Disordered materials, like metallic glasses or silicate glasses, have an atomistic amorphous structure preventing the formation of extended defects such as dislocations. Irreversible deformation in these materials is thus localized, but can organize along shear bands. In this brief review, based on recent publications, we will see if local plasticity can be measured and predicted in disordered atomic assemblies, and in what conditions it can be related to preexisting structural defects. We will then draw a general picture of the plastic mechanical behaviour within the theoretical framework of mechanical instabilities. Finally, we will focus our attention on different scenarii for shear banding in glasses.
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Anne Tanguy 1, 2

@article{CRPHYS_2021__22_S3_117_0, author = {Anne Tanguy}, title = {Elasto-plastic behavior of amorphous materials: a brief review}, journal = {Comptes Rendus. Physique}, pages = {117--133}, publisher = {Acad\'emie des sciences, Paris}, volume = {22}, number = {S3}, year = {2021}, doi = {10.5802/crphys.49}, language = {en}, }
Anne Tanguy. Elasto-plastic behavior of amorphous materials: a brief review. Comptes Rendus. Physique, Plasticity and Solid State Physics, Volume 22 (2021) no. S3, pp. 117-133. doi : 10.5802/crphys.49. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.49/
[1] et al. Imaging atomic rearrangements in two-dimensional silica glass: Watching silica’s dance, Science, Volume 342 (2013), pp. 224-227 | DOI
[2] et al. Ultrathin silica films: The atomic structure of two-dimensional crystals and glasses, Chem. Eur. J., Volume 20 (2014) no. 30, pp. 9176-9183 | DOI
[3] Characterization of nanometer-scale defects in metallic glasses by quantitative high-resolution transmission electron microscopy, Phys. Rev. B, Volume 65 (2002), 144201
[4] Measuring strain distributions in amorphous materials, Nat. Mater., Volume 4 (2005), pp. 33-36 | DOI
[5] Structural aspects of elastic deformation of a metallic glass, Phys. Rev. B, Volume 73 (2006), 064204 | DOI
[6] Role of local order in the small-scale plasticity of model amorphous materials, Phys. Rev. E, Volume 82 (2010), 066116 | DOI
[7] Atomistic basis for the plastic yield criterion of metallic glasses, Nat. Mater., Volume 2 (2003), pp. 449-452 | DOI
[8] Subextensive scaling in the athermal, quasistatic limit of amorphous matter in plastic shear flow, Phys. Rev. Lett., Volume 93 (2004), 016001 | DOI
[9] Unified description of aging and rate effects in yield of glassy solids, Phys. Rev. Lett., Volume 95 (2005), 225504 | DOI
[10] Shear softening and structure in a simulated three-dimensional binary glass, J. Chem. Phys., Volume 122 (2005), 154508
[11] Plastic response of a 2D Lennard–Jones amorphous solid: Detailed analyses of the local rearrangements at very slow strain rate, Eur. Phys. J. E, Volume 20 (2006), pp. 355-364 | DOI
[12] Physics of amorphous solids: Their creation and their mechanical properties, Eur. Phys. J.: Spec. Top., Volume 178 (2009), pp. 81-122
[13] Modeling the mechanics of amorphous solids at different length scale and time scale, Model. Simul. Mat. Sci. Eng., Volume 19 (2011), 083001 | DOI
[14] et al. Predicting plasticity in disordered solids from structural indicators, Phys. Rev. Mater., Volume 4 (2020), 113609
[15] A microscopic mechanism for steady state inhomogeneous flow in metallic glasses, Acta Metall., Volume 25 (1977), pp. 407-415 | DOI
[16] Plastic deformation in metallic glasses, Acta Metall., Volume 27 (1979), pp. 47-58 | DOI
[17] A glass with high crack initiation load: Role of fictive temperature-independent mechanical properties, J. Non-Cryst. Solids, Volume 355 (2009), pp. 563-568 | DOI
[18] Sodium effect on static mechanical behavior of MD-modeled sodium silicate glasses, J. Non-Cryst. Solids, Volume 440 (2016), pp. 12-25 | DOI
