A new approach for calculating strain for particulate media

Discrete element modelling is a viable alternative to conventional continuum-based analysis for analysing problems involving localized deformations of particulate media. However, to aid in the interpretation of the results, it is useful to express the results of discrete element analyses in terms of the continuum parameters of stress and strain. A number of homogenization methods have been proposed to calculate strain in discrete systems; however, two significant limitations of these methods remain. First, none of these methods incorporate particle rotation effects satisfactorily, although significant particle rotation occurs in shear bands in both physical tests and numerical simulations of granular materials. Additionally, observations of the particle displacement fields in shear bands in granular materials indicate that the displacements within the localizations are erratic. Consequently, existing linear, local interpolation approaches produce substantial variations in the strain values calculated in adjacent elements in the region of localization, hindering clear visualization of the strain localization as it evolves. A new method of domain discretization for calculating strain is proposed. This method is capable of capturing particle rotation and employs a non-local meshfree interpolation procedure capable of smoothing the erratic displacements in strain localizations, which better defines their evolution. The proposed method is validated for problems involving both two and three dimensions. A number of methods are compared with the proposed method and pertinent insights are made. Copyright (C) 2003 John Wiley Sons, Ltd.