A spherocylinder, a convex 3D object consisting of a cylinder with two hemispherical ends, can possess a wide range of aspect ratios and is one of the most studied non-spherical particle shapes. ...Previous investigations on disordered spherocylinder packings yielded inconsistent packing characteristics, especially the packing density φ, indicating that density alone is not sufficient to uniquely characterize a packing. In this paper, we delineate in the density–order–metric diagram (i.e. order map) the border curve that separates geometrically feasible and infeasible packings of congruent spherocylinders via the geometric-structure approach, i.e., by generating and analyzing a large number of packing configurations with a diversity of densities and degrees of order generated via a relaxation algorithm. We find that the border curve possesses a sharp transition as the packing density increases, i.e., the initial increase of φ is not associated with any notable increase of the degree of order, while beyond a threshold φ value, the increase of density is strongly positively correlated with the increase of order. This allows us to propose the concept of maximally dense random packing (MDRP) state for spherocylinders, which corresponds to the transition point in the boarder curve and characterizes the on-set of nontrivial spatial correlations among the particles. It can also be considered as the maximally dense packing arrangement of spherocylinders without nontrivial spatial correlations. The degree of order of a spherocylinder packing is quantified via the nematic order parameter (S) and the local order metric (SLocal), which respectively characterize the level of global orientational order and local order in particle clusters. The latter metric SLocal, which measures the average order in the neighborhoods of particles with the second Legendre polynomial, is a new order metric for spherocylinder systems. We find that the packing density of the MDRPs initially increases with the increase of the aspect ratio w from 0, and reaches the maximal value of 0.725 when w=0.5, then drops with further increase of w. The MDRP at w=0.5 is verified to be jammed via a Monte Carlo jamming-testing algorithm and thus, should also represent the maximally random jammed (MRJ) packing state as well.
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•The local order in clusters is identified as a main order form in geometric spherocylinder packing.•A new local order metric SLocal is proposed to quantify the local order in clusters.•The concept of maximally dense random packing (MDRP) state in spherocylinder packings is proposed.•In the MDRP state, the packing properties in terms of the aspect ratio are presented.
Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary ...spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,
Understanding disordered particle packings is of great significance from both theoretical and engineering perspectives. Establishing a quantitative relationship between nonspherical particle shape ...and disordered packing properties is generally challenging, due to the complex geometry and topology. Here we resolve this issue by numerically investigating disordered jammed packings of various frictional congruent nonspherical particles, including superellipsoids and polyhedra, over a wide range of friction coefficients. We discover several universal packing characteristics across different particle shapes and frictions. In the infinite friction limit, the coordination numbers for all shapes approach the identical lower bound for jamming. The resulting “random loose packing” (RLP) state possesses minimal structural correlations, with the packing fraction as a simple monotonic decreasing function of the orientation-averaged excluded volume for different particle shapes. Packings with finite friction can then be understood via a perturbative approach based on RLP. The nature of RLP can be illuminated by the percolation transition of contacting particle network during the quasistatic densification process. Moreover, the large-scale density fluctuations for all jammed frictional packings are also strongly suppressed, broadening the previous claim of hyperuniformity for the frictionless ones.
The shape and size of particles are the main factors which influence the packing density of binary mixtures. However, investigations of the single effect of size and shape on the binary mixtures of ...non-spherical particles are much absent. A systematic computational investigation on the binary packing of spherocylinders considering the single effect of shape and size respectively is carried out with the sphere assembly models and relaxation algorithm. Random packings of binary spherocylinders with the same volume, aspect ratio and diameter are simulated numerically to investigate the single effect of shape, size and their combination respectively. The shape effect is observed to present a linear relationship between the packing density and the volume fraction, while the size effect shows a trend of convex. The combined effect, as the case of the same diameter, can be considered as a linear superposition of the shape and size effect, since we find the particle size and shape determine the mixture density independently with no coupling terms. Accordingly, we propose an explicit empirical formula for evaluating the mixture density of binary spherocylinders, and the predicted densities agree well with the simulation results and previous empirical formula in all the cases of the same volume, aspect ratio and diameter, as well as some general cases. For verification, the monophasic packings of spherocylinders are simulated and the results coincide with previous works.
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► The particle shape and size affect the mixture density independently. ► A new explicit formula as a superposition of the shape and size is proposed. ► The shape effect shows a linear relationship of density and volume fraction. ► The size effect shows convex trend with the same aspect ratio and diameter.
Particle elongation is an important factor affecting the packing properties of rod-like particles. However, rod-like particles can be easily bent into non-convex shapes, in which the effect of ...bending should also be of concerned, To explore the shape effects of elongation and bending, together with the size and volume fraction effects on the disordered packing density of mixtures of non-convex particles, binary and polydisperse mixtures of curved spherocylinders are simulated employing sphere assembly models and the relaxation algorithm in the present work. For binary packings with the same volume, curves of the packing density versus volume fraction have good linearity, while densities are plotted as a series of equidistant curves under the condition of the same shape. The independence of size and shape effects on the packing density is verified for mixtures of curved spherocylinders. The explicit formula used to predict the density of binary mixtures, by superposing the two independent functions of the size and shape parameters, is extended to include a non-convex shape factor. A polydisperse packing with the shape factor following a uniform distribution under the condition of the same volume is equivalent to a binary mixture with certain components. The packing density is thus predicted as the mean of maximum and minimum densities employing a weighing method.
