Fracture Mechanics in Layered and Graded Solids: Analysis Using Boundary Element Methods

Contents\nChapter 1 Introduction\n	1.1 Functionally graded materials\n	1.2 Methods for fracture mechanics\n		1.2.1 General\n		1.2.2 Analytical methods\n		1.2.3 Finite element method\n		1.2.4 Boundary element method\n		1.2.5 Meshless methods\n	1.3 Overview of the book\n	References\nChapter 2 Fundamentals of Elasticity and Fracture Mechanics\n	2.1 Introduction\n	2.2 Basic equations of elasticity\n	2.3 Fracture mechanics\n		2.3.1 General\n		2.3.2 Deformation modes of cracked bodies\n		2.3.3 Three-dimensional stress and displacement fields\n		2.3.4 Stress fields of cracks in graded materials and on the interface of bi-materials\n	2.4 Analysis of crack growth\n		2.4.1 General\n		2.4.2 Energy release rate\n		2.4.3 Maximum principal stress criterion\n		2.4.4 Minimum strain energy density criterion\n		2.4.5 The fracture toughness of graded materials\n	2.5 Summary\n	References\nChapter 3 Yue’s Solution of a 3D Multilayered Elastic Medium\n	3.1 Introduction\n	3.2 Basic equations\n	3.3 Solution in the transform domain\n		3.3.1 Solution formulation\n		3.3.2 Solution expressed in terms of g\n		3.3.3 Asymptotic representation of the solution matrices\rΦ(ρ, z) and  Ψ(ρ, z)\n	3.4 Solution in the physical domain\n		3.4.1 Solutions in the Cartesian coordinate system\n		3.4.2 Closed-form results for singular terms of the solution\n	3.5 Computational methods and numerical evaluation\n		3.5.1 General\n		3.5.2 Singularities of the fundamental solution\n		3.5.3 Numerical integration\n		3.5.4 Numerical evaluation and results\n	3.6 Summary\n	Appendix 1 The matrices of elastic coefficients\n	Appendix 2 The matrices in the asymptotic expressions of Φ(ρ, z) and Ψ(ρ, z)\n	Appendix 3 The matrices Gs[m, z,Φ] and Gt [m, z,Φ]\n	References\nChapter 4 Yue’s Solution-based Boundary Element Method\n	4.1 Introduction\n	4.2 Betti’s reciprocal work theorem\n	4.3 Yue’s solution-based integral equations\n	4.4 Yue’s solution-based boundary integral equations\n	4.5 Discretized boundary integral equations\n	4.6 Assembly of the equation system\n	4.7 Numerical integration of non-singular integrals\n		4.7.1 Gaussian quadrature formulas\n		4.7.2 Adaptive integration\n		4.7.3 Nearly singular integrals\n	4.8 Numerical integration of singular integrals\n		4.8.1 General\n		4.8.2 Weakly singular integrals\n		4.8.3 Strongly singular integrals\n	4.9 Evaluation of displacements and stresses at an internal point\n	4.10 Evaluation of boundary stresses\n	4.11 Multi-region method\n	4.12 Symmetry\n	4.13 Numerical evaluation and results\n		4.13.1 A homogeneous rectangular plate\n		4.13.2 A layered rectangular plate\n	4.14 Summary\n	References\nChapter 5 Application of the Yue’s Solution-based BEM toCrack Problems\n	5.1 Introduction\n	5.2 Traction-singular element and its numerical method\n		5.2.1 General\n		5.2.2 Traction-singular element\n		5.2.3 The numerical method of traction-singular elements\n	5.3 Computation of stress intensity factors\n	5.4 Numerical examples and results\n	5.5 Summary\n	References\nChapter 6 Analysis of Penny-shaped Cracks in Functionally Graded Materials\n	6.1 Introduction\n	6.2 Analysis methods for crack problems in a FGM system of infinite extent\n		6.2.1 The crack problem in a FGM\n		6.2.2 The multi-region method for crack problems of infinite extent\n		6.2.3 The layered discretization technique for FGMs\n		6.2.4 Numerical verifications\n	6.3 The SIFs for a crack parallel to the FGM interlayer\n		6.3.1 General\n		6.3.2 A crack subjected to uniform compressive stresses\n		6.3.3 A crack subjected to uniform shear stresses\n	6.4 The growth of the crack parallel to the FGM interlayer\n		6.4.1 The strain energy density factor of an elliptical crack\n		6.4.2 Crack growth under a remotely inclined tensile loading\n	6.5 The SIFs for a crack perpendicular to the FGM interlayer\n		6.5.1 General\n		6.5.2 Numerical verifications\n		6.5.3 The SIFs for a crack subjected to uniform compressive