6 research outputs found
Jamming in Systems Composed of Frictionless Ellipse-Shaped Particles
We study the structural and mechanical properties of jammed ellipse packings,
and find that the nature of the jamming transition in these systems is
fundamentally different from that for spherical particles. Ellipse packings are
generically hypostatic with more degrees of freedom than constraints. The
spectra of low energy excitations possess two gaps and three distinct branches
over a range of aspect ratios. In the zero compression limit, the energy of the
modes in the lowest branch increases {\it quartically} with deformation
amplitude, and the density of states possesses a -function at zero
frequency. We identify scaling relations that collapse the low-frequency part
of the spectra for different aspect ratios. Finally, we find that the degree of
hypostaticity is determined by the number of quartic modes of the packing.Comment: 4 pages, 4 figure
Constraints and vibrations in static packings of ellipsoidal particles
We numerically investigate the mechanical properties of static packings of
ellipsoidal particles in 2D and 3D over a range of aspect ratio and compression
. While amorphous packings of spherical particles at jamming onset
() are isostatic and possess the minimum contact number required for them to be collectively jammed, amorphous packings of
ellipsoidal particles generally possess fewer contacts than expected for
collective jamming () from naive counting arguments, which
assume that all contacts give rise to linearly independent constraints on
interparticle separations. To understand this behavior, we decompose the
dynamical matrix for static packings of ellipsoidal particles into two
important components: the stiffness and stress matrices. We find that
the stiffness matrix possesses eigenmodes
with zero eigenvalues even at finite compression, where is the number of
particles. In addition, these modes are nearly eigenvectors of the
dynamical matrix with eigenvalues that scale as , and thus finite
compression stabilizes packings of ellipsoidal particles. At jamming onset, the
harmonic response of static packings of ellipsoidal particles vanishes, and the
total potential energy scales as for perturbations by amplitude
along these `quartic' modes, . These findings illustrate
the significant differences between static packings of spherical and
ellipsoidal particles.Comment: 18 pages, 21 figure