Insights from the quantitative calibration of an elasto-plastic model from a Lennard-Jones atomic glass
Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 135-162.

Part of the special issue: Plasticity and Solid State Physics

Quantitative multi-scale modeling of mechanical properties of disordered materials is still an open challenge. Bridging scales requires an intense dialogue between physics and mechanics to keep track of the complexity of the mechanisms at play, especially when passing from a discrete atomistic description to a continuous one. Here, we compare the macroscopic and the local plastic behavior of a model amorphous solid based on two radically different numerical descriptions. On the one hand, we simulate glass samples by atomistic simulations. On the other, we implement a mesoscale elasto-plastic model based on a solid-mechanics description. The latter is extended to consider the anisotropy of the yield surface via statistically distributed local and discrete weak planes on which shear transformations can be activated. To make the comparison as quantitative as possible, we consider the simple case of a quasistatically driven two-dimensional system in the stationary flow state and compare mechanical observables measured on both models over the same length scales. To this end, we first calibrate the macroscale behavior of the elasto-plastic model based on molecular static simulations. We show that the macroscale mechanical response, including its fluctuations, can be quantitatively recovered for a range of elasto-plastic mesoscale parameters. Using a newly developed method that makes it possible to probe the local yield stresses in atomistic simulations, we calibrate the local mechanical response of the elasto-plastic model at different coarse-graining scales. In this case, the calibration shows a qualitative agreement only for an optimized subset of mesoscale parameters and for sufficiently coarse probing length scales. This calibration allows us to establish a length scale for the mesoscopic elements that corresponds to an upper bound of the shear transformation size, a key physical parameter in elasto-plastic models. We find that certain properties naturally emerge from the elasto-plastic model, such as accurate correlations between external stress fluctuations or between local yield stresses and local stress drops. In particular, we show that the elasto-plastic model reproduces the Bauschinger effect, namely the plasticity-induced anisotropy in the macroscale stress–strain response. We discuss the successes and failures of our approach, the impact of different model ingredients and propose future research directions for quantitative multi-scale models of amorphous plasticity.

Online First:
Published online:
DOI: 10.5802/crphys.48
Keywords: Glass, Plasticity, Mesoscale, Atomistic, Yield threshold, Bauschinger effect
David Fernández Castellanos 1; Stéphane Roux 2; Sylvain Patinet 1

1 PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, 75005 Paris, France
2 Université Paris-Saclay, ENS Paris-Saclay, CNRS, LMT-Laboratoire de Mécanique et Technologie, Université Paris-Saclay, 4 avenue des Sciences, 91192 Gif-sur-Yvette, France
@article{CRPHYS_2021__22_S3_135_0,
author = {David Fern\'andez Castellanos and St\'ephane Roux and Sylvain Patinet},
title = {Insights from the quantitative calibration of an elasto-plastic model from a {Lennard-Jones} atomic glass},
journal = {Comptes Rendus. Physique},
pages = {135--162},
publisher = {Acad\'emie des sciences, Paris},
volume = {22},
number = {S3},
year = {2021},
doi = {10.5802/crphys.48},
language = {en},
}
TY  - JOUR
AU  - David Fernández Castellanos
AU  - Stéphane Roux
AU  - Sylvain Patinet
TI  - Insights from the quantitative calibration of an elasto-plastic model from a Lennard-Jones atomic glass
JO  - Comptes Rendus. Physique
PY  - 2021
SP  - 135
EP  - 162
VL  - 22
IS  - S3
PB  - Académie des sciences, Paris
UR  - https://doi.org/10.5802/crphys.48
DO  - 10.5802/crphys.48
LA  - en
ID  - CRPHYS_2021__22_S3_135_0
ER  - 
%0 Journal Article
%A David Fernández Castellanos
%A Stéphane Roux
%A Sylvain Patinet
%T Insights from the quantitative calibration of an elasto-plastic model from a Lennard-Jones atomic glass
%J Comptes Rendus. Physique
%D 2021
%P 135-162
%V 22
%N S3
%U https://doi.org/10.5802/crphys.48
%R 10.5802/crphys.48
%G en
%F CRPHYS_2021__22_S3_135_0
David Fernández Castellanos; Stéphane Roux; Sylvain Patinet. Insights from the quantitative calibration of an elasto-plastic model from a Lennard-Jones atomic glass. Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 135-162. doi : 10.5802/crphys.48. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.48/

