Fracture mechanics : inverse problems and solutions
 Responsibility
 by H.D. Bui.
 Imprint
 Dordrecht : Springer, 2006.
 Physical description
 xxiii, 375 p. : ill. (some col.) ; 25 cm.
 Series
 Solid mechanics and its applications v. 139.
Online
At the library
Engineering Library (Terman)
Stacks
Call number  Note  Status 

TA409 .B85 2006  Unknown 
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Description
Creators/Contributors
 Author/Creator
 Bui, Huy Duong.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Part I Fracture Mechanics: 1. Deformation and Fracture: 1.1. Deformation: Geometric transforms
 Small strain
 Compatibility condition
 Stress. 1.2. Elasticity : Constitutive law
 Tonti's diagram in elasticity
 Plasticity : Experimental yield surfaces
 PrandtReuss equation
 1.3 Fracture : Introduction to Fracture Mechanics
 Stressintensity Factors
 On the physics of separation
 Different types of fractures (ductile fracture, fatigue Paris's law, Dangvan's criterion)
 Brittle fracture criterion. 2. Energetic aspects of fracture 2.1 Griffith's theory of fracture Some expressions of G in quasistatics (Energy release rate). 2.2 Some expressions of G in quasistatics (Energy release rate). 2.3 Irwin's formula. 2.4 Barenblatt's cohesive force model 2.5 Berry's interpretation of energies 2.6 Stability analysis of multiple cracks 2.7 An inverse energetic problem 2.8 Pathindependent integrals in quasistatics : The pathindependent Jintegral
 Associated Jintegrals for separating mixed modes
 The Tintegral in linear thermoelasticity
 Lagrangian derivative of energy and the G0 integral 2.9 Generalization of Griffth's model in three dimensions : A local model of viscous fracture
 A non local model of fracture
 A dissipation rate model for non local brittle fracture
 Convex analysis of three dimensional brittle fracture. 3. Solutions of crack problems 3.1 Mathematical problems in plane elasticity : Plane strain and antiplane strain
 Plane stress condition revisited
 Complex variables in elasticity
 The Hilbert problem. 3.2 The finite crack in an infinite medium : The auxiliary problem
 Dugdale Barenblatt's model
 Remote uniform stress. 3.3 The kinked crack in mixed mode : An integral equation of the kinked crack problem
 The asymptotic equation. 3.4 Crack problems in elastoplasticity: Matching asymptotic solutions
 A complete solution plasticity and damage
 A review of asymptotic solutions in nonlinear materials. 3.5 Inverse geometric problem with Coulomb's friction: Nonuniqueness of solution in friction crack
 Solution to the frictional crack problem without opening
 The energy release rate of a frictional interface crack
 The frictional interface crack problem with an opening zone 4. Thermodynamics of crack propagation 4.1 An elementary example 4.2 Dissipation analysis 4.3 Thermal aspects in crack propagation 4.4 Singularity of the temperature in thermoelasticity 4.5 Asymptotic solution of the coupled equations 5. Dynamic Fracture Mechanics 5.1 Experimental aspects of crack propagation. 5.2 Fundamental equations 5.3 Steady state solutions 5.4 Transient crack problems : Symmetric extension of a crack
 Semiinfinite crack with arbitrary propagation speed 5.5 The WienerHopf technique
 Diffraction of waves impinging a semi infinite crack 5.6 . Pathindependent integrals for moving crack 5.7 A pathindependent integral for crack initiation analysis : Inverse problems in dynamic fracture
 A new experimental method for dynamic toughness. 5.8 Some other applications of dynamic fracture 6. Threedimensional cracks problems 6.1 Fundamental tensors in elastostatics : The KelvinSomigliana's tensor
 The KupradzeBashelishvili tensor
 Singularity analysis 6.2 Fundamental theorems in elastostatics : Solution of the Neumann boundary value problem
 Solution of the Dirichiet boundary value problem
 Direct methods using KelvinSomigliana's tensor 6.3 A planar crack in an infinite elastic medium : The symmetric opening mode I
 The shear modes 6.4 A planar crack in a bounded elastic medium : Singularity analysis
 Solutions of some crack problems 6.5 The angular crack in an unbounded elastic medium 6.6 The edge crack in an elastic halfspace 6.7 On some mathematical methods for BIE in 31) : The Kupradze elastic potentials theory
 On the regularization of hypersingular integrals
 Other regularization methods 6.8 An integral equation in elastoplasticity 7. Non linear fracture mechanics 7.1 Introduction 7.2 Ductile fracture : Rousselier's model
