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

Self-induced marginality in plastically deformed crystals

O. U. Salman1,2, A. Ahadi2, and L. Truskinovsky3

Phys. Rev. Materials 10, 103611 – Published 30 October, 2026

DOI: https://doi.org/10.1103/3rwf-d3yx

Abstract

Quasibrittle plastic yielding is a salient feature of well-annealed glassy materials. We show that a similar mechanical response is characteristic of perfect crystals after they experience mechanically-induced massive nucleation of dislocations. We argue that such ‘preparation’ effectively converts a mechanically crystalline sample into a mechanically pseudoamorphous one. To understand the nature of the associated transformation we study a model 2D crystal subjected to AQS driving. We show that pristine crystals ‘primed’ in this way exhibit both pre- and postyield dislocation avalanches with power-law statistics. The value of the computed exponents is indicative of self-induced marginal stability. Our main tool is the novel mesoscopic tensorial model (MTM) of crystal plasticity representing a conceptual trade-off between continuum and atomic descriptions. It captures the specificity of crystals with different lattice symmetry at relatively low computational cost while relying minimally on phenomenology. Rather strikingly, MTM allows one to deal with a statistically meaningful number of dislocations while accounting in a geometrically exact way for finite deformations. The obtained results challenge the prevailing opinion that crystal and amorphous plasticity are fundamentally different phenomena. As MTM does not deal with dislocations directly, our work reinforces the idea that in both cases it is the elastic incompatibility which evolves through intermittent avalanches.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (166)

  1. M. Zaiser, Scale invariance in plastic flow of crystalline solids, Adv. Phys. 55, 185 (2006).
  2. W. Jian, M. Xiao, W. Sun, and W. Cai, Prediction of yield surface of single crystal copper from discrete dislocation dynamics and geometric learning, J. Mech. Phys. Solids 186, 105577 (2024).
  3. M. Ortiz, Plastic yielding as a phase transition, J. Appl. Mech. 66, 289 (1999).
  4. S. Papanikolaou, Y. Cui, and N. Ghoniem, Avalanches and plastic flow in crystal plasticity: An overview, Modell. Simul. Mater. Sci. Eng. 26, 013001 (2018).
  5. J. Kosterlitz, Kosterlitz–Thouless physics: A review of key issues, Rep. Prog. Phys. 79, 026001 (2016).
  6. M. Khantha and V. Vitek, Mechanism of yielding in dislocation-free crystals at finite temperatures—Part I. Theory, Acta Mater. 45, 4675 (1997).
  7. T. Hochrainer, S. Sandfeld, M. Zaiser, and P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity, J. Mech. Phys. Solids 63, 167 (2014).
  8. J. S. Langer, Statistical thermodynamics of crystal plasticity, J. Stat. Phys. 175, 531 (2019).
  9. P. M. Derlet and R. Maaß, The stress statistics of the first pop-in or discrete plastic event in crystal plasticity, J. Appl. Phys. 120, 225101 (2016).
  10. P. D. Ispánovity, I. Groma, G. Györgyi, F. F. Csikor, and D. Weygand, Submicron plasticity: Yield stress, dislocation avalanches, and velocity distribution, Phys. Rev. Lett. 105, 085503 (2010).
  11. K. M. Kamani and S. A. Rogers, Brittle and ductile yielding in soft materials, Proc. Natl. Acad. Sci. USA 121, e2401409121 (2024).
  12. L. Berthier, G. Biroli, M. L. Manning, and F. Zamponi, Yielding and plasticity in amorphous solids, Nat. Rev. Phys. 7, 313 (2024).
  13. B. Shang, P. Guan, and J. L. Barrat, Elastic avalanches reveal marginal behavior in amorphous solids, Proc. Natl. Acad. Sci. USA 117, 86 (2020).
  14. J. Shang, Y. Wang, D. Pan, Y. Jin, and J. Zhang, The yielding of granular matter is marginally stable and critical, Proc. Natl. Acad. Sci. USA 121, e2402843121 (2024).
  15. M. Singh, M. Ozawa, and L. Berthier, Brittle yielding of amorphous solids at finite shear rates, Phys. Rev. Mater. 4, 025603 (2020).
