Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExcitations of Ellipsoid Packings near Jamming
189
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the vibrational modes of three-dimensional jammed packings of soft ellipsoids of revolution as a function of particle aspect ratio $epsilon$ and packing fraction. At the jamming transition for ellipsoids, as distinct from the idealized case using spheres where $epsilon = 1$, there are many unconstrained and non-trivial rotational degrees of freedom. These constitute a set of zero-frequency modes that are gradually mobilized into a new rotational band as $|epsilon - 1|$ increases. Quite surprisingly, as this new band is separated from zero frequency by a gap, and lies below the onset frequency for translational vibrations, $omega^*$, the presence of these new degrees of freedom leaves unaltered the basic scenario that the translational spectrum is determined only by the average contact number. Indeed, $omega^*$ depends solely on coordination as it does for compressed packings of spheres. We also discuss the regime of large $|epsilon - 1|$, where the two bands merge.
rate research
Read More
We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.
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.
We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power-law in the interparticle overlap with exponent $alpha$, have found that the ensemble-averaged shear modulus $langle G rangle$ increases with pressure $P$ as $sim P^{(alpha-3/2)/(alpha-1)}$ at large pressures. However, a deep theoretical understanding of this scaling behavior is lacking. We show that the shear modulus of jammed packings of frictionless, spherical particles has two key contributions: 1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and 2) discontinuous jumps during compression that arise from changes in the contact network. We show that the shear modulus of the first geometrical family for jammed packings can be collapsed onto a master curve: $G^{(1)}/G_0 = (P/P_0)^{(alpha-2)/(alpha-1)} - P/P_0$, where $P_0 sim N^{-2(alpha-1)}$ is a characteristic pressure that separates the two power-law scaling regions and $G_0 sim N^{-2(alpha-3/2)}$. Deviations from this form can occur when there is significant non-affine particle motion near changes in the contact network. We further show that $langle G (P)rangle$ is not simply a sum of two power-laws, but $langle G rangle sim (P/P_c)^a$, where $a approx (alpha -2)/(alpha-1)$ in the $P rightarrow 0$ limit and $langle G rangle sim (P/P_c)^b$, where $b gtrsim (alpha -3/2)/(alpha-1)$ above a characteristic pressure $P_c$. In addition, the magnitudes of both contributions to $langle Grangle$ from geometrical families and changes in the contact network remain comparable in the large-system limit for $P >P_c$.
We present 3D DEM simulations of jammed bidisperse granular packings to investigate their jamming density, $phi_J$, and bulk modulus, $K$, as a function of the size ratio, $delta$, and concentration of small particles, $X_{mathrm S}$. We determine the partial and total bulk modulus for each packing and obtain a transition behavior at specific densities that depends on the compression level, thus marking the first and second transition of the system. The highest bulk modulus is found at $X^{*}_{mathrm S}(delta = 0.15) approx 0.21$ consistent with the maximum jamming density, where both particle species mix more efficiently. At extreme size ratios, $delta = 0.15$, $X^{*}_{mathrm S}$ divides two structural scenarios for $K$ that depend on whether small particles are jammed or not jointly with large ones. We find that along the second transition line, $K$ rises $20%$ compared to those found at the first transition. However, their values are still low compared to that shown at $X^{*}_{mathrm S}$. This clearly indicates that the jamming of small particles indeed impacts the internal resistance of the system for low $delta$ and low $X_{mathrm S}$. This new result will allow tuning packing bulk modulus and other properties, such as wave speed, when a specific size and concentration of small particles contribute to the jammed structure.
We report numerical results of effective attractive forces on the packing properties of two-dimensional elongated grains. In deposits of non-cohesive rods in 2D, the topology of the packing is mainly dominated by the formation of ordered structures of aligned rods. Elongated particles tend to align horizontally and the stress is mainly transmitted from top to bottom, revealing an asymmetric distribution of local stress. However, for deposits of cohesive particles, the preferred horizontal orientation disappears. Very elongated particles with strong attractive forces form extremely loose structures, characterized by an orientation distribution, which tends to a uniform behavior when increasing the Bond number. As a result of these changes, the pressure distribution in the deposits changes qualitatively. The isotropic part of the local stress is notably enhanced with respect to the deviatoric part, which is related to the gravity direction. Consequently, the lateral stress transmission is dominated by the enhanced disorder and leads to a faster pressure saturation with depth.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
