Mechanics of Generalized Continua: Proceedings of the Iutam-Symposium on the Generalized Cosserat Continuum and the Continuum Theory of Dislocations w

ISBN-13: 9783662302590 / Angielski / Miękka / 2014 / 358 str.

E. Kroner

Opis

5 The symposium was held in Freudenstadt from 28h to 31 ofAugust st nd 1967 and in Stuttgart from 1 to 2 of September 1967. The proposal to hold this symposium originated with the German Society of Applied Mathematics and Mechanics (GAMM) late in 1964 and was examined by a committee of IUTAM especially appointed for this purpose. The basis of this examination was a report in which the present situation in the field and the possible aims of the symposium were surveyed. Briefly, the aims of the symposium were stated to be 1. the unification of the various approaches developed in recent years with the aim of penetrating into the microscopic world of matter by means of continuum theories; 2. the bridging of the gap between microscopic (or atomic) research on mechanics on one hand, and the phenomenological (or continuum mechanical) approach on the other hand; 3. the physical interpretation and the relation to actual material behaviour of the quantities and laws introduced into the new theories, together with applications; 4. the further development of the theories, where necessary, and the clarification of open questions; 5. a stocktaking of present achievements and the prognosis for future developments. The committee agreed unanimously that the topic of the symposium represented an important phase of current developments in continuum mechanics, from the purely theoretical point of view as well as in connection with possible applications to actual materials.

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Spis treści

The Cosserat Continuum and its Generalizations.- Generalized Mechanics of Continuous Media.- Mechanics of Micromorphic Continua.- The Cosserat Surface.- A General Theory of Rods.- The Basic Affine Connection in a Cosserat Continuum.- On the Thermodynamic Potential of Cosserat Continua.- Applications of Theories of Generalized Cosserat Continua to the Dynamics of Composite Materials.- Determination of Elastic Constants of a Structured Material.- A Note on Günther’s Analysis of Couple Stress.- Note on the Statics and Stability of Polar Hyperelastic Materials.- The Characteristic Length of a Polar Fluid.- Couple-Stresses and Singular Stress Concentrations in Elastic Solids.- On the Effect of Stress Concentration in Cosserat Continua.- Stress Functions and Loading Singularities for the Infinitely Extended, Linear Elastic-Isotropic Cosserat Continuum.- On the Action of Concentrated Loads in the Case of a Cosserat Continuum.- Dislocated and Oriented Media.- The Generalized Dual Continuum in Elasticity and Dislocation Theory.- Dislocations in the Generalized Elastic Cosserat Continuum.- Some Considerations on the Mechanics of Granular Materials.- A comment on the communication by Dr, M. Satake On the Influence of Couple-Stresses on the Distribution of Velocities in the Flow of Polar Fluids.- On Plastic Strain.- Continuous Distributions of Dislocations.- Physical Foundations of Dislocation Theory.- Geometry and Continuum Mechanics.- On the Two Main Currents of the Geometrical Theory of Imperfect Continua.- A Dynamic Theory of Continual Dislocations.- Inhomogeneities in Materially Uniform Simple Bodies.- On the Geometric Structure of Simple Bodies, a Mathematical Foundation for the Theory of Continuous Distributions of Dislocations.- Differential Geometry of a Nonlinear Continuum Theory of Dislocations.- Statistical Theory of Dislocations.- Some Remarks about High Velocity Dislocations.- Continuum Theory of Dislocations and Plasticity.- Continuous Distributions of Dislocations in Hyperelastic Materials of Grade 2.- On the Dual Yielding and Related Problems.- The Plane Boundary in Anisotropic Elasticity.- Line Sources of Internal Stresses with zero Burgers Vector.- On the Screw Dislocation in Finite Elasticity.- Lattice Structure and Continuum Mechanics.- Some Considerations of the Relation between Solid State Physics and Generalized Continuum Mechanics.- Theories of Elastic Continua and Crystal Lattice Theories.- The Theory of Elastic Media with Microstructure and the Theory of Dislocations.- Interrelations between Various Branches of Continuum Mechanics.- Properties of Dislocations in Iron—The Importance of the Discrete Nature of the Crystal Lattice.- Applications to other Branches of Physics.- A Modernization of MacCullagh’s Ether Theory.- Space-Time as Generalized Cosserat Continuum.- The Cosserat Continuum with Electronic Spin.- Disclinations and the Cosserat-Continuum with Incompatible Rotations.