Colin Thornton

A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres

Abstract The paper considers the normal impact of elastic-perfectly plastic spheres, with and without interface adhesion, and presents an analytical solution for the coefficient of restitution which is expressed in terms of the impact velocity, the critical sticking velocity and the velocity below which the interaction is assumed to be elastic.

Discrete particle-continuum fluid modelling of gas–solid fluidised beds

Abstract This paper describes a fluidised bed model developed from the DEM-based Aston granular dynamics code in which the solid–solid interaction rules are based on theoretical contact mechanics thereby enabling particles to be directly specified by material properties such as friction, elasticity, elasto-plasticity and auto-adhesion. For the gas phase which is treated as a continuum, the equations of motion are evaluated with a Navier–Stokes solver originally developed for a two-fluid model. The coupling of the discrete particulate phase and the continuous fluid phase equations is an important attribute of such Eulerian–Lagrangian models and two forms of the coupling terms have been examined: one employing the pressure gradient force (PGF model) and the other a buoyancy force based on the fluid density (FDB model). Uniform fluidisation simulations for a superficial gas velocity of 2.5 m s −1 and bed pressure drop-superficial gas velocity simulations for gas flows from 0.3 to 3.0 m s −1 have been carried out in a pseudo-2D bed of 2400 4 mm -diameter spherical particles using the two model formulations. The two formulations yielded minor differences in qualitative fluidisation behaviour with a gas flow of 2.5 m s −1 . However, there were significant differences in the pressure drop-superficial gas velocity profiles in the fixed bed regime and corresponding significant differences in the prediction of minimum fluidisation velocity. The PGF model showed the best agreement with pressure drop-superficial gas velocity trends and minimum fluidisation velocities predicted by empirical correlations. Two new methods for determining the minimum fluidisation velocity have been introduced and found to give predictions in good agreement with those obtained from pressure drop-superficial gas velocity profiles and empirical correlations.

Impact of elastic spheres with and without adhesion

Abstract The paper considers the load—displacement behaviour at the contact of two adhered elastic spheres under combined normal and tangential loading. The first part of the paper deals with computer simulated oblique impact of two elastic spheres with friction. The normal and tangential contact stiffnesses are modelled according to the theories of Hertz, see Johnson ( Contact Mechanics , Cambridge University Press, Cambridge, 1985) and Mindlin and Deresiewicz, ( J. Appl. Mech., Trans. ASME, 20 (1953) 327) and the results show excellent agreement with the experimental work of Maw et al. ( J. Lubrication Tech. Trans., ASME, 103 (1981) 74). The paper then considers impact in the presence of adhesion using the theory developed by Johnson et al. ( Proc. Roy. Soc. Lond., A, 324 (1971) 301) for colinear impact. A new theory, combining the previous work of Savkoor and Briggs ( Proc. Roy. Soc. Lond., A. 356 (1977) 103) and Mindlin and Deresiewicz ( J. Appl. Mech. Trans. ASME, 20 (1953) 327), is presented to describe the tangential behaviour. The new theory differs from the previous models in that a new sliding criterion is proposed. Experimental observations for polyethylene-terephthalate monofilaments, Briscoe and Kremnitzer, ( J. Phys. D: Appl. Phys., 12 (1979) 505) show good agreement with the proposed sliding criterion. Finally, the results of computer simulated oblique impact of elastic spheres with and without adhesion are compared.

Numerical simulation of the impact fracture and fragmentation of agglomerates

Computer simulations of agglomerates impacting a wall have been carried out using the distinct element method. The agglomerates comprised 1000 primary particles in a two-dimensional array. Autoadhesive and frictional interaction laws between the primary particles were employed. Results are presented for a range of impact velocities and surface free energies of the particles. Three regimes of behaviour were observed depending on the relative magnitudes of these quantities; the regimes may be described as shattering, semi-brittle fracture and elastic rebound. The qualitative trends found in the current work are consistent with certain features of phenomena observed in experimental studies and lead to an improved understanding of the microscopic factors that influence the fragmentation behaviour of granular solids.

