Grain‐scale‐based simulation of granular material

Abstract

AbstractIn recent years, new developments in experimental mechanics, e. g., particle‐tracking methods using X‐ray micro‐tomography, have provided a new insight into the material behaviour of granular media. The possibility to capture the individual grain displacement and rotation of all particles within a sample provides a new fundament for a reliable numerical simulation of granulates. This is, in particular, the case for deformation localisation in shear zones as they are observed in bi‐ and triaxial compression tests, where the exact thickness of the localised zone as well as the amount of accompanying grain displacements and rotations are measurable in a precise and direct way. In this context, the Discrete‐Element (DE) Method has become a promising and frequently used modelling technique for granular materials. In contrast to macroscopically based continuum‐mechanical approaches, the DE approach treats each particle as a rigid and uncrushably body and is, therefore, defined on a microscopic level of description. This consequently allows a direct comparison with experimental data from grain‐scale tracking methods. In the present contribution, the DE method is applied in order to solve problems of localisation in granular media. Therefore, constitutive inter‐particle contact laws are formulated for forces and torques which are transferred between interacting particles. With a given solution of initial‐boundary‐value problems on the microscale, a computational homogenisation procedure leads to macroscopic quantities purely stemming from microscopic information. Herein, a particle‐centre‐based volume averaging technique leads to macroscopic quantities which correspond to quantities known from micropolar continuum theories. The contribution presents a framework for the homogenisation in all time steps in a fully 3‐dimensional context and discusses the activation of micropolar effects in the localised zone. Furthermore, the admissible size of the chosen Representative Elementary Volume (REV) is addressed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)