  16. D. Richard, E. Lerner, and E. Bouchbinder, Brittle-to-ductile transitions in glasses: Roles of soft defects and loading geometry, MRS Bull. 46, 902 (2021).
  17. J. Pollard and S. M. Fielding, Yielding, shear banding, and brittle failure of amorphous materials, Phys. Rev. Res. 4, 043037 (2022).
  18. J. Lin, E. Lerner, A. Rosso, and M. Wyart, Scaling description of the yielding transition in soft amorphous solids at zero temperature, Proc. Natl. Acad. Sci. USA 111, 14382 (2014).
  19. G. Parisi, I. Procaccia, C. Rainone, and M. Singh, Shear bands as manifestation of a criticality in yielding amorphous solids, Proc. Natl. Acad. Sci. USA 114, 5577 (2017).
  20. P. M. Derlet and R. Maaß, Micro-plasticity in a fragile model binary glass, Acta Mater. 209, 116771 (2021).
  21. A. Lehtinen, G. Costantini, M. J. Alava, S. Zapperi, and L. Laurson, Glassy features of crystal plasticity, Phys. Rev. B 94, 064101 (2016).
  22. J. P. Sethna, M. K. Bierbaum, K. A. Dahmen, C. P. Goodrich, J. R. Greer, L. X. Hayden, J. P. Kent-Dobias, E. D. Lee, D. B. Liarte, X. Ni, K. N. Quinn, A. Raju, D. Zeb Rocklin, A. Shekhawat, and S. Zapperi, Deformation of crystals: Connections with statistical physics, Annu. Rev. Mater. Res. 47, 217 (2017).
  23. M. Ovaska, A. Lehtinen, M. J. Alava, L. Laurson, and S. Zapperi, Excitation spectra in crystal plasticity, Phys. Rev. Lett. 119, 265501 (2017).
  24. A. Zaccone and E. Scossa-Romano, Approximate analytical description of the nonaffine response of amorphous solids, Phys. Rev. B 83, 184205 (2011).
  25. M. Müller and M. Wyart, Marginal stability in structural, spin, and electron glasses, Annu. Rev. Condens. Matter Phys. 6, 177 (2015).
  26. A. Nicolas, E. E. Ferrero, K. Martens, and J. L. Barrat, Deformation and flow of amorphous solids: Insights from elastoplastic models, Rev. Mod. Phys. 90, 045006 (2018).
  27. D. Rodney, A. Tanguy, and D. Vandembroucq, Modeling the mechanics of amorphous solids at different length scale and time scale, Modell. Simul. Mater. Sci. Eng. 19, 083001 (2011).
  28. M. Popović, T. W. J. de Geus, and M. Wyart, Elastoplastic description of sudden failure in athermal amorphous materials during quasistatic loading, Phys. Rev. E 98, 040901(R) (2018).
  29. A. Tanguy, Elasto-plastic behavior of amorphous materials: A brief review, C. R. Phys. 22, 117 (2021).
  30. M. Talamali, V. Petäjä, D. Vandembroucq, and S. Roux, Strain localization and anisotropic correlations in a mesoscopic model of amorphous plasticity, C. R. Mec. 340, 275 (2012).
  31. J. T. Parley and P. Sollich, Ductile and brittle yielding of athermal amorphous solids: A mean-field paradigm beyond the random-field Ising model, Phys. Rev. E 110, 045002 (2024).
  32. S. Karmakar, E. Lerner, and I. Procaccia, Statistical physics of the yielding transition in amorphous solids, Phys. Rev. E 82, 055103(R) (2010).
  33. M. Ozawa, L. Berthier, G. Biroli, A. Rosso, and G. Tarjus, Random critical point separates brittle and ductile yielding transitions in amorphous materials, Proc. Natl. Acad. Sci. USA 115, 6656 (2018).
  34. T. Divoux, E. Agoritsas, S. Aime, C. Barentin, J.-L. Barrat, R. Benzi, L. Berthier, D. Bi, G. Biroli, D. Bonn, P. Bourrianne, M. Bouzid, E. Del Gado, H. Delanoë-Ayari, K. Farain, S. Fielding, M. Fuchs, J. van der Gucht, S. Henkes, M. Jalaal, et al., Ductile-to-brittle transition and yielding in soft amorphous materials: Perspectives and open questions, Soft Matter 20, 6868 (2024).
