Ph.D Thesis | |

Ph.D Student | Yael Roichman |
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Subject | Force Distribution in Static Granular Piles |

Department | Department of Physics |

Supervisor | Full Professors Levine Dov |

A striking characteristic
of stress transmission in granular matter is the highly singular lines along
which stress propagates. These lines, termed *force chains*, are
indicative of the complex nature of stress propagation in granular matter. A
model which accommodates these singularities is the *force chain model*,
which attributes stress transmission in granular materials to the propagation,
splitting and merging of force chains. In this work, we study the force chain
model on three different length scales:

the transition from the microscopic scale to the mesoscopic scale using a non-interacting Monte-Carlo simulation, the transition from the mesoscopic scale to the macroscopic scale by solving numerically a highly interacting model, the asymptotic limit by calculating a new constitutive relation for nearly isotropic granular materials in a full interacting model. We find that the response function of a homogeneously prestressed isotropic granular material is similar to the response of an elastic material at all length scales (at least to first order in the perturbing force) even when mergers are taken into account. We find numerically that stress profiles of various small systems differing in loading or construction history can be qualitatively reproduced without including mergers, however, the inter-particle force distribution is obtained only when mergers are included. Inserting interactions into the Master Equation for the force chain density results in a non-linear model. We show numerically that non-linear effects are significant mainly in highly stressed systems like a uniformly stressed slab or for applied forces in close proximity.