[19] On the correlation between microscopic structural heterogeneity and embrittlement behavior in metallic glasses, Sci. Rep., Volume 5 (2015), 14786
[20] Fictive temperature-independent density and minimum indentation size effect in calcium aluminosilicate glass, J. Appl. Phys., Volume 104 (2008), 063529 | DOI
[21] Highlighting the impact of shear strain on the SiO glass structure: From experiments to atomistic simulations, J. Non-Cryst. Solids, Volume 533 (2020), 119898 | DOI
[22] High-pressure effects on oxide glasses: I, densification in rigid state, J. Amer. Ceram. Soc., Volume 6 (1963), pp. 461-470 | DOI
[23] Plastic deformation and residual stresses in amorphous silica pillars under uniaxial loading, Acta Mater., Volume 60 (2012), pp. 5555-5566 | DOI
[24] Perfectly plastic flow in silica glass, Acta Mater., Volume 114 (2016), pp. 146-153 | DOI
[25] Plastic response of amorphous silicates, from atomistic simulations to experiments — a general constitutive relation, Mech. Solids, Volume 114 (2017), pp. 1-8 | DOI
[26] Super plastic bulk metallic glasses at room temperature, Science, Volume 315 (2007), pp. 1385-1388 | DOI
[27] et al. Ultrasonic plasticity of metallic glass near room temperature, Appl. Mater. Today, Volume 21 (2020), 100866
[28] Ductile bulk metallic glass, Phys. Rev. Lett., Volume 93 (2004), 255506 | DOI
[29] Improving plasticity of the ZrCuAl bulk metallic glass via thermal rejuvenation, Sci. Bull., Volume 63 (2018), pp. 840-844 | DOI
[30] Bulk metallic glasses: What are they good for?, Mater. Sci. Eng. A, Volume 375–377 (2004), pp. 385-388 | DOI
[31] Amorphous Solids – Low Temperature Properties, Springer, 1981
[32] Densification dependent yield criteria for sodium silicate glasses: An atomistic simulation approach, Acta Mater., Volume 111 (2016), pp. 129-137 | DOI
[33] Heterogeneities in Amorphous Systems Under Shear, Oxford University Press, 2010
[34] Rheological constitutive equation for a model of soft glassy materials, Phys. Rev. E, Volume 58 (1998), pp. 738-759 | DOI
[35] et al. Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses, Proc. Natl Acad. Sci. USA, Volume 105 (2008), pp. 14769-14772 | DOI
[36] et al. Vibrational dynamics and thermodynamics, ideal glass transitions and folding transitions, in liquids and biopolymers, AIP Conf. Proc., Volume 708 (2004), pp. 473-482 | DOI
[37] Energy landscapes for cooperative processes: nearly ideal glass transitions, liquid–liquid transitions and folding transitions, Philos. Trans. Royal Soc. A, Volume 363 (2005), pp. 415-432 | DOI
[38] On the study of local-stress rearrangements during quasi-static plastic shear of a model glass: Do local-stress components contain enough information?, Eur. Phys. J. E, Volume 26 (2008), pp. 283-293 | DOI
[39] Visualizing the behavior of dislocations—seeing is believing, MRS Bull., Volume 33 (2008), pp. 122-131 | DOI
[40] 3D visualization of dislocation arrangement using scanning electron microscope serial sectioning method, Scr. Mater., Volume 101 (2015), pp. 80-83 | DOI
[41] Metallic glasses as structural materials, Scr. Mater., Volume 54 (2006), pp. 321-326 | DOI
[42] Structural relaxation in a scale-free process, Phys. Rev. Lett., Volume 113 (2014), 245702 | DOI
[43] Encyclopedia of Computational Mechanics, John Wiley and Sons, New York, 2017 (ch 10)
[44] Local elasticity map and plasticity in a model Lennard-Jones glass, Phys. Rev. E, Volume 80 (2009), 026112 | DOI
[45] Vibrational modes as a predictor for plasticity in a model glass, Europhys. Lett., Volume 90 (2010), 16004 | DOI
[46] Athermal nonlinear elastic constants of amorphous solids, Phys. Rev. E, Volume 82 (2010), 026105
[47] Event-based relaxation of continuous disordered systems, Phys. Rev. Lett., Volume 77 (1996), pp. 4358-4362 | DOI
[48] Universal breakdown of elasticity at the onset of material failure, Phys. Rev. Lett., Volume 93 (2004), 195501 | DOI
