Evaluation of the Disorder Temperature and Free-Volume Formalisms via Simulations of Shear Banding in Amorphous Solids

Shi, Yunfeng; Katz, Michael B.; Li, Hui; Falk, Michael L.

doi:10.1103/physrevlett.98.185505

Cited by 181 publications

(181 citation statements)

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“…The spontaneous emergence of the shear band and its position, orientation, and structure are all important characteristics of the compressive failure of heterogeneous, disordered, or amorphous materials [1][2][3][4][5]25]. Since localization is preceded by random microcracking, the algorithmic determination of the position of the shear band is rather complex in DEM simulations.…”

Section: Shear Bandmentioning

confidence: 99%

Fragmentation and shear band formation by slow compression of brittle porous media

et al. 2016

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Localized fragmentation is an important phenomenon associated with the formation of shear bands and faults in granular media. It can be studied by empirical observation, by laboratory experiment, or by numerical simulation. Here we investigate the spatial structure and statistics of fragmentation using discrete element simulations of the strain-controlled uniaxial compression of cylindrical samples of different finite size. As the system approaches failure, damage localizes in a narrow shear band or synthetic fault "gouge" containing a large number of poorly sorted noncohesive fragments on a broad bandwidth of scales, with properties similar to those of natural and experimental faults. We determine the position and orientation of the central fault plane, the width of the shear band, and the spatial and mass distribution of fragments. The relative width of the shear band decreases as a power law of the system size, and the probability distribution of the angle of the central fault plane converges to around 30 degrees, representing an internal coefficient of friction of 0.7 or so. The mass of fragments is power law distributed, with an exponent that does not depend on scale, and is near that inferred for experimental and natural fault gouges. The fragments are in general angular, with a clear self-affine geometry. The consistency of this model with experimental and field results confirms the critical roles of preexisting heterogeneity, elastic interactions, and finite system size to grain size ratio on the development of shear bands and faults in porous media.

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Section: Shear Bandmentioning

confidence: 99%

Fragmentation and shear band formation by slow compression of brittle porous media

et al. 2016

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“…However, the deformation modes of nanoscale MG samples observed in molecular simulations have also been inconsistent. A highly inhomogeneous deformation mode resulting in a major shear band has been observed in two-dimensional 4,19 and threedimensional thin-slab samples. 5,20,21 Nonetheless, cylindrical-shaped samples, which are most relevant to experiments, have shown nearly homogeneous flow until necking at high strains 22,23 and only exhibit shear bands upon the introduction of a surface notch.…”

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confidence: 99%

Size-independent shear band formation in amorphous nanowires made from simulated casting

Shi

2010

Applied Physics Letters

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Molecular dynamics simulations indicate that surfaces strongly influence the strain localization behavior of amorphous nanowires in tension. A sample preparation routine that simulates casting was employed to facilitate the relaxation of the sample surface. Samples as short as 15 nm (7.5 nm in diameter)form dominant shear bands during deformation. The elastic energy release during plastic deformation is sufficient to provide the excess potential energy required for the shear band nucleation at rather small sample sizes. The results show that shear band formation is almost size-independent and is bounded only by its own length scale.

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“…On the smallest scales, molecular dynamics and quasi-static simulations generate a wealth of information about particle interactions and emergent macroscopic behavior -including shear banding [1,19,20] -but they are limited to smaller numbers of particles and time scales. On the largest scales, phenomenological models such as viscoelasticity and the Dieterich-Ruina friction law [21,22], which has been studied extensively in the context of rock mechanics, describe stress-strain step and frequency responses, but to date these laws have not been derived from microscopic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Strain localization in a shear transformation zone model for amorphous solids

2007

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We model a sheared disordered solid using the theory of Shear Transformation Zones (STZs). In this mean-field continuum model the density of zones is governed by an effective temperature that approaches a steady state value as energy is dissipated. We compare the STZ model to simulations by Shi, et al.[Y. Shi et al. PRL 98, 185505 (2007)], finding that the model generates solutions that fit the data, exhibit strain localization, and capture important features of the localization process. We show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization. By estimating the effects of these interactions, we derive a criterion that determines which materials exhibit shear bands based on the initial conditions alone. We also show that the shear band width is not set by an inherent diffusion length scale but instead by a dynamical scale that depends on the imposed strain rate.

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Evaluation of the Disorder Temperature and Free-Volume Formalisms via Simulations of Shear Banding in Amorphous Solids

Cited by 181 publications

References 31 publications

Fragmentation and shear band formation by slow compression of brittle porous media

Fragmentation and shear band formation by slow compression of brittle porous media

Size-independent shear band formation in amorphous nanowires made from simulated casting

Strain localization in a shear transformation zone model for amorphous solids

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