  35. G. Picard, A. Ajdari, F. Lequeux, and L. Bocquet, Elastic consequences of a single plastic event: A step towards the microscopic modeling of the flow of yield stress fluids, Eur. Phys. J. E, 15, 371 (2004).
  36. Z. Budrikis, D. Castellanos, S. Sandfeld, M. Zaiser, and S. Zapperi, Universal features of amorphous plasticity, Nat. Commun. 8, 15928 (2017).
  37. W. Cai, A. Arsenlis, C. R. Weinberger, and V. V. Bulatov, A non-singular continuum theory of dislocations, J. Mech. Phys. Solids 54, 561 (2006).
  38. M. Moshe, I. Levin, H. Aharoni, R. Kupferman, and E. Sharon, Geometry and mechanics of two-dimensional defects in amorphous materials, Proc. Natl. Acad. Sci. USA 112, 10873 (2015).
  39. M. Baggioli, M. Landry, and A. Zaccone, Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory, Phys. Rev. E 105, 024602 (2022).
  40. M. J. Bowick and L. Giomi, Two-dimensional matter: Order, curvature and defects, Adv. Phys. 58, 449 (2009).
  41. M. Katanaev and I. Volovich, Theory of defects in solids and three-dimensional gravity, Ann. Phys. 216, 1 (1992).
  42. F. Sozio and A. Yavari, Riemannian and Euclidean material structures in anelasticity, Math. Mech. Solids 25, 1267 (2020).
  43. O. U. Salman and L. Truskinovsky, Minimal integer automaton behind crystal plasticity, Phys. Rev. Lett. 106, 175503 (2011).
  44. O. U. Salman and L. Truskinovsky, On the critical nature of plastic flow: One and two dimensional models, Int. J. Eng. Sci. 59, 219 (2012).
  45. R. Baggio, E. Arbib, P. Biscari, S. Conti, L. Truskinovsky, G. Zanzotto, and O. U. Salman, Landau-type theory of planar crystal plasticity, Phys. Rev. Lett. 123, 205501 (2019).
  46. O. U. Salman, R. Baggio, B. Bacroix, G. Zanzotto, N. Gorbushin, and L. Truskinovsky, Discontinuous yielding of pristine micro-crystals, C. R. Phys. 22, 201 (2021).
  47. N. Perchikov and L. Truskinovsky, Quantized plastic deformation, J. Mech. Phys. Solids 190, 105704 (2024).
  48. R. Baggio, O. U. Salman, and L. Truskinovsky, Homogeneous nucleation of dislocations as a pattern formation phenomenon, Eur. J. Mech. A/Solids 99, 104897 (2023).
  49. R. Baggio, O. U. Salman, and L. Truskinovsky, Inelastic rotations and pseudoturbulent plastic avalanches in crystals, Phys. Rev. E 107, 025004 (2023).
  50. P. Zhang, O. U. Salman, J. Weiss, and L. Truskinovsky, Variety of scaling behaviors in nanocrystalline plasticity, Phys. Rev. E 102, 023006 (2020).
  51. J. Weiss, P. Zhang, O. U. Salman, G. Liu, and L. Truskinovsky, Fluctuations in crystalline plasticity, C. R. Phys. 22, 163 (2021).
  52. A. Arsenlis, W. Cai, M. Tang, M. Rhee, T. Oppelstrup, G. Hommes, T. G. Pierce, and V. V. Bulatov, Enabling strain hardening simulations with dislocation dynamics, Modell. Simul. Mater. Sci. Eng. 15, 553 (2007).
  53. L. A. Zepeda-Ruiz, A. Stukowski, T. Oppelstrup, N. Bertin, N. R. Barton, R. Freitas, and V. V. Bulatov, Atomistic insights into metal hardening, Nat. Mater. 20, 315 (2021).
  54. M. Ponga, K. Bhattacharya, and M. Ortiz, Large scale ab-initio simulations of dislocations, J. Comput. Phys. 407, 109249 (2020).
  55. P. Lafourcade, G. Ewald, T. Carrard, and C. Denoual, Extraction of slip systems and twinning variants from a Lagrangian analysis of molecular dynamics simulations, Mech. Mater. 200, 105189 (2025).
