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Micromechanics of Fracture in Generalized Spaces - Ihar Miklashevich

Micromechanics of Fracture in Generalized Spaces


Published: 1st January 2008
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By the detailed analysis of the modern development of the mechanics of deformable media can be found the deep internal contradiction. From the one hand it is declared that the deformation and fracture are the hierarchical processes which are linked and unite several structural and scale levels. From the other hand the sequential investigation of the hierarchy of the deformation and destruction is not carried out.
The book's aim is filling this mentioned gap and investigates the hot topic of the fracture of non-ideal media. From the microscopic point of view in the book we study the hierarchy of the processes in fractured solid in the whole diapason of practically used scales. According the multilevel hierarchical system ideology under "microscopic" we understand taking into account the processes on the level lower than relative present strata. From hierarchical point of view the conception of "microscopic fracture" can be soundly applied to the traditionally macroscopic area, namely geomechanics or main crack propagation. At the same time microscopic fracture of the nanomaterials can be well-grounded too. This ground demands the investigation on the level of inter-atomic interaction and quantum mechanical description.
The important feature of the book is the application of fibred manifolds and non-Euclidean spaces to the description of the processes of deformation and fracture in inhomogeneous and defected continua. The non-Euclidean spaces for the dislocations' description were introduced by J.F. Nye, B.A. Bilby, E. Kroner, K. Kondo in fiftieth. In last decades this necessity was shown in geomechanics and theory of seismic signal propagation. The applications of non-Euclidean spaces to the plasticity allow us to construct the mathematically satisfying description of the processes. Taking into account this space expansion the media with microstructure are understood as Finsler space media. The bundle space technique is used for the description of the influence of microstructure on the continuum metrics. The crack propagation is studied as a process of movement in Finsler space. Reduction of the general description to the variational principle in engineering case is investigated and a new result for the crack trajectory in inhomogeneous media is obtained. Stability and stochastization of crack trajectory in layered composites is investigated.
The gauge field is introduced on the basis of the structure representation of Lie group generated by defects without any additional assumption. Effective elastic and non-elastic media for nanomaterials and their geometrical description are discussed.
The monograph provides the basis for more detailed and exact description of real processes in the material.
The monograph will be interesting for the researchers in the field of fracture mechanics, solid state physics and geomechanics. It can be used as well by the last year students wishing to become more familiar with some modern approaches to the physics of fracture and continual theory of dislocations.
In Supplement, written by V.V.Barkaline, quantum mechanical concept of physical body wholeness according to H. Primas is discussed with relation to fracture. Role of electronic subsystem in fracture dynamics in adiabatic and non-adiabatic approximations is clarified. Potential energy surface of ion subsystem accounting electron contribution is interpreted as master parameter of fracture dynamics. Its features and relation to non-euclidean metrics of defected solid body is discussed. Quantum mechanical criteria of fracture arising are proposed.
Key Features:
- Crack represent as a quasi-particle
- Finsler metric is taken as intrinsic metric of non-ideal body
- Crack is propagate along the geodesic lines
- Hierarchical nature of the fracture taking into account
- Non-Archimedian numbers are characterized the chaotic properties of hierarchical space
Key Features:
- Crack represent as a quasi-particle
- Finsler metric is taken as intrinsic metric of non-ideal body
- Crack is propagate along the geodesic lines
- Hierarchical nature of the fracture taking into account
- Non-Archimedian numbers are characterized the chaotic properties of hierarchical space

