Richard Wan

Strain in Granular Media: Probabilistic Approach to Dirichlet Tessellation

AbstractDeformations in granular media are described by using a representation of the microkinematics of the underlying assembly through Dirichlet tessellation. Based on a probabilistic analysis of topological rearrangements induced by evolving microstructures in the assembly, homogenization is carried out within a multiscale approach—from deforming individual cells to cell network level—to eventually describe global strain in the granular ensemble. In contrast to other models in the literature, tessellation network properties are directly linked to physical microstructural characteristics of the granular assembly through local coordination number and fabric anisotropy. Because these microstructural variables dictate both strain and stress in a granular medium, this provides a route to establish a stress-strain relationship as an ultimate goal. In this paper, detailed attention is paid to the description of evolving fabric anisotropy and coordination number as a combination of dissipative microstructural ...

Directional plastic flow and fabric dependencies in granular materials

The constitutive modelling of granular materials both at the microstructural level and the continuum level is well established. Much recent effort has been devoted to the theoretical mechanics and computer simulations of granular media through discrete element modelling (DEM). The current study uses DEM to obtain theoretical insights and extract constitutive information such as the nature of the yield and plastic flow behaviour of granular materials. In particular, we look at the influence of granular fabric on the plastic deformation response under a number of conditions. As such, a representative element volume (REV) of a granular material idealized as a numerical DEM sample is subjected to different loading paths to reach the same stress states, but with different fabrics, on the plastic failure surface. At this stage, directional stress probes of equal magnitudes are applied, so that the strain response envelopes thus obtained represent characteristics of the increment of plastic strain, i.e. the nature of the flow rule. The discussion then focuses on the relationship between fabric, stress state, loading path, direction of the plastic strain increment, and whether this direction can be considered unique or not.

Strain Localization as a Function of Topological Changes in Mesoscopic Granular Structures

In this paper, the microphysical aspects leading to the occurrence of a localized failure were investigated by examining the initial emergence of ubiquitous potential slip planes and their link to the shear band development. A Discrete Element Model (DEM) representing a dense granular assembly was considered and subjected to a biaxial compression such that it undergoes localized failure into a persistent shear band. The paper includes both energetic and meso-structural analyses based on so-called minimal closed loops.

Micromechanical Modelling of Granular Materials Through Fabric and Coordination Number Anisotropies

Granular geomaterials involve microphysics at the various scales that give rise to distinct constitutive characteristics such as steady states, plastic limit states and unstable material behaviour. This paper is concerned with the statistics of coordination number and fabric anisotropy at the local level to impart microstructural information to the macroscopic description of the state of the material. As such the evolutions of coordination number (connectivity) distribution and anisotropy (contact normal) distribution curves with deformation history and their correlations are determined through DEM (Discrete Element Modelling). These results are useful as they enter as joint probability distribution functions into homogenization expressions during upscaling to a continuum constitutive model enriched with microstructural information.