Granular Materials at Meso-scale

Granular Materials at Meso-scale

Towards a Change of Scale Approach

1st Edition - August 2, 2016

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  • Authors: Bernard Cambou, Hélène Magoariec, Ngoc-Son Nguyen
  • Hardcover ISBN: 9781785480652
  • eBook ISBN: 9780081010778

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Granular Materials at Meso-scale: Towards a Change of Scale Approach proposes a new way for developing an efficient change of scale—considering a meso-scale defined at the level of local arrays of particles. The change of scale is known to be a very interesting way to improve the modelling of mechanical behavior granular materials. In the past, studies have been proposed using a micro-scale at the grain level to perform change of scale, but limitations have been proven for these approaches. Definition and analysis of the phases are detailed, constituted by sets of meso-domains sharing the same texture characteristics. The authors propose a local constitutive model for the phases, allowing the constitutive model of the representative elementary volume to be definied from a change-of-scale approach and, finally, presenting the validation of obtained modeling on cyclic loadings.

Key Features

  • Proposes a new way for developing an efficient change of scale—considering a meso-scale
  • Explores local meso-domains and texture characteristics
  • Defines meso-strain and stress
  • Analyzes the evolution of these variables and texture characteristics in relation to the applied loading


Academics, researchers, practicing engineers and postgraduate students in the fields of civil engineering, geomechanics, geomaterials, development engineers

Table of Contents

    • Foreword
    • Acknowledgments
    • Preface
    • Symbols
    • Introduction
      • I.1 The different scales considered
    • 1: Previous Approaches and Motivation for the Use of the Meso-scale
      • Abstract
      • 1.1 Change of scale for texture variables
      • 1.2 Change of scale for static variables
      • 1.3 Change of scale for kinematic variables
      • 1.4 Statistical homogenization in granular materials
      • 1.5 Difficulties and limitations for statistical homogenization in granular materials using a micro-scale
    • 2: Definition of a Meso-scale for Granular Materials
      • Abstract
      • 2.1 Brief presentation of the Discrete Element Method
      • 2.2 Description of the four numerical granular samples
      • 2.3 Meso-scale for 2D granular media
      • 2.4 Some proposals for extension to 3D granular media
    • 3: Texture, Stress and Strain at the Meso-scale
      • Abstract
      • 3.1 Description of the internal state at the meso-scale
      • 3.2 Definition of strain at the meso-scale
      • 3.3 Definition of stress at the meso-scale
    • 4: Texture–Stress–Strain Relationship at the Meso-scale
      • Abstract
      • 4.1 Evolution of internal state
      • 4.2 Strain–texture relationship
      • 4.3 Stress–texture relationship
      • 4.4 Mechanical behavior of the granular material at the meso-scale
      • 4.5 Relevance of the meso-variables and of the meso–macro change of scale
    • 5: Change of Scale Based on Phenomenological Modeling at the Meso-scale
      • Abstract
      • 5.1 Phenomenological modeling of the mechanical behavior of phases
      • 5.2 Analysis of the generality of the parameters defined for phases
      • 5.3 Forecast of the mechanical behavior of the phases on a new loading path
      • 5.4 Change of scale: from the mesoscopic phases to the macroscopic sample
    • Conclusions and Prospects
    • Appendix 1: The Simplified Elastic Plastic CJS Model for 2D Materials
    • Appendix 2: Calibration of the Model Parameters
    • Bibliography
    • Index

Product details

  • No. of pages: 196
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2016
  • Published: August 2, 2016
  • Imprint: ISTE Press - Elsevier
  • Hardcover ISBN: 9781785480652
  • eBook ISBN: 9780081010778

About the Authors

Bernard Cambou

Bernard Cambou is an Engineer from Ecole Centrale de Lyon, Ph.D. He holds the position of State University Professor and is a former director of the Civil Engineering Department. He is Professor within the teaching department of Solid Mechanics, Mechanical Engineering and the Laboratory of Tribology and Systems Dynamics, UMR CNRS 5513, École Centrale de Lyon.

Affiliations and Expertise

Emeritus Professor, Ecole Centrale de Lyon, France

Hélène Magoariec

Hélène Magoariec is a Doctor of Engineering in solid mechanics, and lecturer at the Ecole Centrale de Lyon. She is a graduate of the Ecole Centrale de Marseille in 2000 and a doctorate in mechanical engineering from the University of Aix-Marseille II in 2003. In collaboration with the University of Aachen, she joined the Ecole Centrale de Lyon in 2005 and joined the Laboratory of Tribology and System Dynamics (LTDS). Her research activities concern the micromechanics of heterogeneous media, applied to different materials to suit her projects and collaborations, such as metal composites, granular, semi Drivers and since 2010, biological tissues.

Affiliations and Expertise

Laboratoire de Tribologie et Dynamique des Systèmes, Ecole Centrale de Lyon, France

Ngoc-Son Nguyen

Ngoc-Son Nguyen's research interests lie in the field of mechanics of granular materials; these include Computational mechanics, numerical modeling in DEM, multi-scale approach and homogenization technique, shock dynamics and nonlinear wave propagation. He received his PhD in civil engineering in 2009. Since 2010, he has undertaken research at INRIA, Grenoble.

Affiliations and Expertise

Institut de Recherches de Genie Civil et Mécanique, IUT de Saint-Nazaire, Université de Nantes

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