Physics of Asymmetric Continuum: Extreme and Fracture Processes

by Teisseyre, Roman; Nagahama, Hiroyuki; Majewski, Eugeniusz

• ISBN13: 9783540683544
• ISBN10: 3540683542
• Format: Hardcover
• Copyright: 2008-10-24
• Publisher: Springer Verlag
• More Book Details
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Summary

The monograph summarizes some fundamental theories of continua, in particular those with defect content, and develops asymmetric theory of continuum; the idea of spin and twist motions, the latter related to the shear axes oscillations, leads to the complex rotation field governed by the equations analogues to electromagnetic field. Experimental evidence related to seismic rotation motions is discussed from the point of view of interactive processes in an earthquake source zone and for the near-ground effects. Some synchronization effects between spin and twist motions discovered in a near-earthquake field are discussed and corroborated by theoretically derived solutions; this interaction appears as a correlated motion between rotation and strain, shifted in phase. The asymmetric theory includes such correlated solutions which had not been expected in the previous theories of continua. The new approach is extended also for the soliton wave theory with applications to fluid mechanics. Investigated space geometry approach to asymmetric and degenerated continua points to an analogy in the general relativity.

Table of Contents

Introduction to Asymmetric Continuum and Experimental Evidence of Rotation Motions	p. 1
Introduction to Asymmetric Continuum: Fundamental Point Deformations	p. 3
Introduction	p. 3
Self-Field Nuclei: Deviations from Classical Elasticity	p. 8
Basic Deformations and Simple Motions in an Asymmetric Continuum	p. 10
Conclusions	p. 13
Measurement of Short-Period Weak Rotation Signals	p. 17
Definition of Rotation and a Review of the Measurement Methods	p. 17
Classification of Rotation Measurements and Requirements for Recording Instruments	p. 25
The Influence of Recording Error on the Computed Rotation Signal	p. 27
Direct Detection of the Rotational Component	p. 37
Conclusions	p. 42
Buildings as Sources of Rotational Waves	p. 49
Introduction	p. 49
Soil-Foundation Interaction - Near Field	p. 51
Soil-Foundation Interaction - Far Field	p. 62
Summary	p. 62
Two-Pendulum Systems for Measuring Rotations	p. 67
Introduction	p. 67
Theory	p. 68
Testing and Measurements	p. 73
Discussion and Conclusions	p. 73
Theory and Observations: Some Remarks on Rotational Motions	p. 77
Ten Motions and Deformations	p. 77
Recording Spin and Twist	p. 78
Rotation Motions in the Universe	p. 79
Continuum with Defect Densities and Asymmetry of Fields	p. 83
Field Invariant Representation: Dirac Tensors	p. 85
Introduction	p. 85
Axial and Deviatoric Parts of any Symmetric Tensor	p. 85
Dirac Tensors	p. 86
Motion Equations: Classical Elasticity	p. 88
Diagonal and Off-Diagonal Symmetric Tensor Representation	p. 89
Particular Cases	p. 90
Conclusion	p. 93
Asymmetric Continuum: Standard Theory	p. 95
Introduction	p. 95
Standard Asymmetric Theory: Basic Assumptions	p. 97
Spin and Twist Motions	p. 100
Defects: Dislocation and Disclination Densities	p. 101
Balance Laws for the Rotation Field and the EM Analogy	p. 103
Continuum with Internal Nuclei	p. 104
Fracture Processes: Spin and Twist-Shear Coincidence	p. 111
Introduction	p. 111
Approaching Fracture: Constitutive Laws for Mylonite Zones	p. 116
Slip Propagation and Spin Release Hypothesis	p. 118
Conclusions	p. 122
Inplane and Antiplane Fracturing in a Multimode Random Sequence	p. 123
Introduction	p. 123
Standard Asymmetric Theory of Continuum	p. 123
Dislocation Flow on Slip Plane	p. 126
Numerical Simulation of Dislocation Flow Pattern	p. 128
Discussion	p. 136
Charged Dislocations and Various Sources of Electric Field Excitation	p. 137
Introduction	p. 137
Effects of Varying and Transient Polarization Due to Mechanical Stimulation	p. 139
Electrokinetics and the Properties of Water	p. 144
Less-Known Mechanisms of Charge Separation	p. 149
Pre-earthquake Stress Variations as the Source of Rotations and Electric Processes	p. 155
Charge Separation and the Rise of Current	p. 156
Large-Scale Electric Circuits	p. 156