Discrete particle simulation of agglomerate impact coalescence

Abstract This paper describes computer simulations of pendular state wet agglomerates undergoing pair-wise collisions. The simulation method is based upon a ‘soft’ discrete particle formulation. Each agglomerate comprised 1000 primary particles with the interparticle interactions modelled as the combination of the solid–solid contact forces and also the forces developed at discrete liquid bridges between neighbouring particles. For the range of collisional velocities implemented, the agglomerates invariably coalesced. The energy dissipated was associated primarily with the viscous resistance of the fluid and the interparticle friction rather than by liquid bridge bond rupture. The structure of the resultant coalesced agglomerate was highly disordered and depended on the impact velocity. As the impact velocity approached zero, the agglomerates behaved like two rigid bodies bonded together. When the impact velocity was increased, the size of the circumscribing sphere of the coalesced agglomerate decreased and reached a minimum value at a critical velocity above which an increase in the circumscribing sphere size occurred due to extensive flattening. An increase in the viscosity of the interstitial fluid resulted in an increase in the proportion of energy dissipated by viscous resistance and a decrease in the proportion dissipated due to interparticle friction. An increase in the fluid viscosity also resulted in an increase in the critical impact velocity at which the size of the circumscribing sphere of the coalesced agglomerate was a minimum.

Rebound behaviour of spheres for plastic impacts

Abstract This paper presents a study on the rebound behaviour of spheres impacted normally against a target wall using finite element methods. The emphasis is on the prediction of the coefficient of restitution and the effects of material properties and impact velocities on the rebound behaviour of the sphere. Finite deformation during plastic impact is addressed. The finite element results show that, for impacts of small plastic deformation, the coefficient of restitution is mainly dependent on the ratio of the impact velocity Vi to the yield velocity Vy which is consistent with those predicted by the theory of impact mechanics; while for impacts of finite-plastic-deformation it is also dependent on the ratio of the representative Youngs Modulus E* to the yield stress Y. The FEA results suggest that for impacts of finite-plastic-deformation the coefficient of restitution can be approximated to be proportional to [(Vi/Vy)/(E*/Y)]−1/2.

Numerical simulations of agglomerate impact breakage

Abstract The paper reports granular dynamics simulations of a dense spherical agglomerate consisting of a random polydisperse system of autoadhesive particles impacting orthogonally with a target wall. A range of impact velocities has been examined which resulted in rebound, fracture or shattering depending on the magnitude of the impact velocity specified. Visualisations of agglomerate breakage are presented together with data on the evolution of the target wall force, the kinetic energy of the agglomerate, the number of bonds broken and the amount of debris detached during a collision. The evolution of the processes preceding agglomerate breakage is also discussed.

Impact breakage of particle agglomerates

Abstract The paper examines the various factors that influence the breakage of particle agglomerates resulting from impact. Numerical simulations of polydisperse spherical agglomerates impacting orthogonally on a target wall have been performed to study the effects of impact velocity, solid fraction, contact density, and the local arrangement of particles near the impact zone. Results of simulations show distinct fracture patterns for dense agglomerates above a critical impact velocity whereas for loose agglomerates disintegration occurs under identical testing conditions. Either fracture or disintegration may occur for agglomerates with an intermediate packing density. It is also demonstrated that, for agglomerates with intermediate packing densities, the mode of failure can change from disintegration to fracture by either increasing the contact density or changing the location on the agglomerate surface, which is used as the impact site.

A numerical examination of shear banding and simple shear non-coaxial flow rules

Strain localisation and shear band formation is frequently observed during the handling and flow of dense phase particulate materials. However, a complete understanding of how shear bands form and what happens inside shear bands is still lacking. In order to address this problem, discrete particle simulations have been carried out to examine the detailed processes that occur at the grain scale associated with the initiation and development of shear bands. To reliably identify the continuum model applicable within a shear band is difficult due to the small number of particles/contacts involved. However, it is normally accepted that the mode of deformation within a shear band is one of simple shear. Consequently, simple shear simulations have been performed in order to determine the evolution of the stress tensor, dilation rate, and the principal directions of stress and strain-rate. It is demonstrated that the corresponding non-coaxial flow rule is equivalent to that suggested by Tatsuoka et al. (Géotechnique 38 148 (1988)). Furthermore, at fully developed flow when there is no further change in volume, the stress and strain-rate directions are coaxial and the flow rule is that proposed by Hill (The Mathematical Theory of Plasticity (Oxford University Press, 1950) p. 294).

Quasi-static shear deformation of a soft particle system

Abstract The paper presents results of numerical simulations of quasi-static shear deformation of a polydisperse system of soft elastic spheres with interface friction and adhesion. Both axisymmetric compression and axisymmetric extension tests have been simulated. In each case, two shear simulations were performed: one in which the mean stress was maintained constant and the other in which the system was deformed at constant volume. In addition to the macroscopic stress–strain behaviour obtained, details are provided about the evolution of various internal variables associated with the micromechanics occurring at the particle scale.