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Register a new userDivergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials
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Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, for which positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.
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In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from the Voronoi diagram of configurations of oblate ellipsoids, for various aspect ratios $alpha$ and global volume fractions $phi_g$. We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. In particular, we consider the local packing fraction $phi_l$, defined as the particles volume divided by its Voronoi cell volume. We find that the probability $P(phi_l)$ for a Voronoi cell to have a given local packing fraction shows the same scaling behaviour as function of $phi_g$ as observed for random sphere packs. Surprisingly, this scaling behaviour is further found to be independent of the particle aspect ratio. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index $beta=beta_0^{2,0}$, points towards a significant difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape $beta$ of all cells with a given value of $phi_l$ is very similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true. This non-universality has implications for our understanding of jamming of aspherical particles.
Yield stress fluids display complex dynamics, in particular when driven into the transient regime between the solid and the flowing state. Inspired by creep experiments on dense amorphous materials, we implement mesocale elasto-plastic descriptions to analyze such transient dynamics in athermal systems. Both our mean-field and space-dependent approaches consistently reproduce the typical experimental strain rate responses to different applied steps in stress. Moreover, they allow us to understand basic processes involved in the strain rate slowing down (creep) and the strain rate acceleration (fluidization) phases. The fluidization time increases in a power-law fashion as the applied external stress approaches a static yield stress. This stress value is related to the stress over-shoot in shear start-up experiments, and it is known to depend on sample preparation and age. By calculating correlations of the accumulated plasticity in the spatially resolved model, we reveal different modes of cooperative motion during the creep dynamics.
A wide range of materials can exist in microscopically disordered solid forms, referred to as amorphous solids or glasses. Such materials -- oxide glasses and metallic glasses, to polymer glasses, and soft solids such as colloidal glasses, emulsions and granular packings -- are useful as structural materials in a variety of contexts. Their deformation and flow behaviour is relevant for many others. Apart from fundamental questions associated with the formation of these solids, comprehending their mechanical behaviour is thus of interest, and of significance for their use as materials. In particular, the nature of plasticity and yielding behaviour in amorphous solids has been actively investigated. Different amorphous solids exhibit behaviour that is apparently diverse and qualitatively different from those of crystalline materials. A goal of recent investigations has been to comprehend the unifying characteristics of amorphous plasticity and to understand the apparent differences among them. We summarise some of the recent progress in this direction. We focus on insights obtained from computer simulation studies, and in particular those employing oscillatory shear deformation of model glasses.
It is observed that a constant unit vector denoted by $mathbf I$ is needed to characterize a complete orthonormal set of vector diffraction-free beams. The previously found diffraction-free beams are shown to be included as special cases. The $mathbf I$-dependence of the longitudinal component of diffraction-free beams is also discussed.
Atomistic simulations are employed to study structural evolution of pore ensembles in binary glasses under periodic shear deformation with varied amplitude. The consideration is given to porous systems in the limit of low porosity. The initial ensembles of pores are comprised of multiple pores with small sizes, which are approximately normally distributed. As periodic loading proceeds, the ensembles evolve into configurations with a few large-scale pores and significantly reduced number of small pores. These structural changes are reflected in the skewed shapes of the pore-size distribution functions and the appearance of a distinct peak at large length scales after hundreds of shear cycles. Moreover, periodic shear causes substantial densification of solid domains in the porous systems. The structural evolution of pore ensembles is found to stem from the formation of shear-band like regions of enhanced particle mobility after a number of transient cycles. The spatial extent of increased mobility depends strongly on the strain amplitude. A scaling theory is developed to qualitatively describe the transformation of the pore initial configurations of small-size voids into larger-scale void agglomerates.
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