Final Remarks	p. 158
Friction and Fracture Induced Anisotropy: Asymmetric Stresses	p. 163
Introduction	p. 163
2D Uniform Anisotropy	p. 164
2D Fracture/Friction Induced Anisotropy	p. 167
Conclusions	p. 168
Asymmetric Fluid Dynamics: Extreme Phenomena	p. 171
Introduction	p. 171
Standard Asymmetric Fluid Theory	p. 171
Conclusions	p. 174
Fracture Band Thermodynamics	p. 175
Introduction	p. 175
Earthquake Dislocation Theory	p. 176
Fracture Band Model	p. 178
Earthquake Thermodynamics	p. 179
Conclusions	p. 184
Interaction Asymmetric Continuum Theory	p. 187
Introduction	p. 187
Thermal Interaction Field	p. 189
Dislocation Related Polarization: Polarization Gradient Theory	p. 189
Conclusion	p. 191
Fracture Physics Based on a Soliton Approach	p. 193
Introduction	p. 193
The Dilaton Mechanism	p. 193
The Nonlinear Klein-Gordon Equation	p. 194
Coupled Klein-Gordon Equations Applied to Modeling a Two-Layer Model	p. 196
The Generalized Korteweg-de Vries (KdV) Equation	p. 198
The Spin and Twist Strain Solitions	p. 199
Splitting the Spin Strain Solitons Propagating along the Fracture Surface into the Fracture-Zone Related Part and the Elastic Part	p. 200
The Sine-Gordon Model of Moving Dislocations	p. 201
Soliton Ratchets	p. 202
The Generalized Sine-Gordon Model of Rock Fracture	p. 203
Links Between Solitons and Moving Cracks	p. 204
Fracture Solitions in Polymer Chains	p. 204
Chaos of Soliton Systems	p. 204
The Soliton Complexes	p. 204
The Soliton Arrays	p. 205
Conclusions	p. 206
Canonical Approach to Asymmetric Continua	p. 209
Introduction	p. 209
Hamilton's Principle	p. 210
Action of Spin and Twist Fields	p. 211
The Euler-Lagrange Equations	p. 212
Additive Decomposition of the Lagrangian	p. 214
The Canonical Equations (Hamilton's Equations)	p. 214
Conclusions	p. 217
Deformations in Riemannian Geometry	p. 219
Continuum Theory of Defects: Advanced Approaches	p. 221
Geometry of Deformation	p. 221
Deformation Measures and Incompatibility	p. 225
Evolution Equations for Stresses and Dislocations	p. 228
Source/Sink Functions of Dislocation Density	p. 229
Virtual Tearing (Kondo 1964)	p. 231
High-Order Spaces and Non-Locality of Deformation	p. 233
Interaction Between Microscopic and Macroscopic Fields: Comparison Between the Different Approaches	p. 235
Asymmetric and Anholonomic Deformation	p. 237
Micromorphic Continuum with Defects	p. 239
Taylor-Bishop-Hill Model	p. 240
Spinors and Torsion in a Riemann-Cartan Approach to Elasticity with a Continuous Defect Distribution and Analogies to the Einstein-Cartan Theory of Gravitation	p. 249
Introduction	p. 249
The Riemann-Cartan Geometry	p. 252
Spinors and Spin-Spaces	p. 254
Elastic Crystal with a Continuous Defect Distribution	p. 254
The Disclination-Curvature Analogy	p. 256
The Dislocation-Torison Analogy	p. 257
The Rotational and Translational Strain Tensors	p. 257
Description of Moving Defects in 4D	p. 260
Rotational Metric	p. 260
Complex Vielbein, Rotational Field, and Metric	p. 261
Disclination Density and Current Tensor	p. 261
Dislocation Density and Current Tensor	p. 262
Additive Decomposition of the Total Strain Tensors	p. 263
The Einstein-Cartan Theory	p. 264
The Analogy Between the Disclination Density Tensor and the Einstein Tensor	p. 265
The Evolution Equation for the Disclination Density	p. 266
The Evolution Equation for the Disclocation Density	p. 267
Spin Energy Potential	p. 267
Degenerate Asymmetric Continuum in Terms of Spinors: Analogy to Maxwell's Equations	p. 268
Conclusions	p. 268
Twistors as Spin and Twist Solitons	p. 273
Introduction	p. 273
The Twistor Equation	p. 273
Twistor Definition	p. 274
Twistor Quantization Theory Applied to Spin and Twist Solitons	p. 274
The Spin Operator	p. 277
The Twist Operator	p. 278
Spin and Twist Solitons Described by the Nonlinear Schrodinger Equation	p. 278
The Fracture Solitons	p. 281
The Robinson Congruences	p. 282
Conclusions	p. 283
Potentials in Asymmetric Continuum: Approach to Complex Relativity	p. 285
Introduction	p. 285
Natural Potentials	p. 286
Spin and Twist Fields in the Riemannian Space	p. 288
Natural Potentials: Analogy to Electromagnetic Field	p. 289
Complex Relativity Theory	p. 290
Concluding Remarks	p. 290
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