Nonlinear acoustics in granular assemblies

We present a brief review of the problem of acoustic propagation in granular media and discuss recent progress on nonlinear acoustics in granular media. The presentation emphasizes the solitary wave like properties of impulse propagation in granular media at vanishingly small loading conditions and discusses the possible spectroscopic applications of nonlinear impulse acoustics in the detection of buried inclusions. Received: 30 March 2000     

DEM study of monodisperse granular flow in a pipe

Flow of granular material through a pipe has several industrial applications but maintaining a uniform mass flux is quite challenging. In this work, monodisperse granular flow (non-turbulent and non-dense phase particle transport) through a vertical pipe was simulated using discrete element method (DEM). Effects of different geometric and granular parameters on mass flux of cohesive and non-cohesive solids were analyzed and evaluated. Several important parameters and their effects on mass flux were studied like: L/D ratio, pipe diameter to particle diameter ratio (D/D_p), Poisson ratio, and pipe inclination angle. Furthermore, effects of moisture content and Bond number on mass flux were also investigated. These parameters influenced mass flux except Poisson ratio which showed no significant improvement in mass flux upon increasing the value of this ratio.     

Exponential distribution of force chain lengths: a useful statistic that characterizes granular assemblies

The distribution of the lengths of force chains in 2D granular assemblies of photoelastic disks was found to decay exponentially, with the decay length a quantitative measure of the way force is applied to the system. A plausibility argument is provided for why this statistic displays an exponential decay.     

Effects of grain sizes, shapes, and distribution on minimum sizes of representative volume elements of cubic polycrystals

In the literature the concept of representative volume element (RVE) was introduced to correlate the effective or macroscopic properties of materials with the properties of the microscopic constituents and microscopic structures of the materials. However, to date little quantitative knowledge is available about minimum RVE sizes of various engineering materials. In our recent paper [J. Mech. Phys. Solids 50 (2002) 881], a new definition of minimum RVE size was introduced based on the concept of nominal modulus. Numerical experiments using the finite element method (FEM) were then carried out for determining the minimum RVE sizes of more than 500 cubic polycrystals in the plane stress problem, under the assumption that all grains in a polycrystal have the same square shape––called the simple polycrystal model. The major finding is that the minimum RVE sizes for effective elastic moduli have a roughly linear dependence on crystal anisotropy degrees. The present paper takes into account the effect of grain sizes, shapes, and distribution on the minimum RVE sizes for real cubic polycrystals that are formed by crystallization processes. Similar roughly linear dependence is found again, with the slope about 19% lower than that in the simple polycrystal model. This finding is interesting and useful because numerical experiments on minimum RVE sizes for a large number of crystals are quite time-consuming and the simple polycrystal model reduces significantly the FEM pre- and post-processing works. This should be particularly true in numerically testing minimum RVE sizes for three-dimensional polycrystals and for nonelastic properties in future works. With a maximum relative error 5%, all the polycrystals tested have a minimum RVE size of 16 or less times the grain size.     

Enhanced continua and discrete lattices for modelling granular assemblies

This article discusses the derivation of continuum models that can be used for modelling the inhomogeneous mechanical behaviour of granular assemblies. These so-called kinematically enhanced models are of the strain-gradient type and of the strain-gradient micro-polar type, and are derived by means of homogenizing the micro-structural interactions between discrete particles. By analysis of the body wave dispersion curves, the enhanced continuum models are compared to corresponding discrete lattice models. Accordingly, it can be examined up to which deformation level the continuum models are able to accurately describe the discrete particle behaviour. Further, the boundary conditions for the enhanced continuum models are formulated, and their stability is considered. It is demonstrated how to use the body wave dispersion relations for the assessment of stability.     