[1] E. van der Giessen; P. A Schultz; N. Bertin; V. V. Bulatov; W. Cai; G. Csányi; S. M. Foiles; M. G. D. Geers; C. González et al. Roadmap on multiscale materials modeling, Model. Simul. Mater. Sci. Eng., Volume 28 (2020) no. 4, 043001

[2] D. L. McDowell Simulation-assisted materials design for the concurrent design of materials and products, J. Miner. Metals Mater. Soc., Volume 59 (2007) no. 9, pp. 21-25 | DOI

[3] S. Patinet; D. Vandembroucq; A. Hansen; S. Roux Cracks in random brittle solids: from fiber bundles to continuum mechanics, Eur. Phys. J. Spec. Top., Volume 223 (2014) no. 11, pp. 2339-2351 | DOI

[4] B. Devincre; R. Gatti Physically justified models for crystal plasticity developed with dislocation dynamics simulations, AerospaceLab J. (2015) no. 9, pp. 1-7

[5] D. Rodney; A. Tanguy; D. Vandembroucq Modeling the mechanics of amorphous solids at different length scale and time scale, Model. Simul. Mater. Sci. Eng., Volume 19 (2011) no. 8, 083001 | DOI

[6] A. Nicolas; E. E. Ferrero; K. Martens; J.-L. Barrat Deformation and flow of amorphous solids: insights from elastoplastic models, Rev. Mod. Phys., Volume 90 (2018) no. 4, 045006 | DOI

[7] A. S. Argon Plastic deformation in metallic glasses, Acta Metall., Volume 27 (1979) no. 1, p. 47 | DOI

[8] A. Tanguy; F. Leonforte; J.-L. Barrat Plastic response of a 2d Lennard-Jones amorphous solid: detailed analysis of the local rearrangements at very slow strain rate, Eur. Phys. J. E, Volume 20 (2006) no. 3, p. 355 | DOI

[9] E. Lerner; I. Procaccia Locality and nonlocality in elastoplastic responses of amorphous solids, Phys. Rev. E, Volume 79 (2009), 066109 | DOI

[10] G. Molnár; P. Ganster; A. Tanguy; E. Barthel; G. Kermouche Densification dependent yield criteria for sodium silicate glasses – an atomistic simulation approach, Acta Mater., Volume 111 (2016), pp. 129-137 | DOI

[11] D. Rodney; C. Schuh Distribution of thermally activated plastic events in a flowing glass, Phys. Rev. Lett., Volume 102 (2009), 235503 | DOI

[12] A. Nicolas; J. Rottler Orientation of plastic rearrangements in two-dimensional model glasses under shear, Phys. Rev. E, Volume 97 (2018), 063002 | DOI

[13] T. Albaret; A. Tanguy; F. Boioli; D. Rodney Mapping between atomistic simulations and eshelby inclusions in the shear deformation of an amorphous silicon model, Phys. Rev. E, Volume 93 (2016), 053002 | DOI

[14] Mehdi Talamali; Viljo Petäjä; D. Vandembroucq; S. Roux Path-independent integrals to identify localized plastic events in two dimensions, Phys. Rev. E, Volume 78 (2008) no. 1, 016109

[15] S. Patinet; D. Bonamy; L. Proville Atomic-scale avalanche along a dislocation in a random alloy, Phys. Rev. B, Volume 84 (2011) no. 17, 174101 | DOI

