Mechanics of Granular Materials: An Introduction

K. Iwashita, M. Oda

• Publisher: CRC Press
• Year: 2020
• eBook ISBN: 9781000150513
• Topic: Study Aids
• Subtopic: Study Guides

This textbook compiles reports written by about 35 internationally recognized authorities, and covers a range of interests for geotechnical engineers. Topics include: fundamentals for mechanics of granular materials; continuum theory of granular materials; and discrete element approaches.

CHAPTER 1

Fundamentals for mechanics of granular materials

1.1 INTRODUCTION

Granular materials consist of grains in contact and surrounding voids. The micromechanical behavior of granular materials is therefore inherently discontinuous and heterogeneous. The macroscopic (overall or averaged) behavior of granular materials is determined not only by how discrete grains are arranged in space, but also by what kinds of interactions are operating among them. In order to understand the mechanical behavior of granular materials from a microscopic point of view, we should start by specifying the spatial distribution and orientation of grains and their contact conditions. Section 1.2 is devoted to this topic, dealing mathematically with the geometrical aspects of grains and associated voids. Section 1.3 goes on to discuss some new aspects of the mechanics of discrete materials.

Even in the mechanics of granular materials, some continuum mechanical concepts such as stress and strain tensors are necessary to formulate some problems in a consistent manner, since the degree of freedom of contact forces and movements at grain level becomes tremendously large. Section 1.4 defines the stress and strain tensors in terms of microscopic quantities such as interparticle forces and contact displacements. To do this, special emphasis is placed on particle rotation and contact moments since there is some positive evidence supporting the idea that granular materials can be idealized as a polar (generalized) continuum. A tensor, called the fabric tensor, is also introduced to characterize, in a tensor form, the spatial distribution of microscopic quantities such as particle orientation, contact normals, etc. Its application is also utilized to derive some phenomenological constitutive equations.

A final goal in the study of the mechanics of granular materials is to formulate their macro-behavior in terms of micro-quantities. To this end, there exist two well-known theories which explain the relations between micro-fields and macro-fields, i.e. macro-micro relations, in a consistent manner: The average field theory and the homogenization theory. These theories are discussed brief...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• 1. Fundamentals for Mechanics of Granular Materials
• 2. Continuum Theory of Granular Materials
• 3. Discrete Element Approaches
• 4. New Findings from Experimental Studies
• 5. Rapid Flow of Granular Materials
• List of Authors and Editors
• Subject Index