A toroidal approximation of capillary forces in polydisperse granular assemblies

In this paper we propose a numerical procedure for the prediction of capillary forces in polydisperse granular assemblies at a degree of moisture content that corresponds to the so-called pendular regime. The capillary force model is adopted within the Laplace–Young framework with a toroidal approximation of the liquid bridge geometry. Governing equations are first derived in a form that highlights the role of intrinsic parameters such as inter-particle separation distance, ratio of particle radii and liquid volume. A proper scaling of these equations is adopted so that the solution applies to any particle pair configuration. Numerical integration algorithms are provided in a way that facilitates implementations in macroscopic procedures for computer simulations. A qualitative evaluation is undertaken to highlight model predictions of the effects on capillary force of various intrinsic parameters that characterise the particle pair and liquid bridge. The model is validated against the experimental results provided by Willet et al. (Langmuir 16:9396–9405, 2000) for a wide range of liquid volumes and particle-pair polydispersity.     

Plane wave propagation in 2D and 3D monodisperse periodic granular media

Plane wave propagation in periodic ordered granular media comprising of elastic spherical particles is investigated. The spheres are under zero precompression and are assumed to interact via the Hertzian contact potential. Various two- and three-dimensional granular structures such as hexagonal packing (2D and 3D), face-centered cubic and body-centered cubic packings are considered in the present study, with the plane impact either normal or oblique to the granular system. For the normal impact case, 1D chains equivalent to the 2D and 3D structures are obtained. A universal relation between the wavefront speed and the force amplitude is derived, valid for all the granular structures studied. In the angular impact case, the shear component of the amplitude of the particle velocity is found to initially decay exponentially and further in a series of linear regimes. By employing simpler models, semi-analytical predictions are obtained for the decay of shearing effect.     

Pore size distribution,grain growth,and the sintering stress

The effects of a pore size distribution and of the pore separation on the sintering stress is examined using a simple model. The sintering stress is found to be proportional to the mean of the pore sizes weighted according to the Voronoi cell pertaining to each pore, rather than to the simple pore size average. Large heteropores are shown to have little effect on the mean effective sintering stress. Decreases in pore coordination number of such pores, resulting from grain growth can significantly increase the stress intensification factor. The near-constancy of the sintering stress, observed experimentally for many powders over a wide range of sintered densities, does not directly follow from the simple model. It is argued that this constancy results from pore shrinkage, due to densification, which is compensated by pore growth due to coarsening.     

Quantitative evaluation of the effect of irregularly shaped particles in sheared granular assemblies

Assemblies of irregularly shaped particles exhibit higher shear strengths than assemblies of circular particles. We performed a series of 2D discrete element simulations to demonstrate that this particle shape effect is related to the induced moment and the additional dilation at the contacts between particles. We proposed a mechanically based particle shape index that is closely related to such contact behavior. A simple structural model is also investigated to clarify the micromechanical role of the particle shape.     

Ceramic nanoparticle assemblies with tailored shapes and tailored chemistries via biosculpting and shape-preserving inorganic conversion

A novel biosynthetic paradigm is introduced for fabricating three-dimensional (3-D) ceramic nanoparticle assemblies with tailored shapes and tailored chemistries: biosculpting and shape-preserving inorganic conversion (BaSIC). Biosculpting refers to the use of biomolecules that direct the precipitation of ceramic nanoparticles to form a continuous 3-D structure with a tailored shape. We used a peptide derived from a diatom (a type of unicellular algae) to biosculpt silica nanoparticle based assemblies that, in turn, were converted into a new (nonsilica) composition via a shape-preserving gas/silica displacement reaction. Interwoven, microfilamentary silica structures were prepared by exposing a peptide, derived from the silaffin-1A protein of the diatom Cylindrotheca fusiformis, to a tetramethylorthosilicate solution under a linear shear flow condition. Subsequent exposure of the silica microfilaments to magnesium gas at 900 degrees C resulted in conversion into nanocrystalline magnesium oxide microfilaments with a retention of fine (submicrometer) features. Fluid(gas or liquid)/silica displacement reactions leading to a variety of other oxides have also been identified. This hybrid (biogenic/synthetic) approach opens the door to biosculpted ceramic microcomponents with multifarious tailored shapes and compositions for a wide range of environmental, aerospace, biomedical, chemical, telecommunications, automotive, manufacturing, and defense applications.     