[16] M. L. Falk; J. S. Langer Dynamics of viscoplastic deformation in amorphous solids, Phys. Rev. E, Volume 57 (1998) no. 6, pp. 7192-7205 | DOI

[17] V. V. Bulatov; A. S. Argon A stochastic model for continuum elasto-plastic behavior. I. Numerical approach and strain localization, Model. Simul. Mater. Sci. Eng., Volume 2 (1994) no. 2, p. 167 | DOI

[18] E. A. Jagla Shear band dynamics from a mesoscopic modeling of plasticity, J. Stat. Mech. Theory Exp., Volume 2010 (2010) no. 12, 12025

[19] A. Nicolas; K. Martens; L. Bocquet; J.-L. Barrat Universal and non-universal features in coarse-grained models of flow in disordered solids, Soft Matter, Volume 10 (2014), pp. 4648-4661 | DOI

[20] K. Karimi; E. E. Ferrero; J.-L. Barrat. Inertia and universality of avalanche statistics: the case of slowly deformed amorphous solids, Phys. Rev. E, Volume 95 (2017), 013003 | DOI

[21] Z. Budrikis; D. F. Castellanos; S. Sandfeld; M. Zaiser; S. Zapperi Universal features of amorphous plasticity, Nat. Commun., Volume 8 (2017), 15928 | DOI

[22] E. A. Jagla Tensorial description of the plasticity of amorphous composites, Phys. Rev. E, Volume 101 (2020), 043004 | MR

[23] M. Talamali; V. Petäjä; D. Vandembroucq; S. Roux Strain localization and anisotropic correlations in a mesoscopic model of amorphous plasticity, C. R. Méc., Volume 340 (275) no. 4–5, p. 2012 (Recent Advances in Micromechanics of Materials)

[24] B. Tyukodi; S. Patinet; S. Roux; D. Vandembroucq From depinning transition to plastic yielding of amorphous media: a soft-modes perspective, Phys. Rev. E, Volume 93 (2016) no. 6, 063005 | DOI

[25] C. Liu; E. E. Ferrero; F. Puosi; J.-L. Barrat; K. Martens Driving rate dependence of avalanche statistics and shapes at the yielding transition, Phys. Rev. Lett., Volume 116 (2016), 065501

[26] E. R. Homer; C. A. Schuh Mesoscale modeling of amorphous metals by shear transformation zone dynamics, Acta Mater., Volume 57 (2009) no. 9, pp. 2823-2833 | DOI

[27] D. F. Castellanos; M. Zaiser Statistical dynamics of early creep stages in disordered materials, Eur. Phys. J. B, Volume 92 (2019) no. 7, p. 139 | DOI

[28] D. Tüszes; P. D. Ispanovity; M. Zaiser Disorder is good for you: the influence of local disorder on strain localization and ductility of strain softening materials, Int. J. Fract., Volume 205 (2017), p. 139 | DOI

[29] D. F. Castellanos; M. Zaiser Avalanche behavior in creep failure of disordered materials, Phys. Rev. Lett., Volume 121 (2018), 125501

[30] J. S. Langer Shear-transformation-zone theory of plastic deformation near the glass transition, Phys. Rev. E, Volume 77 (2008), 021502

[31] A. R. Hinkle; C. H. Rycroft; M. D. Shields; M. L. Falk Coarse graining atomistic simulations of plastically deforming amorphous solids, Phys. Rev. E, Volume 95 (2017) no. 5, 053001

[32] C. A. Schuh; A. C. Lund Atomistic basis for the plastic yield criterion of metallic glass, Nat. Mater., Volume 2 (2003) no. 7, pp. 449-452 | DOI

[33] F. Puosi; J. Olivier; K. Martens Probing relevant ingredients in mean-field approaches for the athermal rheology of yield stress materials, Soft Matter, Volume 11 (2015) no. 38, pp. 7639-7647 | DOI

