Fracture Mechanics: Inverse Problems and Solutions

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; Prandt-Reuss equation; 1.3 Fracture : Introduction to Fracture Mechanics; Stress-intensity 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 quasi-statics (Energy release rate). 2.2 Some expressions of G in quasi-statics (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 Path-independent integrals in quasi-statics : The path-independent J-integral ; Associated J-integrals 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 elasto-plasticity: Matching asymptotic solutions; A complete solution plasticity and damage; A review of asymptotic solutions in non-linear materials.3.5 Inverse geometric problem with Coulomb's friction: Non-uniqueness 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 thermo-elasticity 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 ; Semi-infinite crack with arbitrary propagation speed 5.5 The Wiener-Hopf technique ; Diffraction of waves impinging a semi- infinite crack 5.6 . Path-independent integrals for moving crack 5.7 A path-independent 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. Three-dimensional cracks problems 6.1 Fundamental tensors in elastostatics : The Kelvin-Somigliana's tensor; The Kupradze-Bashelishvili 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 Kelvin-Somigliana'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 half-space 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