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Generalized Continua as Models for Materials

with Multi-scale Effects or Under Multi-field Actions

  • Book
  • © 2013

Overview

Editors:
  1. Holm Altenbach

    1. , Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

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  2. Samuel Forest

    1. , Centre des Materiaux CNRS UMR 7633, Mines ParisTech, EVRY Cedex, France

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    You can also search for this editor in PubMed   Google Scholar

  3. Anton Krivtsov

    1. University, Dep. of Theoretical Mechanics, St. Petersburg State Polytechnical, St. Petersburg, Russia

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    You can also search for this editor in PubMed   Google Scholar

  • Describes the micro- and macro-behavior, new existence and uniqueness theorems
  • Discusses new trends and applications of generalized continua
  • Explains many effects of the mechanical behaviour of solids and fluids that can not be explained by the available classical models
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advanced Structured Materials (STRUCTMAT, volume 22)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xii
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  2. Shells and Plates with Surface Effects

    • Holm Altenbach, Victor A. Eremeyev
    Pages 1-15

  3. Geometrical Picture of Third-Order Tensors

    • Nicolas Auffray
    Pages 17-40

  4. Continuum Modelling of Shear-Coupled Grain Boundary Migration

    • Stéphane Berbenni, Bhasker Paliwal, Mohammed Cherkaoui
    Pages 41-64

  5. Buckling of Nonlinearly Elastic Plates with Microstructure

    • Svyatoslav Derezin
    Pages 65-76

  6. Material Symmetry Group and Consistently Reduced Constitutive Equations of the Elastic Cosserat Continuum

    • Victor A. Eremeyev, Wojciech Pietraszkiewicz
    Pages 77-90

  7. Nonlinear Localized Strain Waves in a 2D Medium with Microstructure

    • Vladimir I. Erofeev, Vladimir V. Kazhaev, Igor S. Pavlov
    Pages 91-110

  8. Cosserat Anisotropic Models of Trabecular Bone from the Homogenization of the Trabecular Structure: 2D and 3D Frameworks

    • Ibrahim Goda, Mohamed Assidi, Jean-Francois Ganghoffer
    Pages 111-141

  9. Electro-Thermo-Elastic Simulation of Graphite Tools Used in SPS Processes

    • Stefan Hartmann, Steffen Rothe, Nachum Frage
    Pages 143-161

  10. The Use of Moment Theory to Describe the Piezoelectric Effect in Polar and Non-Polar Materials

    • Elena A. Ivanova, Yaroslav E. Kolpakov
    Pages 163-178

  11. Description of Thermal and Micro-Structural Processes in Generalized Continua: Zhilin’s Method and its Modifications

    • Elena Ivanova, Elena Vilchevskaya
    Pages 179-197

  12. Hierarchical Architecture and Modeling of Bio-Inspired Mechanically Adaptive Polymer Nanocomposites

    • Rasa Kazakevi c̆ iūtė-Makovska, Holger Steeb
    Pages 199-215

  13. Justification of the Bending-Gradient Theory Through Asymptotic Expansions

    • Arthur Lebée, Karam Sab
    Pages 217-236

  14. Macroscopic Modeling of Size Effects in Foams Using an Order-Parameter Approach

    • Bernd Lenhof, Alexander Geringer, Stefan Diebels
    Pages 237-254

  15. Measuring Material Coefficients of Higher Gradient Elasticity by Using AFM Techniques and Raman-Spectroscopy

    • Christian Liebold, Wolfgang H. Müller
    Pages 255-271

  16. On the Electrostatic Fields in Dielectric Continua with Self-Similar Properties

    • Thomas M. Michelitsch, Gérard A. Maugin
    Pages 273-282

  17. Nonlinear Generalizations of the Born-Huang Model and Their Continuum Limits

    • Alexey V. Porubov, Eron L. Aero, Boris R. Andrievsky
    Pages 283-290

  18. Buckling of Inhomogeneous Circular Plate of Micropolar Material

    • Denis N. Sheydakov
    Pages 291-301

  19. A Theory of Disclination and Dislocation Fields for Grain Boundary Plasticity

    • V. Taupin, L. Capolungo, C. Fressengeas, A. Das, M. Upadhyay
    Pages 303-320

  20. Material Strain Tensor

    • Pavel A. Zhilin, Holm Altenbach, Elena A. Ivanova, Anton Krivtsov
    Pages 321-331
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Keywords

About this book

This volume presents contributions describing the micro- and macro-behaviours, new existence and uniqueness theorems, the formulation of multi-scale problems, etc. and now it is time to ponder again the state of matter and to discuss new trends and applications.
The main focus is directed on the following items
- Modelling and simulation of materials with significant microstructure,
- Generalized continua as a result of multi-scale models,
- Multi-field actions on materials resulting in generalized material models, and
- Comparison with discrete modelling approaches

Editors and Affiliations

  • , Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  • , Centre des Materiaux CNRS UMR 7633, Mines ParisTech, EVRY Cedex, France

    Samuel Forest

  • University, Dep. of Theoretical Mechanics, St. Petersburg State Polytechnical, St. Petersburg, Russia

    Anton Krivtsov

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