Analysis and DEM simulation of granular material flow patterns in hopper models of different shapes

By using the discrete element method (DEM) a comparison and observations on material flow patterns in plane-wedged, space-wedged, and flat-bottomed hopper were accounted for. Numerical results obtained by combining data of individual particles, statistical processing of particle assemblies and evaluation of the field variables provided the essential characteristics for different regimes of the discharge flow (within steady or unsteady state of flow) and the differences in differently shaped hoppers due to different microscopic inter-particle friction. For validation of the performed simulations, velocity patterns developed in three-dimensional flat-bottomed hopper containing 20,400 pea grains were also analysed. To represent the continuum by avoiding the local effects produced by the individual grains, the simulation results were focused on the mean velocity distributions with data smoothening. The effect of rolling resistance on granular material flow was also considered.     

Transient behavior of granular materials with symmetric conditions for tumbler shapes and fill fractions

The purpose of this research is to continue to find the mechanism behind transient granular behavior. The granular motion in circular tumblers can be described as steady-state, since there is no feature to disrupt the consistency of the top free-surface flowing layer. In polygon tumblers however, the available space for the free surface is perpetually changing, which creates unsteady flow behaviors. The effect of tumbler size and speed were studied previously in a triangular tumbler whereas this follow-up research investigates the effect of both the tumbler shape and fill fraction. For the experiment, various amounts of zirconium silicate beads generate a fluctuating flowing layer inside quasi-2D rotating tumblers of triangle and square shapes. Symmetric fill fractions generate the same flowing layer dimensions but results indicate the rate of increasing or decreasing space at the free surface affects the dynamics of the angle of repose. The balance between the potential and kinetic energy causes the flowing layer and angles of repose to appear as an optimized functional form of a catenary, which is much more apparent in the triangular tumbler with upstream and downstream dimensions changing out of phase compared to the square tumbler where the parallel sides act in-phase with one another.     

Pore size and pore volume effects on alumina and TCP ceramic scaffolds

Controlled porosity alumina and β-tricalcium phosphate ceramic scaffolds with pore sizes in the range of 300–500 μm and pore volumes in the range of 25–45% were processed using the indirect fused deposition process. Samples having different pore sizes with constant volume fraction porosity and different volume fractions porosity with a constant pore size were fabricated to understand the influence of porosity parameters on mechanical and biological properties. In vitro cell proliferation studies were carried out with OPC1 human osteoblast cell line for 28 days with different scaffolds. Variation in pore size did not show any conclusive differences, but samples with higher volume fraction porosity showed some evidence of increased cell growth. Volume fraction porosity also showed a stronger influence on the mechanical properties under uniaxial compression loading. Compression strength dropped significantly for samples with higher volume fraction porosity, but changed marginally when only the pore size was varied.     

Micro-mechanical analysis and modelling of granular materials loaded at constant volume

The present paper is devoted to the analysis and the modelling of the local phenomena, which are observed in a two-dimensional granular media loaded at constant volume. A micro-mechanical approach is followed here combined with a computer simulation method. Local phenomena observed during test are used to provide some necessary elements to build realistic models. The importance of the induced anisotropy during the test is especially shown, as well as its necessary link to the dilatancy. To illustrate the study a model based on a micro-mechanical approach is validated.     

Material transport in the free volume of a fixed granular bed

The hydrodynamic state in the free volume of a granular bed during fluid flow through it is investigated. A mathematical model is proposed to describe material transport. Its parameters are determined experimentally.Translated from Inzhenerno-Flzicheskii Zhurnal, Vol. 25, No. 1, pp. 36–41, July, 1973.     

Effects of particle shapes to achieve angle of repose and force displacement behaviour on granular assembly

Circular or spherical particles in Discrete Element Method (DEM) possess limitations on achieving desired angle of repose for some granular assemblies. However, by using various shapes/clumps of particles, the limitation posed by the circular or spherical particles on achieving angle of repose can be minimized. In this paper, 2D DEM simulation has been used to investigate the effect of particle shapes on (a) angle of repose, where the aim is to achieve the angle of repose of 35° observed in a laboratory scale sand pile experiment, and (b) force displacement behaviour of granular assembly. The simulated results show that the particle shapes have strong influence on the angle of repose but have a less effect on force displacement behaviour on the granular assembly.