Incorporating rolling resistance and contact anisotropy in micromechanical models of granular media

Abstract

Recent findings from non-invasive experiments have shown that rolling resistance and contact anisotropy have a significant influence on the bulk behaviour of granular media. To date, however, there has been no generalised continuum model that accounts for both of these factors. In this paper, we propose a method by which rolling resistance and contact anisotropy may be introduced in a micropolar model of granular media. To capture key microstructures like shear bands, a homogenisation procedure on the scale of a particle and its local void space is developed.

Introduction

Deformation of densely packed granular assemblies under quasistatic conditions is a problem of great interest in a vast number of industrial settings worldwide. These include: storage, handling and processing of chemical and pharmaceutical powders, agricultural grains and food products [5]; design and maintenance of granular pavements and unsealed roads [22]; and management of vehicle-induced soil compaction in forestry, mining, and military training operations [20]. Research efforts on all fronts—experimental, theoretical and computational—remain unabated (see, for example, Herrmann et al. [6] and Oda and Iwashita [15] and the references cited therein), with several critical advances emerging over the last decade. Specifically, experimental techniques that non-invasively probe the internal structures of deforming granular media have now been successfully implemented [16]. A key finding from these studies has been the importance of particle rotations and, in particular, rolling resistance. Contrary to what was previously believed, these studies have also shown that rolling contact, rather than sliding contact, dominated the final stages of shear banding. Since shear bands are the precursors of material failure, this finding raises an important question: to what extent does rolling resistance contribute to failure of granular media?

The 1990s also witnessed the development of discrete element models of granular media which specifically account for rolling resistance. These models showed dramatic improvements in their ability to simulate real granular behaviour. In particular, Sakaguchi et al. [19] achieved more realistic results in simulations of granular flow, while Zhou et al. [23] identified rolling resistance to be a key factor in achieving stability in their sand pile simulations. Iwashita and Oda [7] recently performed an extensive numerical investigation into the effects of rolling resistance in the formation and evolution of shear bands. By introducing rolling friction they were able to achieve a distinct band, inside of which relatively large voids were formed and particles were found to rotate extensively resulting in high gradients of particle rotation at the boundaries of the band. These findings were consistent with observations made from non-invasive experiments [16]. In particular, the success of the ‘Modified Distinct Element Model’ (MDEM) by Iwashita and Oda [7] in capturing large voids inside shear bands is of great importance as the formation and evolution of voids are directly linked with induced contact anisotropy [18].

In the development of generalised continuum models of granular media, the work of Mühlhaus and Vardoulakis [12] has been pivotal in demonstrating how particle rotations may be addressed using micropolar theory. Since then, micropolar models have been developed which incorporate either the influence of rolling resistance [4] or contact anisotropy [9]; however, there has been no model which captures the effects of both of these in granular media. Moreover, past models are typically based on homogenisation procedures in which microstructural properties are averaged over a representative volume element (or ‘RVE’) that contains a large number of particles. Consequently, important microstructural phenomena with characteristic length scales that are below that of an RVE (e.g. shear bands) are effectively ‘smeared out’ in the modelling process.

In this paper, we consider a granular assembly consisting of uniformly sized circular rods. We show how rolling resistance and contact anisotropy may be incorporated in a non-local micropolar model of this system with a resolution that is at the level of a particle and its immediate neighbours. A key feature of this method is that it allows for an explicit connection to be made between both the local and global void distributions and the induced contact anisotropy. The results show that both rolling resistance and contact forces contribute to the couple stress; this conclusion is in contrast with that of Oda [14] in which couple stress is asserted to be solely governed by rolling resistance.