Mechanics of Generalized Continua: One Hundred Years After the Cosserats

ISBN-13: 9781441956941 / Angielski / Twarda / 2010 / 337 str.

Ga(c)Rard A. Maugin; Andrei V. Metrikine

Opis

In their 1909 publication Theorie des corps deformables, Eugene and Francois Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics. The diverse topics covered include: the properties of Cosserat media, micromorphic bodies, micropolar solids and fluids, weakly- and strongly-nonlocal theories, gradient theories of elasticity and plasticity, defect theory, everywhere-defective materials, bodies with fractal structure, as well as other related topics. Mechanics of Generalized Continua can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

Spis treści

Foreword. Preface.- Part I On the Cosserat’s Works. 1. Generalized Continuum Mechanics: What Do We Mean by That? 2. On Semi-Holonomic Cosserat Media.- Part II Cosserat Media (Rigidly Rotating Microstructure). 3. On the Theories of Plates Based on the Cosserat Approach. 4. Cracks in Cosserat Continuum – Macroscopic Modeling. 5. Micropolar Fluids: From Nematic Liquid Crystals to Liquid-like Granular Media. 6. Linear Cosserat Elasticity, Conformal Curvature and Bounded Stiffness. 7. Application of Generalized Continuum Theory to the Problem of Vibration Decay in Complex Mechanical Structures. 8. Measuring of Cosserat Effects and Reconstruction of Moduli Using Dispersive Waves. 9. Natural Lagrangian Strain Measures of the Non-linear Cosserat Continuum. 10. Practical Applications of Simple Cosserat Methods.- Part III Micromorphic Media (Deformable Microstructure). 11. Requirements on Periodic Micromorphic Media. 12. Extending Micromorphic Theory to Atomic Scale.- Part IV From the Discrete to the Continuum Description (Cosserat and other Continua Often in Relation to Dynamical Properties, Homogenization). 13. Nonlinear Theory of Cardinal Rearrangement of the Solid Body Structure in the Field of Intensive Pressure. 14. Generalized Beams and Continua. Dynamics of Reticulated Structures. 15. Wave Propagation in Damaged Materials Using a New Generalized Continuum Model. 16. On the Uniqueness of the Lagrangian of Gradient Elastic Continua. 17. Dynamic Properties of Essentially Nonlinear Generalized Continua. 18. Reissner–Mindlin Shear Moduli of a Sandwich Panel with Periodic Core Material. 19. Waves in Residual-Saturated Porous Media.- Part V Gradient Theory (Weakly Nonlocal Theories). 20. A Personal View on Current Generalized Theories of Elasticity and Plastic Flow. 21. Review and Critique of the Stress Gradient Elasticity Theories of Eringen and Aifantis. 22. On Natural Boundary Conditions in Linear 2nd-Grade Elasticity. 23.Gradient Theory of Media with Conserved Dislocations: Application to Microstructured Materials.- Part VI Complex Structured Media (Often with Application to Dislocations). 24. Dislocations in Generalized Continuum Mechanics. 25. Higher-Order Mesoscopic Theories of Plasticity Based on Discrete Dislocation Interactions.- Part VII Numerical Problems. 26. An Approach Based on Integral Equations for Crack Problems in Standard Couple-Stress Elasticity. 27. A Cosserat Point Element (CPE) for the Numerical Solution of Problems in Finite Elasticity. 28. Discretisation of Gradient Elasticity Problems Using C1 Finite Elements. 29. C1 Discretizations for the Application to Gradient Elasticity. 30. A Generalized Framework and a Multiplicative Formulation of Electromechanical Coupling.- Part VIII Beyond the Cosserats: Original Approaches (Kinematics, Geometry, Fractals). 31. Generalized Variational Principle for Dissipative Continuum Mechanics. 32. Cosserat Continua Described by Mesoscopic Theory. 33. Fractal Solids, Product Measures and Continuum Mechanics. 34. Magnetoelasticity of Thin Shells and Plates Based on the Asymmetrical Theory of Elasticity.

Blurb

In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers.

The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics. The diverse topics covered include: the properties of Cosserat media, micromorphic bodies, micropolar solids and fluids, weakly- and strongly-nonlocal theories, gradient theories of elasticity and plasticity, defect theory, everywhere-defective materials, bodies with fractal structure, as well as other related topics. 

Key features:

- Focuses on recent developments in continuum mechanics and materials design, including numerical examples and newly developed models.

- Presents numerical examples to demonstrate the efficiency of various solution techniques.

- Provides a unique overview of generalized continuum mechanics, illustrating the important applications of this theory in various other scientific disciplines.

- Includes a foreword written by renowned physicist and materials scientist A.C. Eringen.

Mechanics of Generalized Continua can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.