  56. P. Y. Chan, G. Tsekenis, J. Dantzig, K. A. Dahmen, and N. Goldenfeld, Plasticity and dislocation dynamics in a phase field crystal model, Phys. Rev. Lett. 105, 015502 (2010).
  57. M. Salvalaglio, L. Angheluta, Z.-F. Huang, A. Voigt, K. R. Elder, and J. Viñals, A coarse-grained phase-field crystal model of plastic motion, J. Mech. Phys. Solids 137, 103856 (2020).
  58. Z. Zhong, Y. Huang, Y. Gao, R. Li, S. Yao, K. Wang, W. Zhu, and W. Hu, Phase field crystal model simulation of transonic dislocations and mode II crack propagation, Physica B 706, 417154 (2025).
  59. M. Javanbakht and V. I. Levitas, Phase field approach to dislocation evolution at large strains: Computational aspects, Int. J. Solids Struct. 82, 95 (2016).
  60. I. J. Beyerlein and A. Hunter, Understanding dislocation mechanics at the mesoscale using phase field dislocation dynamics, Philos. Trans. A: Math. Phys. Eng. Sci. 374, 20150166 (2016).
  61. M. Koslowski, A. M. Cuitiño, and M. Ortiz, A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals, J. Mech. Phys. Solids 50, 2597 (2002).
  62. Y. U. Wang, Y. M. Jin, and A. G. Khachaturyan, Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films, Acta Mater. 51, 4209 (2003).
  63. B. Devincre, T. Hoc, and L. Kubin, Dislocation mean free paths and strain hardening of crystals, Science 320, 1745 (2008).
  64. P. D. Ispánovity, L. Laurson, M. Zaiser, I. Groma, S. Zapperi, and M. J. Alava, Avalanches in 2D dislocation systems: Plastic yielding is not depinning, Phys. Rev. Lett. 112, 235501 (2014).
  65. D. Gómez-García, B. Devincre, and L. P. Kubin, Dislocation patterns and the similitude principle: 2.5D mesoscale simulations, Phys. Rev. Lett. 96, 125503 (2006).
  66. G. Po, M. Lazar, D. Seif, and N. Ghoniem, Singularity-free dislocation dynamics with strain gradient elasticity, J. Mech. Phys. Solids 68, 161 (2014).
  67. S. Lu, J. Zhao, M. Huang, Z. Li, G. Kang, and X. Zhang, Multiscale discrete dislocation dynamics study of gradient nano-grained materials, Int. J. Plast. 156, 103356 (2022).
  68. N. Bertin, V. V. Bulatov, and F. Zhou, Learning dislocation dynamics mobility laws from large-scale MD simulations, npj Comput. Mater. 10, 192 (2024).
  69. T. Nasir Tak and P. J. Guruprasad, A discrete dislocation dynamics framework for modelling plasticity in two-phase polycrystals, Modell. Simul. Mater. Sci. Eng. 33, 045001 (2025).
  70. K. Starkey, G. Winther, and A. El-Azab, Theoretical development of continuum dislocation dynamics for finite-deformation crystal plasticity at the mesoscale, J. Mech. Phys. Solids 139, 103926 (2020).
  71. Y. Zhang, R. Wu, and M. Zaiser, Continuum dislocation dynamics as a phase field theory with conserved order parameters: formulation and application to dislocation patterning, Modell. Simul. Mater. Sci. Eng. 33, 035011 (2025).
  72. A. Acharya, An action for nonlinear dislocation dynamics, J. Mech. Phys. Solids 161, 104811 (2022).
  73. A. Acharya, A. Roy, and A. Sawant, Continuum theory and methods for coarse-grained, mesoscopic plasticity, Scr. Mater. 54, 705 (2006).
  74. D. Rodney and R. Phillips, Structure and strength of dislocation junctions: An atomic level analysis, Phys. Rev. Lett. 82, 1704 (1999).
  75. B. Van Koten and B. Luskin, Analysis of energy-based blended quasi-continuum approximations, SIAM J. Numer. Anal. 49, 2182 (2011).
  76. R. Miller and E. Tadmor, The quasicontinuum method: Overview, applications and current directions, J. Comput.-Aided Mater. Des. 9, 203 (2002).
