2015-Sustainable Industrial Processing Summit
SIPS 2015 Volume 1: Aifantis Intl. Symp. / Multiscale Material Mechanics
| Editors: | Kongoli F, Bordas S, Estrin Y |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2015 |
| Pages: | 300 pages |
| ISBN: | 978-1-987820-24-9 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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Internal Structure of Granular Media and its Determination Problem
S M Patil1;1INDIAN INSTITUTE OF SCIENCE, Bangalore, India;
Type of Paper: Regular
Id Paper: 171
Topic: 1
Abstract:
Experiments on elastic wave propagation in granular media are tremendous and have covered different systems from the simple one-dimensional chain of disks, to the disorder induced wave localization problems in three dimensions. Recent experiments have explored the method to find the internal structure of granular media by passing waves through the media and determining the 'network structure' through which the waves had traveled from one point to the other. This implies the determination of the arrangement geometry of the particles, where the granular network also has certain topological properties. The "internal structure is defined by the mechanical equilibrium, the geometry and topology" of the network. The determination of internal structure can be approached as a mathematical problem. Given the information on transmitted and received waves of finite amplitude and frequency range through measurements in many points on the enclosed boundary, we can establish the co-ordinates of the particles within the confining boundary, in analogy to the case for the celebrated inverse problem of "hearing the shape of drum". In the present work the discrete calculus equations proposed for mechanically stable static granular media in two dimensions are applied to the wave propagation problem, to deduce the internal structure by imposing extra constraints on the system. To satisfy these equations, infinitesimal perturbations of the granular particle network are considered to only allow the propagation of elastic disturbances. It is found that, based on the number of constraints on the system and its variation, the number of measurements required on the boundary to build a bijective mapping between the structure and wave properties could be properly defined. The internal structure, wave propagation and inverse approach relate to the statistical mechanics framework of granular media, where the temperature or entropy could be expressed as a function of wave characteristics of the network.