Continuum limit of amorphous elastic bodies. III. Three-dimensional systems

Léonforte, Fabien; Boissière, R.; Tanguy, Anne; Wittmer, J. P.; Barrat, Jean‐Louis

doi:10.1103/physrevb.72.224206

Cited by 230 publications

(284 citation statements)

References 30 publications

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“…For example, in 3D Lennard-Jones simulations of elastic deformation of a polydisperse glass, Leonforte and coworkers observed non-uniform non-affine atomic displacements and measured a correlation length of ∼ 23σ [37]. More recently, Dmowski and coworkers suggested, from x-ray scattering data, that only about three-quarters of the atoms in a metallic glass deform elastically, with the remainder being anelastic "liquidlike" material.…”

Section: Characteristics Of Non-affine Displacementsmentioning

confidence: 99%

Length-scale dependence of elastic strain from scattering measurements in metallic glasses

et al. 2012

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Several recent studies have reported that the elastic strain in metallic glasses, as measured from peak shifts in the pair correlation functions of samples under load, increases with distance from an average atom, approaching the macroscopic strain at large distances. We have verified this behavior using high-energy x-ray scattering on metallic glasses loaded under uniaxial compression, uniaxial tension, and pure shear, and show that the apparent length-scale dependence of elastic strain is not an artifact of the assumption of structural isotropy in the data analysis. Molecular dynamics simulations of a binary Lennard-Jones glass loaded in uniaxial tension reproduce, qualitatively, the behavior observed in the experiments when the elastic strain is calculated from the shifts in the peaks of the pair correlation function. Under hydrostatic loading, however, the length-scale dependence of elastic strain observed in the simulations is greatly reduced. This suggests that non-affine atomic displacements, which are smaller under hydrostatic loading than under uniaxial loading, may play a key role in the length-scale dependence of elastic strain. Furthermore, no length-scale dependence is observed in simulations, for either uniaxial or hydrostatic loading, when the elastic strain is calculated from the average local deformation gradient tensor. We explain this apparent contradiction and show that the atomic displacements resulting from elastic loading are largest in the low density regions between atomic shells around an average atom. Finally, we present an analysis of length-scale dependence of elastic strain calculated from the pair correlation function for the case of homogeneous deformation, which is in good agreement with the simulations conducted under hydrostatic loading. For uniaxial loading, however, the analysis diverges from both the experimental and simulated results in the first two near-neighbor atomic shells. This suggests, in agreement with our observations from the molecular dynamics simulations, that the observed length-scale dependence of elastic strain from scattering measurements reflects the nature of the non-affine atomic displacements in the glass.

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Section: Characteristics Of Non-affine Displacementsmentioning

confidence: 99%

Length-scale dependence of elastic strain from scattering measurements in metallic glasses

et al. 2012

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“…The third C K is the contribution from the kinetic energy to the modulus, which is much smaller than the other two terms and can be neglected for dense systems. For amorphous materials, the non-affine term C N is an important contribution, comparable in magnitude with the affine term C B [4,5,7]. The three approaches to measure the local modulus described above evaluate this non-affine component C N in different ways.…”

Section: Introductionmentioning

confidence: 99%

“…The local heterogeneity in the elastic properties is reflected by the existence of a strong non-affine character in the elastic deformation of the material [4][5][6][7]: the displacement field at small scale is not obtained from the macroscopic strain, but the atoms undergo an extra relaxation described as a non-affine displacement, which has long range spatial correlations due to the elastic character of the problem [8,9]. The scale ξ of the elastic heterogeneities can be assessed by measuring the local elastic properties as a function of a coarse graining size, and monitoring the convergence towards macroscopic properties [3].…”

Section: Introductionmentioning

confidence: 99%

Measuring spatial distribution of the local elastic modulus in glasses

Mizuno

Mossa²,

Barrat³

2013

Phys. Rev. E

135

166

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Glasses exhibit spatially inhomogeneous elastic properties, which can be investigated by measuring their elastic moduli at a local scale. Various methods to evaluate the local elastic modulus have been proposed in the literature. A first possibility is to measure the local stress-local strain curve and to obtain the local elastic modulus from the slope of the curve, or equivalently to use a local fluctuation formula. Another possible route is to assume an affine strain and to use the applied global strain instead of the local strain for the calculation of the local modulus. Most recently a third technique has been introduced, which is easy to be implemented and has the advantage of low computational cost. In this contribution, we compare these three approaches by using the same model glass and reveal the differences among them caused by the non-affine deformations.

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“…For Lennard-Jones glasses, Tanguy and co-workers [6][7][8][9] showed that the disorder can give rise to important corrections to naive estimates for the elastic moduli. O'Hern et.…”

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confidence: 99%