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The developments of multi-level computational methodologies for discrete element modelling of granular materials / Tingting Zhao
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DOI (Published version): 10.23889/Suthesis.52441
Granular materials are prevalent in this world while their non-trivial behaviour, which may resemble solid, liquid and/or gas under di˙erent circumstances, is still poorly understood. The challenging mechanics and dynamics of granular materials combined with their ubiquity have made this topic espec...
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Granular materials are prevalent in this world while their non-trivial behaviour, which may resemble solid, liquid and/or gas under di˙erent circumstances, is still poorly understood. The challenging mechanics and dynamics of granular materials combined with their ubiquity have made this topic especially interesting to study. The discrete element method (DEM) is a reliable and e˙ective numerical technique to model many scientific and engineering problems involving granular materials but it is still not a fully mature method. Considering the unique properties of granular materials and the inadequate features of the DEM, this thesis improves the current DEM from three di˙erent aspects and scales.On the micro scale at the particle level, a novel contact model is developed by introducing the statistical Greenwood Williamson (GW) model which can consider the stochastic surface roughness of particles. Two non-dimensional forms of the original formulations are derived which can reduce the computational costs significantly. A Newton-Raphson based numerical solution is proposed which can solve the inter-dependence problem involved. A theoretical inconsistency of the classic GW model is deduced which leads to the development of the extended elastic GW (E-GW) model. An empirical normal contact law is obtained by the curve-fitting method and can be incorporated into the DEM code to conduct the one and three dimension compression tests. An extended elastic-plastic GW (EP-GW) model is developed to allow the plastic deformation at the asperities. Furthermore, the tangential contact model and thermal conductivity model are proposed.On the meso scale at the sample level, a new packing characterisation method is proposed based on the digitalised image matrix of a packing and the subsequent application of the principal component analysis (PCA) with which the configuration of the particle assemblies can be evaluated quantitatively. The procedures of the packing digitalisation and formation of packing image are established for both 2D and 3D cases. The obtained PCA results of the packing image matrix can be revealed by the proposed principal variance function (PVF) and dissimilarity coeÿcient (DC). The values of PVF and DC can indicate the magnitude of e˙ects on a packing caused by the configuration randomness, the particle distribution, the packing density and the particle size distribution. The uniformity and isotropy of a packing can also be investigated by this PCA based approach.On the macro scale at the level of real industrial applications, the existing coarse graining methods are carefully analysed by the exact scaling law and the e˙ective thermal properties of particulate phase change materials are derived by the homogenisation method. An enthalpy based discrete thermal modelling framework for particulate systems with phase change materials is developed which can consider both the heat conduction process and the phase change transition. This proposed methodology is assessed by solving a particle version of the classic one-phase Stefan melting problem. Additional numerical simulations are also conducted to illustrate the e˙ectiveness of this modelling framework.
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College of Engineering