Underconstrained jammed packings of nonspherical hard particles: Ellipses and ellipsoids

Abstract

Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev et al., Science, vol. 303,[990][991][992][993] we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why the isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle (Z = 2d f ), does not apply to nonspherical particles. We develop first-and second-order conditions for jamming, and demonstrate that packings of nonspherical particles can be jammed even though they are hypoconstrained (Z < 2d f ). We apply an algorithm using these conditions to computer-generated hypoconstrained ellipsoid and ellipse packings and demonstrate that our algorithm does produce jammed packings, even close to the sphere point. We also consider packings that are nearly jammed and draw connections to packings of deformable (but stiff) particles. Finally, we consider the jamming conditions for nearly spherical particles and explain quantitatively the behavior we observe in the vicinity of the sphere point.

Force chains and contact network topology in sheared packings of elongated particles

“…The preparation under gravity has strong influence on the particle orientations and thus on the force distributions. On the other hand, a systematic study of the shear behavior of 2D packings of rounded-cap rectangles (RCR) under homogeneous boundary conditions indicates that the shear strength increases with elongation whereas the packing fraction varies unmonotonically [22], as also found for packings of ellipsoidal shapes [20,21]. In all reported cases, the networks resulting from various shapes appear to be highly complex and hardly amenable to simple statistical modeling.…”

“…Systematic studies of particle shape dependence in granular materials have been recently reported for polygonal/polyhedral [14][15][16][17][18], elliptical/ellipsoidal [19][20][21][22] and non-convex shapes [23]. The force chains are found to be reinforced in packings of polygonal and polyhedral particles leading to enhanced shear strength [15,22,24].…”

Free-energy functional for freezing transitions: Hard-sphere systems freezing into crystalline and amorphous structures

“…As in an amorphous or glassy structure the lattice sites are randomly distributed and are not known, the above simplification is not possible. We can, however, calculate and have an idea of inhomogeneity and its difference from that of a crystalline solid using the distribution of R n determined from numerical simulations [20,21]. Thus…”

“…The usual way to construct amorphous structure in experiment or numerical simulation is to compress the system according to some protocol which avoids crystallization [17,20,21]. One of the criteria used to signal the onset of glassy phase in supercooled liquids is emergence of split second peak.…”

A new algorithm for dense ellipse packing and polygonal structures generation in context of FEM or DEM

“…The dynamic methods were widely used for the ellipsoid packing and high densities were reported in published works [15][16][17][18]. For the methods in which ellipsoidal particles are generated by choosing randomly initial position and orientation and letting them fall in an open box under the gravity, an anisotropic behaviour of the packing system was reported [18,19].…”