. Carpick, L. Pastewka, and M. Moseler, Tribol. Lett. 53, 119 (2014).
  16. G. Henkelman, B. P. Uberuaga, and H. Jónsson, J. Chem. Phys. 113, 9901 (2000).
  17. G. Henkelman and H. Jónsson, J. Chem. Phys. 113, 9978 (2000).
  18. F. Boioli, T. Albaret, and D. Rodney, Phys. Rev. E 95, 033005 (2017).
  19. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6n5m-rxc1. See Supplemental Material A for an investigation into the use of nudged elastic band simulations for resolving avalanches, which includes Refs. [8,16–18,20,21]; see Supplemental Material B for detailed descriptions of the arclength continuation algorithms used in this study, which includes Refs. [22–25]; see Supplemental Material C for an overview of the avalanche sizes investigated in this study and details on method limitations, which includes Refs. [26,27]; see Supplemental Material D for an investigation into the reproducibility of stress strain curves with both the AC and AQS methods; see Supplemental Material E for a comparison between the ordering of plastic events in avalanches derived using arclength continuation and damped dynamics, which includes Ref. [28].
  20. D. L. Malandro and D. J. Lacks, J. Chem. Phys. 110, 4593 (1999).
  21. D. Sheppard, R. Terrell, and G. Henkelman, J. Chem. Phys. 128, 134106 (2008).
  22. M. Buze and F. Birks, LACT (LAMMPS Continuation Techniques), https://github.com/mbuze/LACT.
  23. A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in ’t Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton, Comput. Phys. Commun. 271, 108171 (2022).
  24. E. L. Allgower and K. Georg, Introduction to Numerical Continuation Methods (SIAM, Philadelphia, 2003), https://epubs.siam.org/doi/pdf/10.1137/1.9780898719154.fm.
  25. I. Maliyov, P. Grigorev, and T. D. Swinburne, npj Comput. Mater. 11, 22 (2025).
  26. M. I. Baskes, J. E. Angelo, and C. L. Bisson, Model. Simul. Mater. Sci. Eng. 2, 505 (1994).
  27. L. Pastewka, A. Klemenz, P. Gumbsch, and M. Moseler, Phys. Rev. B 87, 205410 (2013).
  28. F. Sammüller and M. Schmidt, J. Chem. Phys. 155, 134107 (2021).
  29. M. Buze and J. R. Kermode, Phys. Rev. E 103, 033002 (2021).
  30. X. Li, Eur. Phys. J. B 86, 258 (2013).
  31. M. Buze, T. Hudson, and C. Ortner, ESAIM: Math. Model. Numer. Anal. 54, 1821 (2020).
  32. S. Pattamatta, R. S. Elliott, and E. B. Tadmor, Proc. Natl. Acad. Sci. U.S.A. 111, E1678 (2014).
  33. K. M. Salerno, C. E. Maloney, and M. O. Robbins, Phys. Rev. Lett. 109, 105703 (2012).
  34. A. Moriel, D. Richard, E. Lerner, and E. Bouchbinder, Phys. Rev. Res. 6, 023167 (2024).
  35. N. Oyama, T. Kawasaki, K. Kim, and H. Mizuno, Phys. Rev. Lett. 132, 148201 (2024).
  36. U. A. Dattani, S. Karmakar, and P. Chaudhuri, Phys. Rev. E 106, 055004 (2022).
  37. J. Duan, Y. J. Wang, L. H. Dai, and M. Q. Jiang, Phys. Rev. Mater. 7, 013601 (2023).
  38. O. U. Salman and L. Truskinovsky, Phys. Rev. Lett. 106, 175503 (2011).
  39. R. Baggio, O. U. Salman, and L. Truskinovsky, Phys. Rev. E 107, 025004 (2023).
  40. F. Birks, I. Ghanem, L. Pastewka, J. Kermode, and M. Buze, 10.5281/zenodo.18393712 (2026).

Outline

Information

Phys. Rev. Lett. 136, 206101– Published 20 May, 2026
  • Received 30 January 2026
  • Accepted 23 April 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation