Generalized Continua as Models for Materials

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

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

• Complex Microstructure
• Coordinate-free Derivation
• Cosserat Continuum
• Generalized Continua
• Grain Boundary Modeling
• Multi-field Actions
• Multi-scale Effects

• , 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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