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Granular materials at the meso-scale : towards a change of scale approach

Cambou, Bernard / Magoariec, Hélène / Nguyen, Ngoc Son

2.4. Some proposals for extension to 3D granular mediaChapter 3: Texture, Stress and Strain at the Meso-scale ; 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; Chapter 4: Texture-Stress-Strain Relationship at the Meso-scale ; 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

Chapter 1: Previous Approaches and Motivation for the Use of the Meso-scale 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; Chapter 2: Definition of a Meso-scale for Granular Materials ; 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

Chapter 5: Change of Scale Based on Phenomenological Modeling at the Meso-scale 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; Appendices ; Appendix 1: The Simplified Elastic Plastic CJS Model for 2D Materials ; Appendix 2: Calibration of the Model Parameters ; Bibliography; Index; Back Cover

Front Cover ; Granular Materials at the Meso-scale: Towards a Change of Scale Approach ; Copyright ; Contents; Foreword; Acknowledgments; Preface; Symbols; Mathematical symbols; Stress and strain defined at different scales for 2D materials; Variables defined at the sample level; Local variables defined for contacts and internal variables; Local variables defined for particles; Variables defined for triangular elements; Variables defined for meso-domains; Variables defined for phases; Variables used in the CJS model for each phase; Introduction; I.1. The different scales considered

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