Preface to English Editionp. ix
Introduction: selection from preface to the first editionp. x
Collective effects in mechanics of deformed bodiesp. x
Generalized mechanics of the continuump. x
Micromechanics and physicsp. xi
Acknowledgementsp. xiii
List of Basic Definitions and Abbreviationsp. xv
List of Figuresp. xvii
Deformation Models of Solids: Descriptionp. 1
Description of hierarchy systemsp. 1
General description of hierarchy structuresp. 1
Hierarchical spacep. 6
Peculiarities of parameter space structure associated with fracturep. 7
Continual approximation in damage descriptionp. 8
Deformed continuum fiberingp. 11
Hierarchy in continuum models of a deformed solidp. 12
Mechanical properties of an ideal continuump. 13
Hierarchy of systems and structures in fracture mechanicsp. 15
Hierarchical pattern of fracture process: applications of general systems theoryp. 19
Crack fractality, hierarchy and behaviorp. 21
Self-organization processes at plastic deformation and fracturep. 25
Certain Outcomesp. 25
Space Geometry Fundamentalsp. 27
Construction principles of various space typesp. 28
Affine spacep. 28
Vectors, covectors, and 1-forms and tensorsp. 29
Euclidean spacep. 31
Generalization: affine connectivity spaces and Riemann spacep. 33
Tangent spacesp. 42
Main fibrationp. 44
Vertical and horizontal liftp. 47
Minimum pathsp. 47
Covariant differentiationp. 48
Effect of microscopic defects on continuump. 50
Basics of continuous approximation for imperfect crystalsp. 53
Finsler geometry and its applications to mechanics of a deformed bodyp. 55
Finsler spacep. 56
h- and v-connectivitiesp. 56
Fracture geometry of solidsp. 57
Metrical Finsler spacesp. 60
Indicatrix and orthogonality condition in Finsler spacep. 62
Description of plastic deformation in generalized spacep. 64
Geometry of nanotube continuump. 67
Certain Outcomesp. 69
Microscopic Crack in Defect Mediump. 71
Fundamentals of quantum fracture theoryp. 73
Bond energy and electronic structurep. 74
Thermofluctuation fracture initiationp. 77
Influence of material defect structure on crack propagationp. 78
Crack-defect interaction in classical elasticity and plasticity theoryp. 78
Defect fields and intrinsic metric of continuap. 79
Crack trajectory and characteristics of fracture spacep. 81
Crack trajectory in heterogeneous medium with defects in the general casep. 86
Driving force acting on crackp. 88
Gauge crack theoryp. 91
Connection of defective material structure with crack surface shapep. 94
Equation of crack front as function of metric and field of defectsp. 94
Break propagation in a mediump. 97
Macroscopic group properties of deformation process and gauge fields introduction procedurep. 99
Kinematicsp. 100
Dynamicsp. 102
Group structure of deformation curvep. 103
Four-dimensional formalism and conservation lawsp. 108
Certain Outcomesp. 111
Application of General Formalism in Macroscopic Fracturep. 113
Macroscopic variational approach to fracturep. 114
Thermodynamics of crack growth and influence of weakened bond zone on crack equationp. 119
Crack trajectory equation as a variational problemp. 127
Propagation stability and influence of material inhomogeneity on crack trajectoryp. 130
Stability of crack trajectoryp. 130
Crack propagation in real mediap. 137
Trajectory in linear approximationp. 139
Influence of weakened bonds zone on crack trajectoryp. 144
Crack propagation across singular borderp. 146
Crack trajectory in media with random structure. Trajectory stochastizationp. 150
Correlation function and stochastization lengthp. 151
Fokker-Planck-Kolmogorov equation and probability description of crack trajectoryp. 153
Physical reasons of crack trajectory stochastizationp. 161
Deformation and fracture with account of electromagnetic fieldsp. 166
Destruction of piezoelectric materialsp. 168
Crack propagation in piezoelectric materialp. 170
Certain Outcomesp. 175
Surface, Fractals and Scaling in Mechanics of Fracturep. 179
Some conceptions of theory of fractalsp. 180
Roughness of fracture surfacep. 181
Fractal shape of fracture surfacep. 183
Physical way of fractal crack behaviorp. 184
Problem statementp. 184
Equation of beam bendingp. 186
Solution analysisp. 187
Crackonp. 190
Movement of dynamical systemp. 190
Mass of crackonp. 191
Crackon in mediump. 194
Acoustic approximationp. 194
Crack-Generated energy flowp. 196
Fractal dimensionalityp. 198
Internal geometry of the media and fractal properties of the fracturep. 199
Damage mechanics and stable growth of microcrackp. 200
Distribution of microcracks in a samplep. 201
Fractal characteristics of a macroscopic crackp. 202
Exclusion principles and fractal dimension of crack trajectoryp. 207
Defect structure and fractal properties of a real crackp. 211
Microscopic fracture of geo massifsp. 214
Energy fluxp. 214
Ray path and energy storage in geomechanicsp. 215
Chaotic hierarchical dynamical systems and application of non-standard analysis for its descriptionp. 217
Iterated function systemp. 218
Entropy of IFSp. 219
Entropy of hierarchical spacep. 221
Certain Conclusionsp. 222
Spaces: Some Definitionsp. 225
Certain Relations of Vector Analysisp. 227
Groups: Basic Definitions and Propertiesp. 229
Dimensionsp. 233
Bibliographyp. 239
Indexp. 255
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780080453187
ISBN-10: 008045318X
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 280
Published: 1st January 2008
Publisher: Elsevier Science & Technology
Country of Publication: GB
Dimensions (cm): 24.0 x 16.5  x 1.27
Weight (kg): 0.67