  77. Z. Zhang, J. Zhang, Y. Ni, C. Wang, K. Jiang, and X. Ren, Multiscale Simulation of Surface Defect Influence in Nanoindentation by the Quasi-Continuum Method in Proceedings (MDPI, 2018), Vol. 2, p. 1113.
  78. P. Engel, Geometric Crystallography: An Axiomatic Introduction to Crystallography (Springer, Netherlands, 1986).
  79. L. Michel, Fundamental concepts for the study of crystal symmetry, Phys. Rep. 341, 265 (2001).
  80. R. L. E. Schwarzenberger, Classification of crystal lattices, Proc. Cambridge Philos. Soc. 72, 325 (1972).
  81. M. Pitteri and G. Zanzotto, Continuum Models for Phase Transitions and Twinning in Crystals (Chapman and Hall/CRC, Boca Raton, 2002).
  82. J. L. Ericksen, Nonlinear elasticity of diatomic crystals, Int. J. Solids Struct. 6, 951 (1970).
  83. J. L. Ericksen, in Nonlinear Elasticity, edited by R. W. Dickey (Academic Press, New York, 1973), pp. 161–173.
  84. J. L. Ericksen, Special topics in elastostatics, Adv. Appl. Mech. 17, 189 (1977).
  85. J. L. Ericksen, Some phase transitions in crystals, Arch. Ration. Mech. Anal. 73, 99 (1980).
  86. J. L. Ericksen, Weak martensitic transformations in Bravais lattices, Arch. Ration. Mech. Anal. 107, 23 (1989).
  87. G. Parry, On the elasticity of monatomic crystals, Math. Proc. Cambridge Philos. Soc. 80, 189 (1976).
  88. G. P. Parry, On the crystallographic point groups and on Cauchy symmetry, in Mathematical Proceedings of the Cambridge Philosophical Society (Cambridge University Press, 1977), pp. 165–175.
  89. G. P. Parry, Low-dimensional lattice groups for the continuum mechanics of phase transitions in crystals, Arch. Ration. Mech. Anal. 145, 1 (1998).
  90. I. Folkins, Functions of two-dimensional Bravais lattices, J. Math. Phys. 32, 1965 (1991).
  91. S. Conti and G. Zanzotto, A variational model for reconstructive phase transformations in crystals, and their relation to dislocations and plasticity, Arch. Ration. Mech. Anal. 173, 69 (2004).
  92. K. Bhattacharya, S. Conti, G. Zanzotto, and J. Zimmer, Crystal symmetry and the reversibility of martensitic transformations, Nature (London) 428, 55 (2004).
  93. M. Koslowski, R. LeSar, and R. Thomson, Avalanches and scaling in plastic deformation, Phys. Rev. Lett. 93, 125502 (2004).
  94. C. Denoual, A. M. Caucci, L. Soulard, and Y. P. Pellegrini, Phase-field reaction-pathway kinetics of martensitic transformations in a model Fe3Ni alloy, Phys. Rev. Lett. 105, 035703 (2010).
  95. Y. Gao, Y. Wang, and Y. Zhang, Deformation pathway and defect generation in crystals: A combined group theory and graph theory description, IUCrJ 6, 96 (2019).
  96. P. Biscari, M. Urbano, A. Zanzottera, and G. Zanzotto, Intermittency in crystal plasticity informed by lattice symmetry, J. Elast. 123, 85 (2016).
  97. E. Arbib, P. Biscari, C. Patriarca, and G. Zanzotto, Ericksen-Landau modular strain energies for reconstructive phase transformations in 2D crystals, J. Elast. 155, 747 (2024).
  98. Y. Gao, Y. Zhang, and Y. Wang, Determination of twinning path from broken symmetry: A revisit to deformation twinning in BCC metals, Acta Mater. 196, 280 (2020).
  99. Y. Gao, A Cayley graph description of the symmetry breaking associated with deformation and structural phase transitions in metallic materials, Materialia 9, 100588 (2020).
  100. Y. Gao, T. Yu, and Y. Wang, Phase transformation graph and transformation pathway engineering for shape memory alloys, Shap. Mem. Superelasticity 6, 115 (2020).
