Guo-Jie Gao

Frequency distribution of mechanically stable disk packings

Relative frequencies of mechanically stable (MS) packings of frictionless bidisperse disks are studied numerically in small systems. The packings are created by successively compressing or decompressing a system of soft purely repulsive disks, followed by energy minimization, until only infinitesimal particle overlaps remain. For systems of up to 14 particles, most of the MS packings were generated. We find that the packings are not equally probable as has been assumed in recent thermodynamic descriptions of granular systems. Instead, the frequency distribution, averaged over each packing-fraction interval Deltaphi , grows exponentially with increasing phi. Moreover, within each packing-fraction interval, MS packings occur with frequencies f{k} that differ by many orders of magnitude. Also, key features of the frequency distribution do not change when we significantly alter the packing-generation algorithm; for example, frequent packings remain frequent and rare ones remain rare. These results indicate that the frequency distribution of MS packings is strongly influenced by geometrical properties of the multidimensional configuration space. By adding thermal fluctuations to a set of the MS packings, we were able to examine a number of local features of configuration space near each packing. We measured the time required for a given packing to break to a distinct one, which enabled us to estimate the energy barriers that separate one packing from another. We found a gross positive correlation between the packing frequencies and the heights of the lowest energy barriers {0}; however, there is significant scatter in the data. We also examined displacement fluctuations away from the MS packings to assess the size and shape of the local basins near each packing. The displacement modes scale as d{i} approximately epsilon{0}{gamma{i}} with gamma{i} ranging from approximately 0.6 for the largest eigenvalues to 1.0 for the smallest ones. These scalings suggest that the packing frequencies are not determined by the local volume of configuration space near each packing, which would require that the dependence of f{k} on epsilon{0} is much stronger than the dependence we observe. The scatter in our data implies that in addition to epsilon{0} there are also other, as yet undetermined variables that influence the packing probabilities.

Experimental demonstration of nonuniform frequency distributions of granular packings.

We developed an experimental method to generate mechanically stable (MS) packings of frictionless disks and performed coordinated experiments and simulations to characterize MS packings in small systems. For a given system geometry, MS packings occur as discrete, well-separated points in configuration space with probabilities that vary by many orders of magnitude and are robust with respect to the packing preparation. Over a continuous range of system geometries, MS packings occur as distinct geometrical families and only a small fraction of families are sampled via quasistatic dynamics. These results suggest that the most frequent MS packings may dominate the structural and mechanical properties of dense granular media.

Studying the elastic properties of nanocrystalline copper using a model of randomly packed uniform grains

We develop a new Voronoi protocol, which is a space tessellation method, to generate a fully dense (containing no voids) model of nanocrystalline copper with precise grain size control; we also perform uniaxial tensile tests using molecular dynamical (MD) simulations to measure the elastic moduli of the grain boundary and the grain interior components at 300 K. We find that the grain boundary deforms more locally compared with the grain core region under thermal vibrations and is elastically less stiff than the core component at finite temperature. The elastic modulus of the grain boundary is lower than 30% of that of the grain interior. Our results will aid in the development of more accurate continuum models of nanocrystalline metals.

Size-dependent transition of deformation mechanism, and nonlinear elasticity in Ni3Al nanowires

A size-dependent transition of deformation mechanism is revealed in Ni3Al nanowire under atomistic uniaxial tension. Deformation twinning is replaced by phase transformation when the diameter of Ni3Al nanowire reduces to a critical value near 4 nm. Enhanced size-dependent nonlinear elasticity is observed in the nanowires, in comparison to their bulk counterpart which is benchmarked by combined density functional and atomistic study. This study provide fundamental understanding on the size-dependent deformation mechanisms of nanostructured alloys.

Geometrical families of mechanically stable granular packings

We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N<16), we find that the dynamics is deterministic and highly contracting. That is, if the system is initialized in a MS packing at a given shear strain, it will quickly lock into a periodic orbit at subsequent shear strain, and therefore sample only a very small fraction of the possible MS packings in steady state. In studies with N>16, we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.

Enumeration of distinct mechanically stable disk packings in small systems

We create mechanically stable (MS) packings of bidisperse disks using an algorithm in which we successively grow or shrink soft repulsive disks followed by energy minimization until the overlaps are vanishingly small. We focus on small systems because this enables us to enumerate nearly all distinct MS packings. We measure the probability of obtaining an MS packing at packing fraction φ and find several notable results. Firstly, the probability is highly non-uniform. When averaged over narrow packing fraction intervals, the most probable MS packing occurs at the highest φ and the probability decays exponentially with decreasing φ. Even more striking, within each packing-fraction interval, the probability can vary by many orders of magnitude. By using two different packing-generation protocols, we show that these results are robust and the packing frequencies do not change qualitatively with different protocols.