Mehdi Pouragha

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 ...

Instability Analysis of Granular Media via a Purely Micromechanical Constitutive Model

In this paper, we develop a rate independent, incrementally linear constitutive model for 2D granular materials within a robust multiscale framework where micromechanical interactions and microstructural rearrangements between particles are being described statistically. The model when implemented into a finite element code allows us to explore the different microscopic states both inside and outside of the strain localization zone that develops during shearing in a biaxial test. A major finding is the discovery of similarities in microstructural characteristics inside a shear band during localized failure and critical state in diffuse failure.

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.