 The micromechanics of plasticity
 Gurson's model
 Extension of porous plasticity models to aggregates 7.3 Bifurcation problems in plasticity 7.4 A finite strain theory of cavitation in solids : Abeyratne and Hou's solution in finite elasticity
 Solution for creeping materials 8. The fluidfilled crack 8.1 Introduction 8.2 The Leak Before Break inverse problem : Empirical models of fluid flow in a crack breach
 variable breach area 8.3 Wear mechanics : Wear criterion and wear rate conservation of mass
 Rheology of the third body
 The Wequation in the sliding of a punch on an halfplane
 Identification of constants. 8.3 Hydraulic fracturing of rocks : equations in hydraulic fracturing of rocks 8.4 Capillary phenomenon in fracture mechanics : The equilibrium crack partially filled with a fluid
 Capillary stress intensity factor 8.5 Viscous fluid flow solution near the moving crack tip : Equation for the fluidfilled moving crack
 Numerical results Part II Inverse problems and solutions 9. Methods for defect and crack detection by scattering of waves 9.1 Introduction 9.2 Scattering of acoustic waves : Rigid indusion
 Flat cavity
 Finite spectrum and finite number of incident waves 9.3 Diffraction of elastic waves 9.4 Non destructive testing of materials : A case study 9.5 Timereversal mirror (ThM) : Experimental validation of ThM
 The mathematics of time reversal mirror 10. Tomographic evaluation of materials 10.1 Introduction 10.2 Xrays Tomography : Inverse Radons transform
 Example of Crack detection. 10.3 Attenuated Radon transform : Novikovs inversion formula. 10.4 Conical Radon transform in Compton scattering : The Conical Radon transform
 Nguyen & Truong's inversion formula. 11. The Reciprocity Gap Functional (RGF) for crack detection 11.1 Distributed defects and cracks. Calderons solution. 11.2 Planar crack identification in quasistatic * elasticity : Determination of the normal to the crack plane
 Determination of the crack plane
 Determination of the crack shape 11.3 The instantaneous RG functional 11.3 Inverse problem for the heat diffusion equation: Solution for the crack plane location
 solution for the crack shape 11.4 Inverse acoustic scattering of a crack in time domain 11.5 Elastodynamic scattering of a crack in time domain : The observation equation in elastodynamics 11.7 The earthquake inverse problem 12. Methods of solution to Inverse Problems 12.1 The illposedness of the inverse problem 12.2 General considerations on inverse problems 12.3 Tikhonov's regularization 12.4 Control theory : Control of an evolution equation
 Pontryagin's minimum principle
 Bellman's dynamic programming 12.5 The dynamic formulation of quasi static elasticity. : Smoothing operators
 The transfer matrix operator in elasticity. 12.6 Quasireversibility methods : Cauchy problem for elliptic equation. 12.7 Control theory for partial derivative equations : Inverse problem to determine the heat conduction coeficient field
 Inverse problem to determine a constitutive law. 12.8 Stochastic inversion methods. Appendix : Problems and solutions Index References.
 (source: Nielsen Book Data)
 Publisher's summary

This book is an attempt to present, in a unified manner, different topics of Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve twodimensional and threedimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to undergraduate students. These new topics take into consideration the thermodynamics of continuous media, including thermal and dynamical aspects. In addition, the book introduces the notion of duality or symmetry in Solids Mechanics. The loss of symmetry is exploited to provide a unique and powerful tool, called the reciprocity gap functional introduced by the author's groups, to solve explicitly some important inverse problems arising in crack determination as well as in the earthquake inverse problem. With its emphasis, initially on physical or experimental backgrounds, and then on analysis and theoretical results, rather than on numerical computations, this monograph is intended to be used by students and researchers in solids mechanics, mechanical engineering and applied mathematics.
(source: Nielsen Book Data)
Subjects
 Subjects
 Fracture mechanics.
Bibliographic information
 Publication date
 2006
 Series
 Solid mechanics and its applications ; v. 139
 ISBN
 140204836X (hd.bd.)
 1402048378 (ebook)
 9781402048364 (hd.bd.)
 9781402048371 (ebook)