stresses\n		6.5.4 The SIFs for a crack subjected to uniform shear stresses\n	6.6 The growth of the crack perpendicular to the FGM interlayer\n		6.6.1 The crack growth under a remotely inclined tensile loading\n		6.6.2 The crack growth under a remotely inclined compressive loading\n	6.7 Summary\n	References\nChapter 7 Analysis of Elliptical Cracks in Functionally Graded Materials\n	7.1 Introduction\n	7.2 The SIFs for an elliptical crack parallel to the FGM interlayer\n		7.2.1 General\n		7.2.2 Elliptical crack under a uniform compressive stress\n		7.2.3 Elliptical crack under a uniform shear stress\n	7.3 The growth of an elliptical crack parallel to the FGM interlayer\n	7.4 The SIFs for an elliptical crack perpendicular to the FGM interlayer\n		7.4.1 General\n		7.4.2 Elliptical crack under a uniform compressive stress\n		7.4.3 Elliptical crack under a uniform shear loading\n	7.5 The growth of an elliptical crack perpendicular to the FGM interlayer\n		7.5.1 Crack growth under a remotely inclined tensile loading\n		7.5.2 Crack growth under a remotely inclined compressive loading\n	7.6 Summary\n	References\nChapter 8 Yue’s Solution-based Dual Boundary Element Method\n	8.1 Introduction\n	8.2 Yue’s solution-based dual boundary integral equations\n		8.2.1 The displacement boundary integral equation\n		8.2.2 The traction boundary integral equation\n		8.2.3 The dual boundary integral equations for crack problems\n	8.3 Numerical implementation\n		8.3.1 Boundary discretization\n		8.3.2 The discretized boundary integral equation\n	8.4 Numerical integrations\n		8.4.1 Numerical integrations for the displacement BIE\n		8.4.2 Numerical integrations for the traction BIE\n	8.5 Linear equation systems for the discretized dual BIEs\n	8.6 Numerical verifications\n		8.6.1 Calculation of stress intensity factors\n		8.6.2 The effect of different meshes and the coefficientD on the SIF values\n	8.7 Summary\n	Appendix 4 Finite-part integrals and Kutt’s numerical quadrature\n		A4.1 Introduction\n		A4.2 Kutt’s numerical quadrature\n	References\nChapter 9 Analysis of Rectangular Cracks in the FGMs\n	9.1 Introduction\n	9.2 A square crack in FGMs of infinite extent\n		9.2.1 General\n		9.2.2 A square crack parallel to the FGM interlayer\n		9.2.3 A square crack having a 45◦\r angle with the FGM interlayer\n		9.2.4 A square crack perpendicular to the FGM interlayer\n	9.3 A square crack in the FGM interlayer\n	9.4 A rectangular crack in FGMs of infinite extent\n		9.4.1 General\n		9.4.2 A rectangular crack parallel to the FGM interlayer\n		9.4.3 A rectangular crack with long sides perpendicular to the FGM interlayer\n		9.4.4 A rectangular crack with short sides perpendicular to the FGM interlayer\n	9.5 A square crack in a FGM of finite extent\n	9.6 Square cracks in layered rocks\n		9.6.1 General\n		9.6.2 The crack dimensions and the parameters of layered rocks\n		9.6.3 A square crack subjected to a uniform compressive load\n		9.6.4 A square crack subjected to a non-uniform compressive load\n	9.7 Rectangular cracks in layered rocks\n		9.7.1 General\n		9.7.2 A rectangular crack subjected to a linear compressive load\n		9.7.3 A rectangular crack subjected to a nonlinear compressive load\n	9.8 Summary\n	References\nChapter 10 Boundary element analysis of fracturemechanics in transversely isotropic bi-materials\n	10.1 Introduction\n	10.2 Multi-region BEM analysis of cracks in transversely isotropic bi-materials\n		10.2.1 General\n		10.2.2 Calculation of the stress intensity factors\n		10.2.3 A penny-shaped crack perpendicular to the interface of transversely isotropic bi-materials\n		10.2.4 An elliptical crack perpendicular to the interface of transversely isotropic bi-materials\n	10.3 Dual boundary element analysis of a square crack in transversely isotropic bi-materials\n		10.3.1 General\n		10.3.2 Numerical verification\n		10.3.3 Numerical results and discussions\n	10.4 Summary\n	Appendix 5 The fundamental solution of transversely isotropic bi-materials\n	References