[34] A. Nicolas; F. Puosi; H. Mizuno; J.-L. Barrat Elastic consequences of a single plastic event: towards a realistic account of structural disorder and shear wave propagation in models of flowing amorphous solids, J. Mech. Phys. Solids, Volume 78 (2015), pp. 333-351 | DOI | MR

[35] F. Boioli; T. Albaret; D. Rodney Shear transformation distribution and activation in glasses at the atomic scale, Phys. Rev. E, Volume 95 (2017), 033005 | DOI

[36] M. Tsamados; A. Tanguy; C. Goldenberg; J.-L. Barrat Local elasticity map and plasticity in a model Lennard-Jones glass, Phys. Rev. E, Volume 80 (2009), 026112 | DOI

[37] A. Tanguy; B. Mantisi; M. Tsamados Vibrational modes as a predictor for plasticity in a model glass, Europhys. Lett., Volume 90 (2010) no. 1, 16004 | DOI

[38] J. Ding; S. Patinet; M. L. Falk; Y. Cheng; E. Ma Soft spots and their structural signature in a metallic glass, Proc. Natl Acad. Sci., Volume 111 (2014) no. 39, 14052 | DOI

[39] R. L. Jack; A. J. Dunleavy; C. Patrick Royall Information-theoretic measurements of coupling between structure and dynamics in glass formers, Phys. Rev. Lett., Volume 113 (2014), 095703

[40] E. D. Cubuk; S. S. Schoenholz; J. M. Rieser; B. D. Malone; J. Rottler; D. J. Durian; E. Kaxiras; A. J. Liu Identifying structural flow defects in disordered solids using machine-learning methods, Phys. Rev. Lett., Volume 114 (2015), 108001

[41] S. Patinet; D. Vandembroucq; M. L. Falk Connecting local yield stresses with plastic activity in amorphous solids, Phys. Rev. Lett., Volume 117 (2016), 045501 | DOI

[42] E. D. Cubuk; R. J. S. Ivancic; S. S. Schoenholz; D. J. Strickland; A. Basu; Z. S. Davidson; J. Fontaine; J. L. Hor; Y.-R. Huang; Y. Jiang et al. Structure-property relationships from universal signatures of plasticity in disordered solids, Science, Volume 358 (2017) no. 6366, p. 1033 | DOI

[43] D. Wei; J. Yang; M.-Q. Jiang; B.-C. Wei; Y.-J. Wang; L.-H. Dai Revisiting the structure–property relationship of metallic glasses: common spatial correlation revealed as a hidden rule, Phys. Rev. B, Volume 99 (2019), 014115

[44] B. Xu; M. L. Falk; S. Patinet; P. Guan Atomic nonaffinity as a predictor of plasticity in amorphous solids, Phys. Rev. Mater., Volume 5 (2021) no. 2, 025603

[45] V. Bapst; T. Keck; A. Grabska-Barwińska; C. Donner; E. D. Cubuk; S. S. Schoenholz; A. Obika; A. W. R. Nelson; T. Back; D. Hassabis; P. Kohli Unveiling the predictive power of static structure in glassy systems, Nat. Phys., Volume 16 (2020) no. 4, p. 448 | DOI

[46] 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 et al. Predicting plasticity in disordered solids from structural indicators, Phys. Rev. Mater., Volume 4 (2020), 113609

[47] A. Barbot; M. Lerbinger; A. Hernandez-Garcia; R. García-García; M. L. Falk; D. Vandembroucq; S. Patinet Local yield stress statistics in model amorphous solids, Phys. Rev. E, Volume 97 (2018), 033001 | DOI

[48] A. Barbot; M. Lerbinger; A. Lemaître; D. Vandembroucq; S. Patinet Rejuvenation and shear banding in model amorphous solids, Phys. Rev. E, Volume 101 (2020), 033001 | DOI

