Mechanics of Generalized Continua: One Hundred Years After the Cosserats (Advances in Mechanics and Mathematics Book 21)

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. Front Matter....Pages I-XIX Front Matter....Pages 1-1 Generalized Continuum Mechanics: What Do We Mean by That?....Pages 3-13 On Semi-Holonomic Cosserat Media....Pages 15-24 Front Matter....Pages 25-25 On the Theories of Plates Based on the Cosserat Approach....Pages 27-35 Cracks in Cosserat Continuum—Macroscopic Modeling....Pages 37-45 Micropolar Fluids: From Nematic Liquid Crystals to Liquid-Like Granular Media....Pages 47-54 Linear Cosserat Elasticity, Conformal Curvature and Bounded Stiffness....Pages 55-63 Application of Generalized Continuum Theory to the Problem of Vibration Decay in the Complex Mechanical Structures....Pages 65-70 Measuring of Cosserat Effects and Reconstruction of Moduli Using Dispersive Waves....Pages 71-78 Natural Lagrangian Strain Measures of the Non-Linear Cosserat Continuum....Pages 79-86 Practical Applications of Simple Cosserat Methods....Pages 87-95 Front Matter....Pages 97-97 Requirements on Periodic Micromorphic Media....Pages 99-107 Extending Micromorphic Theory to Atomic Scale....Pages 109-117 Front Matter....Pages 119-119 Nonlinear Theory of Cardinal Rearrangement of the Solid Body Structure in the Field of Intensive Pressure....Pages 121-129 Generalized Beams and Continua. Dynamics of Reticulated Structures....Pages 131-141 Wave Propagation in Damaged Materials Using a New Generalized Continuum Model....Pages 143-148 On the Uniqueness of the Lagrangian of Gradient Elastic Continua....Pages 149-160 Dynamic Properties of Essentially Nonlinear Generalized Continua....Pages 161-168 Reissner–Mindlin Shear Moduli of a Sandwich Panel with Periodic Core Material....Pages 169-177 Waves in Residual-Saturated Porous Media....Pages 179-187 Front Matter....Pages 189-189 A Personal View on Current Generalized Theories of Elasticity and Plastic Flow....Pages 191-202 Front Matter....Pages 189-189 Review and Critique of the Stress Gradient Elasticity Theories of Eringen and Aifantis....Pages 203-210 On Natural Boundary Conditions in Linear 2nd-Grade Elasticity....Pages 211-221 Gradient Theory of Media with Conserved Dislocations: Application to Microstructured Materials....Pages 223-232 Front Matter....Pages 233-233 Dislocations in Generalized Continuum Mechanics....Pages 235-244 Higher-Order Mesoscopic Theories of Plasticity Based on Discrete Dislocation Interactions....Pages 245-250 Front Matter....Pages 251-251 An Approach Based on Integral Equations for Crack Problems in Standard Couple-Stress Elasticity....Pages 253-262 A Cosserat Point Element (CPE) for the Numerical Solution of Problems in Finite Elasticity....Pages 263-268 Discretization of Gradient Elasticity Problems Using C 1 Finite Elements....Pages 269-277 C 1 Discretizations for the Application to Gradient Elasticity....Pages 279-286 A Generalized Framework and a Multiplicative Formulation of Electro-Mechanical Coupling....Pages 287-294 Front Matter....Pages 295-295 Generalized Variational Principle for Dissipative Continuum Mechanics....Pages 297-305 Cosserat Continua Described by Mesoscopic Theory....Pages 307-314 Fractal Solids, Product Measures and Continuum Mechanics....Pages 315-323 Magnetoelasticity of Thin Shells and Plates Based on the Asymmetrical Theory of Elasticity....Pages 325-337