Mechanics of Generalized Continua: Proceedings of the IUTAM-Symposium on The Generalized Cosserat Continuum and the Continuum Theory of Dislocations with Applications, Freudenstadt and Stuttgart (Germany) 1967

✍ Scribed by R. S. Rivlin (auth.), Professor Dr. rer. nat. Ekkehart Kröner (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1968
• Tongue: English
• Leaves: 370
• Series: IUTAM Symposia
• Edition: 1
• Category: Library

✦ Synopsis

5 The symposium was held in Freudenstadt from 28\h 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.

✦ Table of Contents

Front Matter....Pages I-XII
Generalized Mechanics of Continuous Media....Pages 1-17
Mechanics of Micromorphic Continua....Pages 18-35
The Cosserat Surface....Pages 36-48
A General Theory of Rods....Pages 49-56
The Basic Affine Connection in a Cosserat Continuum....Pages 57-62
On the Thermodynamic Potential of Cosserat Continua....Pages 63-68
Applications of Theories of Generalized Cosserat Continua to the Dynamics of Composite Materials....Pages 69-79
Determination of Elastic Constants of a Structured Material....Pages 80-82
A Note on Günther’s Analysis of Couple Stress....Pages 83-86
Note on the Statics and Stability of Polar Hyperelastic Materials....Pages 87-89
The Characteristic Length of a Polar Fluid....Pages 90-94
Couple-Stresses and Singular Stress Concentrations in Elastic Solids....Pages 95-108
On the Effect of Stress Concentration in Cosserat Continua....Pages 109-113
Stress Functions and Loading Singularities for the Infinitely Extended, Linear Elastic-Isotropic Cosserat Continuum....Pages 114-119
On the Action of Concentrated Loads in the Case of a Cosserat Continuum....Pages 120-125
Dislocated and Oriented Media....Pages 126-140
The Generalized Dual Continuum in Elasticity and Dislocation Theory....Pages 141-151
Dislocations in the Generalized Elastic Cosserat Continuum....Pages 152-155
Some Considerations on the Mechanics of Granular Materials....Pages 156-159
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....Pages 160-162
On Plastic Strain....Pages 163-165
Physical Foundations of Dislocation Theory....Pages 166-179
Geometry and Continuum Mechanics....Pages 180-199
On the Two Main Currents of the Geometrical Theory of Imperfect Continua....Pages 200-213
A Dynamic Theory of Continual Dislocations....Pages 214-238
Inhomogeneities in Materially Uniform Simple Bodies....Pages 239-246
On the Geometric Structure of Simple Bodies, a Mathematical Foundation for the Theory of Continuous Distributions of Dislocations....Pages 247-250
Differential Geometry of a Nonlinear Continuum Theory of Dislocations....Pages 251-261
Statistical Theory of Dislocations....Pages 262-264
Some Remarks about High Velocity Dislocations....Pages 265-268
Continuum Theory of Dislocations and Plasticity....Pages 269-278
Continuous Distributions of Dislocations in Hyperelastic Materials of Grade 2....Pages 279-282
On the Dual Yielding and Related Problems....Pages 283-285
The Plane Boundary in Anisotropic Elasticity....Pages 286-289
Line Sources of Internal Stresses with zero Burgers Vector....Pages 290-293
On the Screw Dislocation in Finite Elasticity....Pages 294-297
Some Considerations of the Relation between Solid State Physics and Generalized Continuum Mechanics....Pages 298-311
Theories of Elastic Continua and Crystal Lattice Theories....Pages 312-320
The Theory of Elastic Media with Microstructure and the Theory of Dislocations....Pages 321-329
Interrelations between Various Branches of Continuum Mechanics....Pages 330-340
Properties of Dislocations in Iron—The Importance of the Discrete Nature of the Crystal Lattice....Pages 341-343
A Modernization of MacCullagh’s Ether Theory....Pages 344-346
Space-Time as Generalized Cosserat Continuum....Pages 347-349
The Cosserat Continuum with Electronic Spin....Pages 350-354
Disclinations and the Cosserat-Continuum with Incompatible Rotations....Pages 355-358

✦ Subjects

Mechanics