Fracture Mechanics

Inverse Problems and Solutions

By: Huy Duong Bui

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Hardcover | 21 July 2006

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408 Pages

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This book is an outgrowth of my involvement in two groups of research in solid mechanics, created in 1960 for the French nuclear energy program. At this time, it was decided that France, as a no-oil reservoir country, must be powered by nuclear energy, which represents today 80% of the total - tional energy supply. Long before the construction of the first nuclear plant at Fessenheim in 1973, Electricite de France (EdF) created its first solid mechanics laboratory, appointed researchers and sent them to the universities or abroad in order to learn about theories and new methods of assessment of the safety of structures. Working at EdF, I was training in Professor Jean Mandel's laboratory at Ecole Polytechnique (LMS), Paris. My friend Rene Labbens, working at Framatome (the builder of nuclear plants) was training at the Lehigh University, under the guidance of professors G. R. Irwin and G. C. Sih. We had to work hard, both academically at the u- versities laboratories and performing engineering tasks for our employer. This dual position was a great chance for many of us, since we discovered that real industrial problems are the source of new subjects and research problems to be solved by theoreticians in the universities and conversely we immediately knew if our theoretical work was good or not for appli- tions as revealed in our daily works conducted for our industrial employer.

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From the reviews: "This monograph is mainly a scope of research results of group of scientists of Ecole Polytechnique-Paris. The results concern crack theory and associated fields as fracture, yielding and material science. ! There are many problems for discussions, e.g. the Dugodale-Barenblatt cracks are absolutely different from physical point of view. ! Altogether the monograph is an interesting and valuable contribution and can be used by researchers and graduate students." (Jozef Golecki, Zentralblatt MATH, Vol. 1108 (10), 2007)

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Non-Fiction Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Solids Stress & Fracture Science Physics Technology in General Engineering in General Mechanical Engineering

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Published: 10th October 2011

