Coarse graining atomistic simulations of plastically deforming amorphous solids

Abstract

The primary mode of failure in disordered solids results from the formation and persistence of highly localized regions of large plastic strains known as shear bands. Continuum-level field theories capable of predicting this mechanical response rely upon an accurate representation of the initial and evolving states of the amorphous structure. We perform molecular dynamics simulations of a metallic glass and propose a methodology for coarse graining discrete, atomistic quantities, such as the potential energies of the elemental constituents. A strain criterion is established and used to distinguish the coarse-grained degrees-of-freedom inside the emerging shear band from those of the surrounding material. A signal-to-noise ratio provides a means of evaluating the strength of the signal of the shear band as a function of the coarse graining. Finally, we investigate the effect of different coarse graining length scales by comparing a two-dimensional, numerical implementation of the effective-temperature description in the shear transformation zone (STZ) theory with direct molecular dynamics simulations. These comparisons indicate the coarse graining length scale has a lower bound, above which there is a high level of agreement between the atomistics and the STZ theory, and below which the concept of effective temperature breaks down.

Strain localization in dry sheared granular materials: A compactivity-based approach

“…The initial conditions may be tuned to generate a wide variety of localization patterns. The influence of different initial conditions on shear band dynamics and establishing a link between the Gaussian filter width and the characteristics of the microstructure [63] will be a focus of a future investigation.…”

Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations

“…The quality of the approximations for both cases is quantified in terms of the average principal angleθ of Eq. (27) and the Frobenius norm between the approximationF and the true solution F. Figure 18 shows histograms of the average principal angle and the Frobenius norm computed at each of the simplex centers. In terms of the principal angles in Figs.…”

Correlations of non-affine displacements in metallic glasses through the yield transition

“…The size of these zones has been estimated to range from a few [16] to many tens of atoms [17,18]. Knowledge of the size of the zones could help to fundamentally understand this class of materials on an atomic level and be used in mesoscale simulations that incorporate STZs [19][20][21]. The size of STZs has been linked to the Poisson ratio [22] as well as the brittle or ductile character of fracture of BMGs [23][24][25].…”