Mechanics of Generalized Continua, 2010 One Hundred Years After the Cosserats Advances in Mechanics and Mathematics Series, Vol. 21

On the Cosserat's works.- Generalized Continuum Mechanics: What Do We Mean by That?.- On Semi-Holonomic Cosserat Media.- Cosserat media (rigidly rotating microstructure).- On the Theories of Plates Based on the Cosserat Approach.- Cracks in Cosserat Continuum—Macroscopic Modeling.- Micropolar Fluids: From Nematic Liquid Crystals to Liquid-Like Granular Media.- Linear Cosserat Elasticity, Conformal Curvature and Bounded Stiffness.- Application of Generalized Continuum Theory to the Problem of Vibration Decay in the Complex Mechanical Structures.- Measuring of Cosserat Effects and Reconstruction of Moduli Using Dispersive Waves.- Natural Lagrangian Strain Measures of the Non-Linear Cosserat Continuum.- Practical Applications of Simple Cosserat Methods.- Micromorphic media (deformable microstructure).- Requirements on Periodic Micromorphic Media.- Extending Micromorphic Theory to Atomic Scale.- From the discrete to the continuum description (Cosserat and other continua often in relation to dynamical properties, homogenization).- Nonlinear Theory of Cardinal Rearrangement of the Solid Body Structure in the Field of Intensive Pressure.- Generalized Beams and Continua. Dynamics of Reticulated Structures.- Wave Propagation in Damaged Materials Using a New Generalized Continuum Model.- On the Uniqueness of the Lagrangian of Gradient Elastic Continua.- Dynamic Properties of Essentially Nonlinear Generalized Continua.- Reissner–Mindlin Shear Moduli of a Sandwich Panel with Periodic Core Material.- Waves in Residual-Saturated Porous Media.- Gradient theory (weakly nonlocal theories).- A Personal View on Current Generalized Theories of Elasticity and Plastic Flow.- Review and Critique of the Stress Gradient Elasticity Theories of Eringen and Aifantis.- OnNatural Boundary Conditions in Linear 2nd-Grade Elasticity.- Gradient Theory of Media with Conserved Dislocations: Application to Microstructured Materials.- Complex structured media (often with application to dislocations).- Dislocations in Generalized Continuum Mechanics.- Higher-Order Mesoscopic Theories of Plasticity Based on Discrete Dislocation Interactions.- Numerical problems.- An Approach Based on Integral Equations for Crack Problems in Standard Couple-Stress Elasticity.- A Cosserat Point Element (CPE) for the Numerical Solution of Problems in Finite Elasticity.- Discretization of Gradient Elasticity Problems Using C1 Finite Elements.- C1 Discretizations for the Application to Gradient Elasticity.- A Generalized Framework and a Multiplicative Formulation of Electro-Mechanical Coupling.- Beyond the Cosserats: Original approaches (kinematics, geometry, fractals).- Generalized Variational Principle for Dissipative Continuum Mechanics.- Cosserat Continua Described by Mesoscopic Theory.- Fractal Solids, Product Measures and Continuum Mechanics.- Magnetoelasticity of Thin Shells and Plates Based on the Asymmetrical Theory of Elasticity.

Showcases several areas of continuum mechanics that are outgrowths of the work of the Cosserat brothers Focuses on recent developments in continuum mechanics and materials design, presenting several applications of these theories Provides an overview of research from many different areas of continuum mechanics Can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics Includes supplementary material: sn.pub/extras