Structure-property relationships from universal signatures of plasticity in disordered solids

Abstract

When deformed beyond their elastic limits, crystalline solids flow plastically via particle rearrangements localized around structural defects. Disordered solids also flow, but without obvious structural defects. We link structure to plasticity in disordered solids via a microscopic structural quantity, “softness,” designed by machine learning to be maximally predictive of rearrangements. Experimental results and computations enabled us to measure the spatial correlations and strain response of softness, as well as two measures of plasticity: the size of rearrangements and the yield strain. All four quantities maintained remarkable commonality in their values for disordered packings of objects ranging from atoms to grains, spanning seven orders of magnitude in diameter and 13 orders of magnitude in elastic modulus. These commonalities link the spatial correlations and strain response of softness to rearrangement size and yield strain, respectively.

“Softness” as the structural origin of plasticity in disordered solids: a quantitative insight from machine learning

“…1b evidently illustrates that E varies with r and the distribution of moduli for both crystalline and disordered solids. Please note that the mechanical softness derived from Equation (5) differs fundamentally from the softness of Cubuk et al [7]; however, these two should have a good correlation given that both are also correlated with the non-affine deformation in disordered solids under mechanical stress.…”

“…In principle, the particles with higher "softness" show a better spatial correlation with the regions undergoing large rearrangements. More importantly, Cubuk and co-workers [7] discovered that the normalized spatial correlation function…”

“…Prior to the "softness" proposed by Cubuk et al [7], there are already a number of theories or models developed in the literature to explain the origin of plasticity in disordered solids. These include the free volume model originally proposed by Cohen and Turnbull [9] and developed by Spaepen et al [3], which defined free volume as the excess space among atoms and assumed that plastic flow should result from a number of individual atomic jumps in and out of free volume.…”

“…In a recent paper published in Science by Cubuk et al [7], the authors defined a microstructural quantity, termed "softness", based on a supervised machine learning model [8]. To determine the "softness" of particle i, a set of structural functions are defined, as listed below:…”

“…Here, μ, ξ, λ, L and ζ are all parameters related to particles, as defined in Ref. [7]. For data training, one has to determine particles that are prone to rearrange their positions with their neighbors.…”