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Mechanics of Generalized Continua

  • Holm Altenbach
  • Gérard A. Maugin
  • Vladimir Erofeev
Book

Part of the Advanced Structured Materials book series (STRUCTMAT, volume 7)

Table of contents

  1. Front Matter
    Pages i-xix
    PDF

  2. Historical Background and Future Trends

    1. Front Matter
      Pages 1-1
      PDF
    2. A Historical Perspective of Generalized Continuum Mechanics
      Gérard A. Maugin
      Pages 3-19

  3. Historical Background and Future Trends

    1. Front Matter
      Pages 21-21
      PDF
    2. Micropolar Shells as Two-dimensional Generalized Continua Models
      Holm Altenbach, Victor A. Eremeyev, Leonid P. Lebedev
      Pages 23-55
    3. Structural Dynamics and Generalized Continua
      Céline Chesnais, Claude Boutin, Stéphane Hans
      Pages 57-76
    4. A Bending-gradient Theory for Thick Laminated Plates Homogenization
      Arthur Lebée, Karam Sab
      Pages 77-95

  4. Advanced Constitutive Models

    1. Front Matter
      Pages 97-97
      PDF
    2. Internal Length Scale Effects on the Local and Overall Behavior of Polycrystals
      Stéphane Berbenni
      Pages 99-136
    3. Formulations of Strain Gradient Plasticity
      Samuel Forest, Albrecht Bertram
      Pages 137-149
    4. On one Model of Generalized Continuum and its Thermodynamical Interpretation
      Elena A. Ivanova
      Pages 151-174
    5. Micromechanical Bases of Superelastic Behavior of Certain Biopolymers
      Rasa Kazakevičiūtė-Makovska, Holger Steeb
      Pages 175-192
    6. Construction of Micropolar Continua from the Homogenization of Repetitive Planar Lattices
      Francisco Dos Reis, Jean-François Ganghoffer
      Pages 193-217

  5. Dynamics and Stability

    1. Front Matter
      Pages 219-219
      PDF
    2. Nonlinear Waves in the Cosserat Continuum with Constrained Rotation
      Vladimir I. Erofeev, Aleksandr I. Zemlyanukhin, Vladimir M. Catson, Sergey F. Sheshenin
      Pages 221-230
    3. Wave Propagation in Quasi-continuous Linear Chains with Self-similar Harmonic Interactions: Towards a Fractal Mechanics
      Thomas M. Michelitsch, Gérard A. Maugin, Franck C. G. A. Nicolleau, Andrzej F. Nowakowski, Shahram Derogar
      Pages 231-244
    4. Nonlinear Dynamic Processes in Media with Internal Structure
      Alexey V. Porubov, Boris R. Andrievsky, Eron L. Aero
      Pages 245-254
    5. Buckling of Elastic Composite Rods made of Micropolar Material Subjected to Combined Loads
      Denis Sheydakov
      Pages 255-271

  6. Geometry and Defects

    1. Front Matter
      Pages 273-273
      PDF
    2. Theory of Isolated and Continuously Distributed Disclinations and Dislocations in Micropolar Media
      Mikhail I. Karyakin, Leonid M. Zubov
      Pages 275-290
    3. On the Form-Invariance of Lagrangian Function for Higher Gradient Continuum
      Nirmal Antonio Tamarasselvame, Lalaonirina R. Rakotomanana
      Pages 291-322

  7. Further Applications

    1. Front Matter
      Pages 323-323
      PDF
    2. Cahn-Hilliard Generalized Diffusion Modeling Using the Natural Element Method
      Paul Fischer, Amirtham Rajagopal, Ellen Kuhl, Paul Steinmann
      Pages 325-337
    3. Constitutive Models of Mechanical Behavior of Media with Stress State Dependent Material Properties
      Evgeny V. Lomakin
      Pages 339-350

About this book

Introduction

This collection on „Mechanics of Generalized Continua - from Micromechanical Basics to Engineering Applications“ brings together leading scientists in this field from France, Russian Federation, and Germany. The attention in this publication is be focussed on the most recent research items, i.e., - new models, - application of well-known models to new problems, - micro-macro aspects, - computational effort, - possibilities to identify the constitutive equations, and - old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

Keywords

asymmetric elasticity constitutive equations metamaterials micro-macro interactions

Editors and affiliations

  • Holm Altenbach
    • 1
  • Gérard A. Maugin
    • 2
  • Vladimir Erofeev
    • 3
  1. 1.Halle-Wittenberg, Zentrum für IngenieurwissenschaftenMartin-Luther-UniversitätHalle (Saale)Germany
  2. 2., Institut Jean Le Rond d’AlembertUPMC (Paris)Paris Cedex 05France
  3. 3.IMASH RANNizhny NovgorodRussian Federation

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