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 two-dimensional and three-dimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to under-graduate 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.
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
From the reviews:
"This monograph is mainly a scope of research results of group of scientists of École 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)
This book presents, in a unified manner, a variety of topics in Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to under-graduate students. Emphasizing physical or experimental back-grounds, then analysis and theoretical results, this monograph is intended for use by students and researchers in solid mechanics, mechanical engineering and applied mathematics.
The most up to date book on Fracture Mechanics
A unique book dealing with Fracture Mechanics and Inverse problems
An attractive physical, experimental and mathematical approach of Fracture Mechanics