Stress characterization in isostatic granular materials [electronic resource]

Stress propagation in granular media is an interesting and relatively open research problem. Compared to liquids or elastic solids, stress patterns in granular media show unusual features. For example, the nonuniform stress fields that have been observed in many experimental and numerical studies of granular systems cannot be readily explained with conventional models. The primary challenge in understanding of the nonuniform stress patterns in granular systems lies in the development of a continuum stress model. Central to the development of such a model is the derivation of a constitutive equation that would close the system of balance equations. Isostatic granular systems play a key role in the understanding of nonuniform stress fields. Modeling of stress fields at the macroscopic level for isostatic granular systems requires introduction of stress-structure constitutive relations instead of conventional stress-strain relations. In particular, we focus on the constitutive relation proposed by Ball and Blumenfeld for two-dimensional granular systems, which couples the local geometry and the continuum stress tensor at the grain level. The resulting continuum model cannot be readily applied macroscopically since geometric averaging, such as area averaging, for coarse-graining the parameters of the constitutive equation, also known as the fabric tensor, leads to a zero fabric tensor. To address the issue Blumenfeld suggests to upscale on a specific subset of the grains in the domain. Our analytical evaluations, as well as numerical experiments, show that the suggested upscaling approach can be applied to a specific family of granular materials. To evaluate the accuracy of the proposed continuum model we compare the stress behavior, as predicted by the continuum model, with discrete force solutions. We argue that solving for the discrete forces under isostatic conditions is different from the common practice used in Discrete Element Modeling, in the sense that isostatic structures must remain intact during the process. Despite the conventional assumption in the field, we demonstrate that an arbitrary structure of dry cohensionless grains with proper average number of contacts per grain may not comprise a physical isostatic system. Consequently, we present an algorithm to check if there exists a boundary load under which a given structure can remain static. We also develop an algorithm for computation of intergranular forces of an isostatic system under an under-determined boundary load, which resembles the boundary load of the continuum simulation. We observe minor discrepancies between the discrete force solution, assumed to reflect the actual physical processes, and the predictions of the continuum model. Utilizing the discrete force solution, we propose an alternative model-fitting based technique for estimation of the fabric tensor, which enables us to obtain a non-zero fabric tensor for the constitutive equation at the macroscopic level.

Keywords: Energy Resources Engineering.
Advisor: Gerritsen Margot (Margot G.) primary advisor. Thesis advisor
Benson Sally advisor. Thesis advisor
Blumenfeld Raphael