Microcontinuum Analysis of Granular Materials
Date Issued
2008
Date
2008
Author(s)
Lan, Jeng-Yin
Abstract
Materials with microstructure characteristics are called complex materials. Nowadays, these kinds of materials have been applied widely in several technologies. Although granular materials are everywhere in our daily life, they are kind of complex materials, which are difficult to be analyzed for their multiple macroscopic mechanical behaviors. Recently, many studies mentioned that two microstructure effects, local dilatant and rotational behavior, play significant roles in the process of deformation for granular materials. There are two analytical approaches widely used in the continuum theory of granular materials to deal with the behavior of microstructure: one of which is the Goodman-Cowin (GC) theory for dealing with the local dilatant effect, the other is the Cosserat type continua on the analysis of the local rotational behavior of granular assemblies. The key issue of this study is to analyze the mechanical behavior of granular materials by using the microcontinuum theory. Based on this work, we regard the microcontinuum theory to have a considerably predominance to analyze complex materials and propose one of the possible application for this theory. This thesis is divided into three parts. Firstly, we clearly describe the framework and the related quantities of microcontinuum theory. By simply decomposing the various field quantities of the microcontinuum into the dilatancy, shearing, and rotational parts, a microcontinuum can be classified into seven classes. Each class has its micro-deformation and can be used to characterize the behavior of different materials. Secondly, we used one of the microcontinuum classes, called a microdilatation continuum, in which only the dilatant motion is taken into account, to analyze dry granular materials. Furthermore, we presented the derivation of GC theory by using this model and render a newly physical meaning for equations and quantities of GC theory from the aspect of microcontinuum. Moreover, we model the granular materials by another microcontinuum class, called microstretch continuum, which include the two microstructure effects concerned by the GC theory and the Cosserat type continua. A DEM simulation of a granular system under a biaxial compression is constructed. By calculating the bulk part and the rotational part of the gyration tensor, which respectively measure the local dilatancy and the local rotation, we verify the feasibility and necessity of the microstretch continuum as a basic framework of analysis granular assembly.
Subjects
Microcontinuum theory
Microstructure effect
Goodman-Cowin theory
Granular materials
Distinct element method(DEM)
Strain localization
Type
thesis
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