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Preface	p. xiii
Notations	p. xvii
Color plates	p. xxi
Deformation and Fracture	p. 1
Deformation	p. 2
Geometric transforms	p. 2
Small strain	p. 3
Compatibility conditions	p. 4
Stress	p. 5
Elasticity	p. 6
Constitutive laws	p. 6
Tonti's diagram in elasticity	p. 7
Plasticity	p. 10
Experimental yield surfaces	p. 10
Prandtl-Reuss equations	p. 13
Generalized standard materials	p. 17
Fracture	p. 18
Introduction to fracture mechanics	p. 18
Stress intensity factors	p. 19
On the physics of separation	p. 21
Different types of fracture	p. 23
Brittle fracture criterion	p. 28
Energetic Aspects of Fracture	p. 29
Griffith's theory of fracture	p. 29
Some expressions of G in quasi-statics	p. 31
Irwin's formula	p. 32
Barenblatt's cohesive force model	p. 34
Berry's interpretation of energies	p. 35
Stability analysis of multiple cracks	p. 37
An inverse energetic problem	p. 40
Path-independent integrals in quasi-statics	p. 43
The path-independent J-integral	p. 44
Associated J-integrals for separating mixed modes	p. 45
The T-integral in linear thermo-elasticity	p. 47
Lagrangian derivative of energy and the G-[theta] integral	p. 50
Generalization of Griffith's model in three dimensions	p. 52
A local model of viscous fracture	p. 54
A non local model of fracture	p. 55
A dissipation rate model for non local brittle fracture	p. 56
Convex analysis of three-dimensional brittle fracture	p. 57
Solutions of Cracks Problems	p. 61
Mathematical problems in plane elasticity	p. 61
Plane strain and antiplane strain	p. 61
Plane stress condition revisited	p. 62
Complex variables in elasticity	p. 63
The Hilbert problem	p. 65
The finite crack in an infinite medium	p. 68
The auxiliary problem	p. 69
Dugdale-Barenblatt's model	p. 72
The kinked crack in mixed mode	p. 73
An integral equation of the kinked crack problem	p. 74
The asymptotic equation	p. 76
Crack problems in elastoplasticity	p. 78
Matching asymptotic solutions	p. 79
A complete solution in plasticity and damage	p. 80
A review of non linear asymptotic solutions	p. 85
Inverse geometric problem with Coulomb's friction	p. 87
Non-uniqueness of solutions	p. 88
Frictional crack problem without opening	p. 89
The energy release rate of a frictional interface crack	p. 92
The frictional interface crack with an opening zone	p. 93
Thermodynamics of Crack Propagation	p. 97
An elementary example	p. 97
Dissipation analysis	p. 99
Thermal aspects of crack propagation	p. 101
Singularity of the temperature in thermo-elasticity	p. 106
Asymptotic solution of the coupled equations	p. 107
Dynamic Fracture Mechanics	p. 113
Experimental aspects of crack propagation	p. 113
Fundamental equations	p. 115
Steady state solutions	p. 116
Transient crack problems	p. 118
Symmetric extension of a crack	p. 118
Semi-infinite crack with arbitrary propagation speed	p. 121
Diffraction of time harmonic plane wave by a crack	p. 122
Path-independent integrals	p. 126
Path-independent integrals for moving cracks	p. 126
A path-independent integral for crack initiation	p. 128
Inverse problems in dynamic fracture	p. 129
An experimental method for dynamic toughness	p. 130
Identification of energies in dynamic fracture	p. 132
Three-Dimensional Crack Problems	p. 135
Fundamental tensors in elastostatics	p. 135
The Kelvin-Somigliana tensor	p. 135
The Kupradze-Bashelishvili tensor	p. 136
Fundamental theorems in elastostatics	p. 137
Solution of the Neumann boundary value problem	p. 138
Solution of the Dirichlet boundary value problem	p. 139
Direct methods using Kelvin-Somigliana's tensor	p. 141
A planar crack in an infinite elastic medium	p. 143
The symmetric opening mode I	p. 143
The shear modes	p. 144
A planar crack in a bounded elastic medium	p. 145
Singularity analysis	p. 147
Solutions to some crack problems	p. 149
The angular crack in an infinite elastic medium	p. 153
The edge crack in an elastic half-space	p. 155
On some mathematical methods for BIE in 3D	p. 160
The Kupradze elastic potential theory	p. 160
On the regularization of hypersingular integrals	p. 162
Other regularization methods	p. 165
An integral equation in elasto-plasticity	p. 169
Non Linear Fracture Mechanics	p. 173
Introduction	p. 173
Ductile fracture	p. 175
Rousselier's model	p. 176
The micromechanics of plasticity	p. 182
Gurson's model	p. 186
Extension of porous plasticity models to aggregates	p. 187
Bifurcation problems in plasticity	p. 189
A finite strain theory of cavitation in solids	p. 193
Abeyaratne and Hou's solution in finite elasticity	p. 196
Solution for a creeping material	p. 197
The Fluid-Filled Crack	p. 199
Introduction	p. 199
The leak before break inverse problem	p. 200
Empirical models of fluid flow in a crack breach	p. 201
Variable breach area	p. 205
Wear mechanics	p. 210
Wear criterion and wear rate	p. 212
Conservation of mass	p. 214
Rheology of the third body	p. 214
The W-equation for a sliding punch on a half-plane	p. 216
Identification of constants	p. 218
Hydraulic fracturing of rocks	p. 218
The physical problems	p. 218
Equations in hydraulic fracturing of rocks	p. 220
Capillary phenomenon in fracture mechanics	p. 222
The equilibrium crack partially filled with a fluid	p. 223
Capillary stress intensity factor	p. 228
Viscous fluid flow solution near a moving crack tip	p. 229
Equations of the fluid-filled moving crack	p. 229
Numerical results	p. 230
Crack Detection by Scattering of Waves	p. 233
Introduction	p. 233
Scattering of acoustic waves	p. 234
Detection of a rigid inclusion	p. 235
Detection of a flat cavity	p. 238
Finite spectrum and finite number of incident waves	p. 240
Diffraction of elastic waves	p. 243
Non destructive testing of materials. A case study	p. 246
Time reversal mirror (TRM)	p. 248
Experimental validation of TRM	p. 250
The mathematics of time reversal mirror	p. 251
Tomographic Evaluation of Materials	p. 253
Introduction	p. 253
X-rays tomography	p. 254
Inverse Radon's transform	p. 255
Example of crack detection	p. 257
Attenuated Radon transform	p. 258
Functional tomography by SPECT and PET	p. 258
Novikov's inversion formula	p. 260
Conical Radon's transform in Compton scattering	p. 260
The conical Radon transform	p. 261
Nguyen and Truong's inversion formula	p. 263
The Reciprocity Gap Functional for Crack Detection	p. 267
Distributed defect and crack	p. 267
Planar crack identification in quasi-static elasticity	p. 270
Determination of the normal to the crack plane	p. 271
Determination of the crack plane	p. 272
Determination of the crack shape	p. 272
The instantaneous RG functional	p. 273
Inverse problem for the heat diffusion equation	p. 277
Solution for the crack plane location	p. 279
Solution for the crack shape	p. 280
Inverse acoustic scattering of a crack in time domain	p. 281
Elastodynamic scattering of a crack in time domain	p. 283
The observation equation in elastodynamics	p. 284
Solution	p. 286
The earthquake inverse problem and solution	p. 287
Methods of Solution to Inverse Problems	p. 293
The ill-posedness of the inverse problem	p. 293
General considerations on inverse problems	p. 295
Tikhonov's regularization	p. 296
Optimal choice of the regularization parameter	p. 298
Error estimate	p. 299
Optimal control theory	p. 300
State equation and optimal control	p. 301
Adjoint system of equations	p. 302
The dynamic system of quasi-static elasticity	p. 305
Smoothing operators	p. 309
Transfer matrix operator in elasticity	p. 310
Quasi-reversibility method	p. 313
Control of partial derivative equations	p. 314
Inverse problems in parabolic systems	p. 314
Identification of materials	p. 317
Stochastic inversion methods	p. 318
Tarentola's inversion method	p. 318
Kalman's filter	p. 319
Duality in solid mechanics and inverse problems	p. 320
Residual Stresses in Fracture Mechanics	p. 323
An approximate theory of residual stress	p. 323
A theory of fracture with initial stresses	p. 324
Energy release rate	p. 325
Residual stress identification	p. 326
Origin of the residual stresses	p. 326
Determination of the residual stresses	p. 327
Weak Interface Singularities	p. 329
The interface crack between dissimilar materials	p. 329
Discontinuous Neumann boundary conditions	p. 332
Thermo-plastic discontinuity on a composite tube	p. 333
Problems and Solutions	p. 337
References	p. 349
Index	p. 371
Table of Contents provided by Ingram. All Rights Reserved.

Fracture Mechanics

Inverse Problems and Solutions

At a Glance

Hardcover

Industry Reviews

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