[49] The use of ultrasound to measure dislocation density, JOM, Volume 67 (2015), pp. 1856-1863 | DOI
[50] Thermal transport in a 2D nanophononic solid: Role of bi-phasic materials properties on acoustic attenuation and thermal diffusivity, Nanomaterials, Volume 9 (2019), 1471
[51] Mapping between atomistic simulations and Eshelby inclusions in the shear deformation of an amorphous silicon model, Phys. Rev. E, Volume 93 (2016), 053002 | DOI
[52] Enhancing the plasticity of metallic glasses: Shear band formation, nanocomposites and nanoglasses investigated by molecular dynamics simulations, Mech. Mater., Volume 67 (2013), pp. 94-103 | DOI
[53] The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond. A, Volume 241 (1957) no. 1226, pp. 376-396
[54] Strain localization and percolation of stable structure in amorphous solids, Phys. Rev. Lett., Volume 95 (2005), 095502
[55] Amorphous systems in athermal, quasistatic shear, Phys. Rev. E, Volume 74 (2006), 016118 | DOI
[56] Evaluation of the disorder temperature and free-volume formalisms via simulations of shear banding in amorphous solids, Phys. Rev. Lett., Volume 98 (2007), 185505
[57] Paradoxal phenomena between the homogeneous and inhomogeneous deformations of metallic glasses, Appl. Phys. Lett., Volume 94 (2009), 021907
[58] Simulating the mechanical response of amorphous solids using atomistic methods, Eur. Phys. J. B, Volume 75 (2010), pp. 405-413 | DOI
[59] Rheological properties versus local dynamics in model disordered materials at low temperature, Eur. Phys. J. E, Volume 37 (2014), 43
[60] Connecting local yield stresses with plastic activity in amorphous solids, Phys. Rev. Lett., Volume 117 (2016), 045501 | DOI
[61] Shear transformation distribution and activation in glasses at the atomic scale, Phys. Rev. E, Volume 95 (2017), 033005 | DOI
[62] Comportement Mécanique des Matériaux, Hermes, Paris, 1995
[63] Molecular dynamics study of cristobalite silica using a charge transfer three-body potential: phase transformation and structural disorder, J. Chem. Phys., Volume 118 (2003), pp. 1487-1498 | DOI
[64] The elastic stability of square perforated plates under combinations of bending, shear and direct load, Thin-Walled Struct., Volume 4 (1986) no. 3, pp. 239-246 | DOI
[65] Constitutive law for the densification of fused silica, with applications on polishing and microgrinding, J. Am. Ceram. Soc., Volume 79 (1996), pp. 1441-1452 | DOI
[66] Deformation of fused silica: nanoindentation and densification, Proc. SPIE, Volume 3424 (1998), pp. 72-81 | DOI
[67] Impact of pressure on plastic yield in amorphous solids with open structure, Phys. Rev. E, Volume 93 (2016), 033001 | DOI
[68] Continuum limit of amorphous elastic bodies iii: three-dimensional systems, Phys. Rev. B, Volume 72 (2005), 224206 | DOI
[69] Atomistic response of a model silica glass under shear and pressure, Eur. Phys. J. E, Volume 85 (2012), 304
[70] Effect of composition and pressure on the shear strength of sodium silicate glasses: An atomic scale simulation study, Phys. Rev. E, Volume 95 (2017), 043001 | DOI
[71] Microplasticity, Interscience Publishers, New-York, 1968
[72] et al. Brillouin scattering of vitreous silica under high pressure, Ann. Phys., Volume 4 (1995), pp. 91-98
[73] Glass specific behavior in the damping of acoustic-like vibrations, Phys. Rev. Lett., Volume 96 (2006), 045502 | DOI
[74] Mesoscale modeling of amorphous metals by shear transformation zone dynamics, Acta Mater., Volume 57 (2009), pp. 2823-2833 | DOI
[75] Three-dimensional shear transformation zone dynamics model for amorphous metals, Model. Simul. Mat. Sci. Eng., Volume 18 (2010), 065009 | DOI
[76] Catastrophe Theory and its Application, Pitman, London, 1978
[77] Singularity Theory and an Introduction to Catastrophe Theory, Springer-Verlag, 1976 | DOI
[78] Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Springer-Verlag, New-York, 1997
