On the linear elastic responses of the 2D bonded discrete element model

Gao‐Feng Zhao & Qiuyue Yin & Adrian R. Russell & Yingchun Li & Wei Wu & Qin Li

The bonded discrete element model (DEM) is a numerical tool that is becoming widely used when studying fracturing, fragmentation, and failure of solidsin various disciplines. However, its abilities to solve elastic problems are usually overlooked. In this work, the main features of the 2D bonded DEM whichinfluence Poisson's ratio and Young's modulus, and accuracy when solvingelastic boundary value problems, are investigated. Outputs of numerical simulations using the 2D bonded DEM, the finite element method, a hyper elasticityanalysis, and the distinct lattice spring model (DLSM) are compared in theinvestigation. It is shown that a shear interaction (local) factor and a geometric(global) factor are two essential elements for the 2D bonded DEM to reproducea full range of Poisson's ratios. It is also found that the 2D bonded DEM mightbe unable to reproduce the correct displacements for elastic boundary valueproblems when the represented Poisson's ratio is close to 0.5 or the long‐rangeinteraction is considered. In addition, an analytical relationship between theshear stiffness ratio and the Poisson's ratio, derived from a hyper elasticityanalysis and applicable to discontinuum‐based models, provides good agreement with outputs from the 2D bonded DEM and DLSM. Finally, it is shownthat the selection of elastic parameters used the 2D bonded DEM has a significant effect on fracturing and fragment patterns of solids.

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