Sphericity, as one of the most important shape parameter for non-spherical objects, is extensively applied in evaluating the porosity or packing density of particles. In this paper, the sphericities ...of common non- spherical objects are deduced and investigated. Maximum sphericities and optimum shapes of these objects are presented as well. A decreasing order of sphericity from sphere （1.0） to regular tetrahedron （0.671） for objects with constant sphericity is given. Similar trends are found in most sphericity-aspect ratio relationships, which exhibit single Peak and the sphericity increases with the growth of aspect ratio before the peak point and decreases afterward. The peak loci of aspect ratio are all around 1.0 which makes the shape approaching to a sphere. The information in the paper could be useful as literature for general application.
We generate the maximally random jammed (MRJ) packings and maximally dense random packings (MDRPs) of bi-axially elongated superballs with different shape parameters. On the MRJ packing state, the ...packings of ellipsoids, general superellipsoids and cuboids are on different random degrees and the shape elongation effects on the disordered-packing densities are not uniform. The effects of order degree and particle shape are compounded. However, we find uniform shape elongation effects on the MDRP state. Bi-axial elongation will improve the random-packing densities. The packing densities reach the maximum when the aspect ratio is about 1.5 for all the surface shape parameters and oblateness. The influence of order degree is eliminated on the MDRP state, which demonstrates the advantages of the MDRP state as a platform for comparing the packing density of disordered packings. Our work helps to explore the shape effects on disordered packings of non-spherical particles.
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•We obtain the MRJ packings and MDRPs of biaxially elongated superballs.•We find uniform biaxial elongation effects for all the superballs on the MDRP state.•1.5 is a special aspect ratio value which corresponds to the maximal random-packing density.•Biaxial shape elongation effects are weakened with the increase of the surface shape parameter.
The shape of a frustum is a bivariate function of aspect ratio (w) and base radii ratio (c). To investigate the shape influences on the packing density of frustums, random packings of cones (c=0), ...truncated cones and cylinders (c=1) with various heights and diameters are studied through numerical simulations. An improved relaxation algorithm with assembly sphere models for non-spherical particles is applied in the numerical simulations, and the randomness of the packings of the frustums considered is verified. Base on the simulation results, the relationship between the packing density and shape parameters is illustrated, and an empirical formula is proposed to reflect the correlation. It shows that, for the particles having the same w, truncated cones can be packed denser than cones, but looser than cylinders. The packing density of truncated cones first increases and then decreases with the growth of w, while the packing density increases monotonically with the increase of c. No obvious peak is found on the curve of packing density versus c for the random packing of truncated cones, which is different from the reported results for ordered packing where a peak was identified. Furthermore, we observe that the packing density of truncated cones is a linear superposition of the c effect on w effect, and the effects of c and w on the packing density can be treated independently. The optimal aspect ratios of truncated cones, which give the highest packing densities, are all around 0.8. The highest packing densities of cylinders and cones are also the upper and lower bound of the random packing density of truncated cones.
The shape of a frustum is a bivariate function of aspect ratio (w) and base radii ratio (c). The packing density of truncated cones first increases and then decreases with the growth of w, but increases monotonically with the increase of c. The packing density of truncated cones is a linear superposition of the c effect on w effect. The optimal aspect ratios of truncated cones are all around 0.8. Display omitted
► The shape influences on the packing density of frustums are investigated. ► The sphere assembly model and relaxation algorithm are applied. ► The optimal aspect ratios of truncated cones are all around 0.8. ► An empirical formula is proposed to predict the packing density. ► The influence of shape parameters is further discussed.
Uniaxially variable (rod-like) particles are common in nature and industry. However, the aspect ratio effects on the random packings for differently shaped rod-like particles are not uniform by their ...innate definitions of aspect ratios. In this work, we propose new definitions of effective aspect ratios that take the surface shape information into account and observe uniform shape elongation effects on the random packing densities. The packing density reaches a maximal value with the effective aspect ratio to be about 1.5. We also observe symmetric high-density regions on the packing-density map. Finally, we carry out the Voronoi analysis and find that the surface shape of particles plays a more important role in changing the local packing properties than the aspect ratio. Our work provides a uniform definition for the aspect ratio of differently shaped rod-like particles and leads to a better understanding towards the particle shape effects on random packings.
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•We obtain the random packings of uniaxially variable superellipsoids.•We propose new definitions of effective aspect ratio for superellipsoids.•We observe uniform shape elongation effects on the random packing densities.•Symmetric high-density regions are observed on the packing density map.
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