  101. Y. Gao, Y. Zhang, L. K. Aagesen, J. Yu, M. Long, and Y. Wang, Defect-free plastic deformation through dimensionality reduction and self-annihilation of topological defects in crystalline solids, Phys. Rev. Res. 2, 013146 (2020).
  102. E. Arbib, P. Biscari, L. Bortoloni, C. Patriarca, and G. Zanzotto, Crystal elasto-plasticity on the Poincaré half-plane, Int. J. Plast. 130, 102728 (2020).
  103. E. Arbib, N. Barrera, P. Biscari, and G. Zanzotto, Reconstructive martensitic phase transitions: Intermittency, anti-transformation, plasticity, irreversibility, J. Appl. Mech. 92, 081007 (2025).
  104. P. Engel, Geometric Crystallography: An Axiomatic Introduction to Crystallography (Springer Science & Business Media, Dordrecht, 2012).
  105. G. Puglisi and L. Truskinovsky, Thermodynamics of rate-independent plasticity, J. Mech. Phys. Solids 53, 655 (2005).
  106. B. M. Irons, Engineering applications of numerical integration in stiffness methods, AIAA J. 4, 2035 (1966).
  107. J. H. Bramble and M. Zlámal, Triangular elements in the finite element method, Math. Comput. 24, 809 (1970).
  108. S. Bochkanov and V. Bystritsky, Available from: www.alglib.net (2013).
  109. C. Sanderson and R. Curtin, Armadillo: A template-based C++ library for linear algebra, J. Open Source Softw. 1, 26 (2016).
  110. M. Fishman, S. White, and E. Stoudenmire, The ITensor software library for tensor network calculations, SciPost Phys. Codebases 4 (2022).
  111. R. W. Ogden, Non-linear Elastic Deformations (Courier Corporation, 1997).
  112. Y. Grabovsky and L. Truskinovsky, Normality condition in elasticity, J. Nonlinear Sci. 24, 1125 (2014).
  113. H. C. Simpson and S. J. Spector, in Mechanics and Thermodynamics of Continua: A Collection of Papers Dedicated to BD Coleman on His Sixtieth Birthday (Springer Berlin Heidelberg, Berlin, Heidelberg, 1989), pp. 159–179.
  114. Y. Grabovsky and L. Truskinovsky, Marginal material stability, J. Nonlinear Sci. 23, 891 (2013).
  115. D. J. Steigmann, M. Bîrsan, and M. Shirani, in Lecture Notes on the Theory of Plates and Shells: Classical and Modern Developments (Springer Nature Switzerland, Cham, 2023), pp. 61–76.
  116. R. Maaß and P. M. Derlet, Micro-plasticity and recent insights from intermittent and small-scale plasticity, Acta Mater. 143, 338 (2018).
  117. G. Sparks and R. Maaß, Nontrivial scaling exponents of dislocation avalanches in microplasticity, Phys. Rev. Mater. 2, 120601(R) (2018).
  118. G. Sparks, Y. Cui, G. Po, Q. Rizzardi, J. Marian, and R. Maaß, Avalanche statistics and the intermittent-to-smooth transition in microplasticity, Phys. Rev. Mater. 3, 080601(R) (2019).
  119. Q. Rizzardi, P. M. Derlet, and R. Maaß, Intermittent microplasticity in the presence of a complex microstructure, Phys. Rev. Mater. 6, 073602 (2022).
  120. J. Duan, Y. J. Wang, L. H. Dai, and M. Q. Jiang, Elastic interactions of plastic events in strained amorphous solids before yield, Phys. Rev. Mater. 7, 013601 (2023).
  121. H. Bei, S. Shim, G. M. Pharr, and E. P. George, Effects of pre-strain on the compressive stress–strain response of Mo-alloy single-crystal micropillars, Acta Mater. 56, 4762 (2008).
  122. D. Chrobak, N. Tymiak, A. Beaber, O. Ugurlu, W. W. Gerberich, and R. Nowak, Deconfinement leads to changes in the nanoscale plasticity of silicon, Nat. Nanotechnol. 6, 480 (2011).
  123. Z. Wang, Z. Shan, J. Li, J. Sun, and E. Ma, Pristine-to-pristine regime of plastic deformation in submicron-sized single crystal gold particles, Acta Mater. 60, 1368 (2012).
