Front Matter
 Chapter 1 Introduction
  1.1 Functionally graded materials
  1.2 Methods for fracture mechanics
  1.3 Overview of the book
  References
 Chapter 2 Fundamentals of Elasticity and Fracture Mechanics
  2.1 Introduction
  2.2 Basic equations of elasticity
  2.3 Fracture mechanics
  2.4 Analysis of crack growth
  2.5 Summary
  References
 Chapter 3 Yue’s Solution of a 3D Multilayered Elastic Medium
  3.1 Introduction
  3.2 Basic equations
  3.3 Solution in the transform domain
  3.4 Solution in the physical domain
  3.5 Computational methods and numerical evaluation
  3.6 Summary
  Appendix 1 The matrices of elastic coefficients
  Appendix 2 The matrices in the asymptotic expressions of Φ(ñ , z) and Ψ(ñ , z)
  Appendix 3 The matrices Gs[m, z,Ö] and Gt [m, z,Ö]
  References
 Chapter 4 Yue’s Solution-based Boundary Element Method
  4.1 Introduction
  4.2 Betti’s reciprocal work theorem
  4.3 Yue’s solution-based integral equations
  4.4 Yue’s solution-based boundary integral equations
  4.5 Discretized boundary integral equations
  4.6 Assembly of the equation system
  4.7 Numerical integration of non-singular integrals
  4.8 Numerical integration of singular integrals
  4.9 Evaluation of displacements and stresses at an internal point
  4.10 Evaluation of boundary stresses
  4.11 Multi-region method
  4.12 Symmetry
  4.13 Numerical evaluation and results
  4.14 Summary
  References
  Contents ix
 Chapter 5 Application of the Yue’s Solution-based BEM toCrack Problems
  5.1 Introduction
  5.2 Traction-singular element and its numerical method
  5.3 Computation of stress intensity factors
  5.4 Numerical examples and results
  5.5 Summary
  References
 Chapter 6 Analysis of Penny-shaped Cracks in Functionally GradedMaterials
  6.1 Introduction
  6.2 Analysis methods for crack problems in a FGM system of infinite extent
  6.3 The SIFs for a crack parallel to the FGM interlayer
  6.4 The growth of the crack parallel to the FGM interlayer
  6.5 The SIFs for a crack perpendicular to the FGM interlayer
  6.6 The growth of the crack perpendicular to the FGM interlayer
  6.7 Summary
  References
 Chapter 7 Analysis of Elliptical Cracks in Functionally Graded Materials
  7.1 Introduction
  7.2 The SIFs for an elliptical crack parallel to the FGM interlayer
  7.3 The growth of an elliptical crack parallel to the FGM interlayer
  7.4 The SIFs for an elliptical crack perpendicular to the FGM interlayer
  7.5 The growth of an elliptical crack perpendicular to the FGM interlayer
  7.6 Summary
  References
 Chapter 8 Yue’s Solution-based Dual Boundary Element Method
  8.1 Introduction
  8.2 Yue’s solution-based dual boundary integral equations
  8.3 Numerical implementation
  8.4 Numerical integrations
  8.5 Linear equation systems for the discretized dual BIEs
  8.6 Numerical verifications
  8.7 Summary
  Appendix 4 Finite-part integrals and Kutt’s numerical quadrature
  References
 Chapter 9 Analysis of Rectangular Cracks in the FGMs
  9.1 Introduction
  9.2 A square crack in FGMs of infinite extent
  9.3 A square crack in the FGM interlayer
  9.4 A rectangular crack in FGMs of infinite extent
  9.5 A square crack in a FGM of finite extent
  9.6 Square cracks in layered rocks
  9.7 Rectangular cracks in layered rocks
  9.8 Summary
  References
 Chapter 10 Boundary element analysis of fracturemechanics in transverselyisotropic bi-materials
  10.1 Introduction
  10.2 Multi-region BEM analysis of cracks in transversely isotropic bi-materials
  10.3 Dual boundary element analysis of a square crack in transversely isotropicbi-materials
  10.4 Summary
  Appendix 5 The fundamental solution of transversely isotropic bi-materials
  References