The discrete modelling and understanding of the particle dynamics in fluidized bed apparatuses, mixers, mills and others are based on the knowledge about the physical properties of particles and their mechanical behaviour during slow, fast and repeated stressing. In this paper model parameters (modulus of elasticity, stiffness, yield pressure, restitution coefficient and strength) of spherical granules ( γ -Al 2 O 3 , zeolites 4A and 13X, sodium benzoate) with different mechanical behaviour have been measured by single particle compression and impact tests. Starting with the elastic compression behaviour of granules as described by Hertz theory, a new contact model was developed to describe the force-displacement behaviour of elastic-plastic granules. The aim of this work is to understand the energy absorption during compression (slow stressing velocity of 0.02 mm/s) and impact (the impact velocity of 0.5-4.5 m/s) of granules. For all examined granules the estimated energy absorption during the impact is found to be far lower than that during compression. Moreover, the measured restitution coefficient is independent of the impact velocity in the examined range and independent of the load intensity by compression (i.e. maximum compressive load). In the case of repeated loading with a constant load amplitude, the granules show cyclic hardening with increasing restitution coefficient up to a certain saturation in the plastic deformation. A model was proposed to describe the increase of the contact stiffness with the number of cycles. When the load amplitude is subsequently increased, further plastic deformation takes place and the restitution coefficient strongly decreases.

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The fundamentals of particulate solids consolidation and flow behaviour using a reasonable combination of particle and continuum mechanics are explained. By means of the model "stiff particles with soft contacts" the combined influence of elastic, plastic and viscoplastic repulsion in particle contacts is derived. Consequently, contact normal force displacement FN(hK) and adhesion force models FH(FN) are presented to describe the stationary, instantaneous and time consolidation behaviour in particle contacts as well as in the bulk. On this particle mechanical basis, the stationary, instantaneous and time yield loci as well as uniaxial compressive strength O"c (0" 1), effective angle of internal friction tf>e(0" 1), bulk density pb(0"1) are derived and shown for a very cohesive sub-micron titania powder. Finally, these models in combination with accurate shear cell test results are used as constitutive functions for computer aided silo design for reliable flow and pressure calculations.