[79] Instabilities and correlations of an elastic lattice in a random potential, Europhys. Lett., Volume 23 (1993) no. 9, pp. 623-628 | DOI
[80] The Mathematical Theory of Plasticity, Clarendon Press, Oxford, 1950
[81] On the nonlocal nature of dislocation nucleation during nanoindentation, J. Mech. Phys. Solids, Volume 56 (2008), pp. 1203-1223 | DOI
[82] Vibrational modes identify soft spots in a sheared disordered packing, Phys. Rev. Lett., Volume 107 (2011), 108302 | DOI
[83] Connecting structural relaxation with the low frequency modes in a hard-sphere colloidal glass, Phys. Rev. Lett., Volume 107 (2011), 188303 | DOI
[84] et al. Soft spots and their structural signature in a metallic glass, Proc. Natl Acad. Sci. USA, Volume 111 (2014), pp. 14052-14056 | DOI
[85] Dynamics of viscoplastic deformation in amorphous solids, Phys. Rev. E, Volume 57 (1998), pp. 7192-7205 | DOI
[86] Deformation and failure of amorphous solidlike materials, Condens. Matter Phys., Volume 2 (2011), pp. 353-373
[87] Direct observation of percolation in the yielding transition of colloidal glasses, Phys. Rev. Lett., Volume 118 (2017), 148001 | DOI
[88] Anharmonic versus relaxational sound damping in glasses. ii. Vitreous silica, Phys. Rev. B, Volume 72 (2005), 214205 | DOI
[89] Buckling of rectangular and hexagonal honeycomb under combined axial compression and transverse shear, Int. J. Solids Struct., Volume 50 (2013), pp. 3934-3946 | DOI
[90] Stabilité et mécanique non-linéaire, Hermes Science Publications, 2000
[91] et al. Numerical investigation, experimental validation and macroscopic yield criterion of al5056 honeycombs under mixed shear-compression loading, J. Impact Eng., Volume 108 (2017), pp. 348-360 | DOI
[92] et al. Poroelastic theory applied to the adsorption-induced deformation of vitreous silica, J. Phys. Chem. B, Volume 118 (2014), pp. 14519-14525 | DOI
[93] Avalanche localization and crossover scaling in amorphous plasticity, Phys. Rev. E, Volume 88 (2013), 062403 | DOI
[94] Statistical physics of the yielding transition in amorphous solids, Phys. Rev. E, Volume 82 (2010), 055103(R)
[95] Reversibility and criticality in amorphous solids, Nat. Commun., Volume 6 (2015), 8805 | DOI
[96] Yielding of glass under shear: A directed percolation transition precedes shear-band formation, Phys. Rev. E, Volume 94 (2016), 042605 | DOI
[97] Perfect plasticity in a random medium, J. Phys. II France, Volume 2 (1992), pp. 1007-1021 | DOI
[98] The elastic field outside an ellipsoidal inclusion, Proc. R. Soc. Lond. A, Volume 252 (1959) no. 1271, pp. 561-569
[99] Avalanches, thresholds, and diffusion in mesoscale amorphous plasticity, Phys. Rev. E, Volume 100 (2019), 043003 | DOI
[100] Deformation and flow of amorphous solids: a review of mesoscale elastoplastic models, Rev. Mod. Phys., Volume 90 (2018), 045006 | DOI
[101] An extremal model of amorphous plasticity, Phys. Rev. Lett., Volume 89 (2002), 195506
[102] Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter, Soft Matter, Volume 8 (2012), pp. 4197-4205 | DOI
[103] Universal features of amorphous plasticity, Nat. Commun., Volume 8 (2017), 15928 | DOI
[104] Shear bands topology in the deformed bulk metallic glasses, Metals, Volume 10 (2020), 374 | DOI
[105] Strain localization above the yielding point in cyclically deformed glasses, Phys. Rev. X, Volume 9 (2019), 021018
[106] et al. Glass stability changes the nature of yielding under oscillatory shear, Phys. Rev. Lett., Volume 124 (2020), 225502
[107] Emergence of cooperativity in plasticity of soft glassy materials, Phys. Rev. Lett., Volume 112 (2014), 246001 | DOI
[108] Mechanical behavior of amorphous alloys, Acta Mater., Volume 55 (2007), pp. 4067-4109 | DOI
[109] Length scale effects on the shear localization process in metallic glasses: A theoretical and computational study, J. Mech. Phys. Solids, Volume 59 (2011) no. 8, pp. 1552-1575 | DOI
