Coefficient of tangential restitution for the linear dashpot model

The linear dashpot model for the inelastic normal force between colliding spheres leads to a constant coefficient of normal restitution, $\epsilon_n=$const., which makes this model very popular for the investigation of dilute and moderately dense granular systems. For two frequently used models for the tangential interaction force we determine the coefficient of tangential restitution $\epsilon_t$, both analytically and by numerical integration of Newton's equation. Although $\epsilon_n=$const. for the linear-dashpot model, we obtain pronounced and characteristic dependencies of the tangential coefficient on the impact velocity $\epsilon_t=\epsilon_t(\vec{g})$. The results may be used for event-driven simulations of granular systems of frictional particles.Comment: 12 pages, 12 figure

Collision of Viscoelastic Spheres: Compact Expressions for the Coefficient of Normal Restitution

The coefficient of restitution of colliding viscoelastic spheres is analytically known as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While beeing analytically exact, this result is not suitable for applications in efficient event-driven Molecular Dynamics (eMD) or Monte Carlo (MC) simulations. Based on the analytic result, here we derive expressions for the coefficient of restitution which allow for an application in efficient eMD and MC simulations of granular Systems.Comment: 4 pages, 4 figure

Coefficient of Restitution for Viscoelastic Spheres: The Effect of Delayed Recovery

The coefficient of normal restitution of colliding viscoelastic spheres is computed as a function of the material properties and the impact velocity. From simple arguments it becomes clear that in a collision of purely repulsively interacting particles, the particles loose contact slightly before the distance of the centers of the spheres reaches the sum of the radii, that is, the particles recover their shape only after they lose contact with their collision partner. This effect was neglected in earlier calculations which leads erroneously to attractive forces and, thus, to an underestimation of the coefficient of restitution. As a result we find a novel dependence of the coefficient of restitution on the impact rate.Comment: 11 pages, 2 figure

Structural features of jammed-granulate metamaterials

Granular media near jamming exhibit fascinating properties, which can be harnessed to create jammed-granulate metamaterials: materials whose characteristics arise not only from the shape and material properties of the particles at the microscale, but also from the geometric features of the packing. For the case of a bending beam made from jammed-granulate metamaterial, we study the impact of the particles' properties on the metamaterial's macroscopic mechanical characteristics. We find that the metamaterial's stiffness emerges from its volume fraction, in turn originating from its creation protocol; its ultimate strength corresponds to yielding of the force network. In contrast to many traditional materials, we find that macroscopic deformation occurs mostly through affine motion within the packing, aided by stress relieve through local plastic events, surprisingly homogeneously spread and persistent throughout bending

Fractal Substructure of a Nanopowder

The structural evolution of a nano-powder by repeated dispersion and settling can lead to characteristic fractal substructures. This is shown by numerical simulations of a two-dimensional model agglomerate of adhesive rigid particles. The agglomerate is cut into fragments of a characteristic size l, which then are settling under gravity. Repeating this procedure converges to a loosely packed structure, the properties of which are investigated: a) The final packing density is independent of the initialization, b) the short-range correlation function is independent of the fragment size, c) the structure is fractal up to the fragmentation scale l with a fractal dimension close to 1.7, and d) the relaxation time increases linearly with l.Comment: 4 pages, 8 figure