  124. Y. Cui, G. Po, and N. Ghoniem, Influence of loading control on strain bursts and dislocation avalanches at the nanometer and micrometer scale, Phys. Rev. B 95, 064103 (2017).
  125. J. R. Greer and J. T. M. De Hosson, Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect, Prog. Mater. Sci. 56, 654 (2011).
  126. S. S. Brenner, Tensile strength of whiskers, J. Appl. Phys. 27, 1484 (1956).
  127. S. S. Brenner, Growth and properties of “whiskers”, Science 128, 569 (1958).
  128. A. Sharma, J. Hickman, N. Gazit, E. Rabkin, and Y. Mishin, Nickel nanoparticles set a new record of strength, Nat. Commun. 9, 4102 (2018).
  129. D. Mordehai, O. David, and R. Kositski, Nucleation-controlled plasticity of metallic nanowires and nanoparticles, Adv. Mater. 30, 1706710 (2018).
  130. E. T. Lilleodden and W. D. Nix, Microstructural length-scale effects in the nanoindentation behavior of thin gold films, Acta Mater. 54, 1583 (2006).
  131. S. G. Corcoran, R. J. Colton, E. T. Lilleodden, and W. W. Gerberich, Anomalous plastic deformation at surfaces: Nanoindentation of gold single crystals, Phys. Rev. B 55, R16057 (1997).
  132. J. Weiss, W. B. Rhouma, T. Richeton, S. Dechanel, F. Louchet, and L. Truskinovsky, From mild to wild fluctuations in crystal plasticity, Phys. Rev. Lett. 114, 105504 (2015).
  133. J. M. Tarp, L. Angheluta, J. Mathiesen, and N. Goldenfeld, Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model, Phys. Rev. Lett. 113, 265503 (2014).
  134. M. C. Miguel and S. Zapperi, Fluctuations in plasticity at the microscale, Science 312, 1151 (2006).
  135. M. J. Alava, L. Laurson, and S. Zapperi, Crackling noise in plasticity, Eur. Phys. J. Spec. Top. 223, 2353 (2014).
  136. B. Tyukodi, C. A. Lemarchand, J. S. Hansen, and D. Vandembroucq, Finite-size effects in a model for plasticity of amorphous composites, Phys. Rev. E 93, 023004 (2016).
  137. E. Lerner, I. Procaccia, C. Rainone, and M. Singh, Protocol dependence of plasticity in ultrastable amorphous solids, Phys. Rev. E 98, 063001 (2018).
  138. M. Ozawa, L. Berthier, G. Biroli, and G. Tarjus, Rare events and disorder control the brittle yielding of well-annealed amorphous solids, Phys. Rev. Res. 4, 023227 (2022).
  139. J. P. Sethna, K. A. Dahmen, and C. R. Myers, Crackling noise, Nature (London) 410, 242 (2001).
  140. N. Oyama, H. Mizuno, and A. Ikeda, Unified view of avalanche criticality in sheared glasses, Phys. Rev. E 104, 015002 (2021).
  141. H. Salmenjoki, L. Laurson, and M. J. Alava, Avalanche correlations and stress-strain curves in discrete dislocation plasticity, Phys. Rev. Mater. 5, 073601 (2021).
  142. M. Ovaska, L. Laurson, and M. J. Alava, Quenched pinning and collective dislocation dynamics, Sci. Rep. 5, 10580 (2015).
  143. X. Zhang, X. Zhang, Q. Li, and F. Shang, Strain avalanches in microsized single crystals: Avalanche size predicted by a continuum crystal plasticity model, Chin. Phys. Lett. 33, 106401 (2016).
  144. B. Tyukodi, D. Vandembroucq, and C. E. Maloney, Avalanches, thresholds, and diffusion in mesoscale amorphous plasticity, Phys. Rev. E 100, 043003 (2019).
  145. E. E. Ferrero and E. A. Jagla, Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates, Soft Matter 15, 9041 (2019).
  146. S. Franz and S. Spigler, Mean-field avalanches in jammed spheres, Phys. Rev. E 95, 022139 (2017).
  147. L. Berthier, G. Biroli, P. Charbonneau, E. I. Corwin, S. Franz, and F. Zamponi, Gardner physics in amorphous solids and beyond, J. Chem. Phys. 151, 010901 (2019).