[110] Shear transformation zone dynamics model for metallic glasses incorporating free volume as a state variable, Acta Mater., Volume 61 (2013), pp. 3347-3359 | DOI
[111] Mechanical noise dependent aging and shear banding behavior of a mesoscopic model of amorphous plasticity, Phys. Rev. B, Volume 84 (2011), 134210 | DOI
[112] Elasto-plastic description of brittel failure in athermal amorphous materials during quasistatic loading, Phys. Rev. E, Volume 98 (2018), 040901 | DOI
[113] et al. Random critical point separates brittle and ductile yielding transitions in amorphous materials, Proc. Natl Acad. Sci. USA, Volume 115 (2018), pp. 6656-6661 | DOI
[114] Rejuvenation and shear banding in model amorphous solids, Phys. Rev. E, Volume 101 (2020), 033001 | DOI
[115] Micromechanical model for deformation in solids with universal predictions for stress–strain curves and slip avalanches, Phys. Rev. Lett., Volume 102 (2009), 175501
[116] A study of the static yield stress in a binary Lennard–Jones glass, J. Chem. Phys., Volume 120 (2004), pp. 2788-2801 | DOI
[117] Nonequilibrium dynamics and fluctuation–dissipation relation in a sheared fluid, J. Chem. Phys., Volume 116 (2002), 6228 | DOI
[118] Brittle yielding of amorphous solids at finite shear rates, Phys. Rev. Mater., Volume 4 (2020), 025603
[119] Size-dependent shear fracture and global tensile plasticity of metallic glasses, Acta Mater., Volume 57 (2009), pp. 257-266
[120] Propagative and diffusive regimes of acoustic damping in bulk amorphous material, Phys. Rev. E, Volume 98 (2018), 023005
[121] Shear banding in a contact problem between metallic glasses, Metals, Volume 11 (2021), 257 | DOI
[122] Shear banding, aging and noise dynamics in soft glassy materials, Soft Matter, Volume 5 (2009), pp. 2378-2382 | DOI
[123] Competing indentation deformation mechanisms in glass using different strengthening methods, Front. Mater., Volume 3 (2016), 52
[124] Plane strain indentation of a Zr-based metallic glass: Experiments and numerical simulation, Acta Mater., Volume 54 (2006), pp. 179-180 | DOI
[125] Stress-induced structural transformation and shear banding during simulated nanoindentation of a metallic glass, Acta Mater., Volume 55 (2007), pp. 4317-4324 | DOI
[126] Driven interfaces: From flow to creep through model reduction, J. Stat. Phys., Volume 164 (2016), pp. 1394-1428 | DOI
[127] From weak to strong pinning: A finite-size study, Eur. Phys. J. B, Volume 38 (2004), pp. 71-82 | DOI
[128] Theory of Crystal Dislocations, Clarendon Press, Oxford, 1967
[129] et al. Simultaneous improvement of plasticity and strength of metallic glasses by tailoring residual stress: Role of stress gradient on shear banding, Mater. Des., Volume 197 (2021), 109246 | DOI
[130] et al. Macroscopic tensile plasticity of bulk metallic glass through designed artificial defects, Mater. Sci. Eng. A, Volume 534 (2012), pp. 365-373
[131] Plasticity-induced anisotropy in amorphous solids: The bauschinger effect, Phys. Rev. E, Volume 82 (2010), 026104
[132] Origin of the Bauschinger effect in amorphous solids, Phys. Rev. Lett., Volume 124 (2020), 205503 | DOI
[133] Kinetic Monte Carlo study of activated states and correlated shear-transformation-zone activity during the deformation of an amorphous metal, Phys. Rev. B, Volume 81 (2010), 064204 | DOI
[134] Potential energy landscape activations governing plastic flows in glass rheology, Proc. Natl Acad. Sci. USA, Volume 17 (2019), pp. 18790-18797 | DOI
[135] Detailed analysis of plastic shear in the Raman spectra of SiO glass, J. Non-Cryst. Solids, Volume 6 (2015), pp. 6-19 | DOI
[136] Nonlinear quasilocalized excitations in glasses: True representatives of soft spots, Phys. Rev. E, Volume 101 (2020), 032130 | DOI
[137] High frequency thermomechanical study of heterogeneous materials with interfaces, Ph. D. Thesis, Université de Lyon (2020)
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