[49] S. Patinet; A. Barbot; M. Lerbinger; D. Vandembroucq; A. Lemaître Origin of the bauschinger effect in amorphous solids, Phys. Rev. Lett., Volume 124 (2020), 205503 | DOI

[50] C. Liu; S. Dutta; P. Chaudhuri; K. Martens Elastoplastic Approach Based on Microscopic Insights for the Steady State and Transient Dynamics of Sheared Disordered Solids, Phys. Rev. Lett., Volume 126 (2021) no. 13, 138005 | DOI | MR

[51] C. Maloney; A. Lemaître Universal breakdown of elasticity at the onset of material failure, Phys. Rev. Lett., Volume 93 (2004) no. 19, 195501 | DOI

[52] S. Sandfeld; Z. Budrikis; S. Zapperi; D. Fernandez Castellanos Avalanches, loading and finite size effects in 2d amorphous plasticity: results from a finite element model, J. Stat. Mech.: Theor. Exp., Volume 2 (2015), P02011

[53] K. Karimi; J.-L. Barrat Role of inertia in the rheology of amorphous systems: a finite-element-based elastoplastic model, Phys. Rev. E, Volume 93 (2016) no. 2, 022904 | DOI

[54] M. Vasoya; B. Kondori; A. A. Benzerga; A. Needleman Energy dissipation rate and kinetic relations for eshelby transformations, J. Mech. Phys. Solids, Volume 136 (2020), 103699 | DOI | MR

[55] J. D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond. Ser. A, Volume 241 (1957) no. 1226, pp. 376-396 | MR | Zbl

[56] V. V. Bulatov; A. S. Argon A stochastic model for continuum elasto-plastic behavior. II. A study of the glass transition and structural relaxation, Model. Simul. Mater. Sci. Eng., Volume 2 (1994) no. 2, p. 185 | DOI

[57] L. Ma; A. M. Korsunsky The principle of equivalent eigenstrain for inhomogeneous inclusion problems, Int. J. Solids Struct., Volume 51 (2014) no. 25, pp. 4477-4484 | DOI

[58] J. Rottler; M. O. Robbins Yield conditions for deformation of amorphous polymer glasses, Phys. Rev. E, Volume 64 (2001), 051801 | DOI

[59] L. Li; E. R. Homer; C. A. Schuh Shear transformation zone dynamics model for metallic glasses incorporating free volume as a state variable, Acta Mater., Volume 61 (2013) no. 9, pp. 3347-3359 | DOI

[60] G. Picard; A. Ajdari; F. Lequeux; 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, Volume 15 (2004) no. 4, pp. 371-381 | DOI

[61] K. Karimi; E. E. Ferrero; J.-L. Barrat Inertia and universality of avalanche statistics: the case of slowly deformed amorphous solids, Phys. Rev. E, Volume 95 (2017) no. 1, 013003 | DOI

[62] E. A. Jagla Different universality classes at the yielding transition of amorphous systems, Phys. Rev. E, Volume 96 (2017), 023006

[63] F. Puosi; J. Rottler; J-L. Barrat Time-dependent elastic response to a local shear transformation in amorphous solids, Phys. Rev. E, Volume 89 (2014), 042302 | DOI

[64] A. Lemaître Structural relaxation is a scale-free process, Phys. Rev. Lett., Volume 113 (2014), 245702 | DOI

[65] A. F. Voter Introduction to the Kinetic Monte Carlo Method, Radiation Effects in Solids, Springer, 2007, pp. 1-23

Cited by Sources:

Articles of potential interest

Elasto-plastic behavior of amorphous materials: a brief review

Anne Tanguy

C. R. Phys (2021)

Discontinuous yielding of pristine micro-crystals

Oguz Umut Salman; Roberta Baggio; Brigitte Bacroix; ...

C. R. Phys (2021)

Fluctuations in crystalline plasticity

Jérôme Weiss; Peng Zhang; Oğuz Umut Salman; ...

C. R. Phys (2021)