  148. R. C. Dennis and E. I. Corwin, Jamming energy landscape is hierarchical and ultrametric, Phys. Rev. Lett. 124, 078002 (2020).
  149. F. Pázmándi, G. Zaránd, and G. T. Zimányi, Self-organized criticality in the hysteresis of the Sherrington-Kirkpatrick model, Phys. Rev. Lett. 83, 1034 (1999).
  150. P. Le Doussal, M. Müller, and K. J. Wiese, Equilibrium avalanches in spin glasses, Phys. Rev. B.Cond. Matt. Mater. Phys. 85, 214402 (2012).
  151. K. Lamp, N. Küchler, and J. Horbach, Brittle yielding in supercooled liquids below the critical temperature of mode coupling theory, J. Chem. Phys. 157, 034501 (2022).
  152. S. Rossi and G. Tarjus, Emergence of a random field at the yielding transition of a mean-field elasto-plastic model, J. Stat. Mech. (2022) 093301.
  153. I. Regev and T. Lookman, The irreversibility transition in amorphous solids under periodic shear, in Avalanches in Functional Materials and Geophysics, edited by E. Salje, A. Saxena, and A. Planes (Springer International Publishing, Cham, 2017), pp. 227–259.
  154. I. Regev and T. Lookman, Critical diffusivity in the reversibilityirreversibility transition of amorphous solids under oscillatory shear, J. Phys.: Cond. Matt. 31, 045101 (2019).
  155. I. Regev, I. Attia, K. Dahmen, S. Sastry, and M. Mungan, Topology of the energy landscape of sheared amorphous solids and the irreversibility transition, Phys. Rev. E 103, 062614 (2021).
  156. C. Ruscher and J. Rottler, Avalanches in the athermal quasistatic limit of sheared amorphous solids: An atomistic perspective, Tribol. Lett. 69, 64 (2021).
  157. G. Grinstein, Scale Invariance, Interfaces, and Non-Equilibrium Dynamics (Springer US, Boston, MA, 1995), pp. 261–293.
  158. A. Zippelius, M. Fuchs, A. Rosso, J. P. Sethna, and M. Wyart, Emergent dynamics in glasses and disordered systems: Correlations and avalanches, Spin Glass Theory and Far Beyond (World Scientific, 2023), pp. 277–305.
  159. Edited by P. Charbonneau, E. Marinari, G. Parisi, F. Ricci-tersenghi, G. Sicuro, and F. Zamponi, Spin Glass Theory and Far Beyond: Replica Symmetry Breaking after 40 Years (World Scientific, 2023).
  160. N. Oyama, H. Mizuno, and A. Ikeda, Shear-induced criticality in glasses shares qualitative similarities with the Gardner phase, Soft Matter 19, 6074 (2023).
  161. Y. Xing, Y. Yuan, H. Yuan, S. Zhang, Z. Zeng, X. Zheng, C. Xia, and Y. Wang, Origin of the critical state in sheared granular materials, Nat. Phys. 20, 646 (2024).
  162. See Supplemental Material at http://link.aps.org/supplemental/10.1103/3rwf-d3yx for a movie showing the spatiotemporal dynamics and morphology of plastic avalanches in the postyield regime.
  163. S. Rossi, G. Biroli, M. Ozawa, G. Tarjus, and F. Zamponi, Finite-disorder critical point in the yielding transition of elastoplastic models, Phys. Rev. Lett. 129, 228002 (2022).
  164. D. Fernández Castellanos, S. Roux, and S. Patinet, Insights from the quantitative calibration of an elasto-plastic model from a Lennard-Jones atomic glass, C. R. Phys. 22, 135 (2021).
  165. P. Zhang, P. Cheng, J. Zhang, G. Liu, J. Weiss, and J. Sun, Coupled size and temperature effects on intermittent plasticity of BCC micro-crystals, Acta Mater. 260, 119201 (2023).
  166. Y. Li, I. Lalani, M. Maron, W. Hixson, B. Wang, N. Ghoniem, and G. Po, Temperature-activated dislocation avalanches signaling brittle-to-ductile transition in BCC micropillars, Scr. Mater. 277, 117233 (2026).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation