[内容简介]

This book describes the basics and developments of the new XFEM approach to fracture analysis of structures and materials. It provides state of the art techniques and algorithms for fracture analysis of structures including numeric examples at the end of each chapter as well as an accompanying website which will include MATLAB resources, executables, data files, and simulation procedures of XFEM.

• The first reference text for the extended finite element method (XFEM) for fracture analysis of structures and materials
• Includes theory and applications, with worked numerical problems and solutions, and MATLAB examples on an accompanying website with further XFEM resources
• Provides a comprehensive overview of this new area of research, including a review of Fracture Mechanics, basic through to advanced XFEM theory, as well as current problems and applications
• Includes a chapter on the future developments in the field, new research areas and possible future applications of the method

[目录]

Chapter 1 Introduction

1.1 Composite structures

1.2 Failure of composites

1.2.1 Matrix cracking

1.2.2 Delamination

1.2.3 Fibre/matrix debonding

1.2.4 Fibre breakage

1.2.5 Macro models of cracking in composites

1.3 Crack analysis

1.3.1 Local and non-local formulations

1.3.2 Theoretical methods for failure analysis

1.4 Analytical solutions for composites

1.4.1 Continuum models

1.4.2 Fracture mechanics of composites

1.5 Numerical techniques

1.5.1 Boundary element method

1.5.2 Finite element method

1.5.3 Adaptive finite/discrete element method

1.5.4 Meshless methods

1.5.5 Extended finite element method

1.5.6 Extended isogeometric analysis

1.5.7 Multiscale analysis

1.6 Scope of the book

Chapter 2 Fracture Mechanics, a Review

2.1 Introduction

2.2 Basics of elasticity

2.2.1 Stress–strain relations

2.2.2 Airy stress function

2.2.3 Complex stress functions

2.3 Basics of LEFM

2.3.1 Fracture mechanics

2.3.2 Infinite tensile plate with a circular hole

2.3.3 Infinite tensile plate with an elliptical hole

2.3.4 Westergaard analysis of a line crack

2.3.5 Williams solution of a wedge corner

2.4 stress intensity factor

2.4.1 Definition of the stress intensity factor

2.4.2 Examples of stress intensity factors for LEFM

2.4.3 Griffith energy theories

2.4.4 Mixed mode crack propagation

2.5 Classical solution procedures for K and G

2.5.1 Displacement extrapolation/correlation method

2.5.2 Mode I energy release rate

2.5.3 Mode I stiffness derivative/virtual crack model

2.5.4 Two virtual crack extensions for mixed mode cases

2.5.5 Single virtual crack extension based on displacement decomposition

2.6 Quarter point singular elements

2.7 J integral

2.7.1 Generalisation of J

2.7.2 Effect of crack surface traction

2.7.3 Effect of body force

2.7.4 Equivalent domain integral (EDI) method

2.7.5 Interaction integral method

2.8 Elastoplastic fracture mechanics (EPFM)

2.8.1 Plastic zone

2.8.2 Crack tip opening displacements (CTOD)

2.8.3 J integral for EPFM

Chapter 3 Extended Finite Element Method

3.1 Introduction

3.2 Historic development of XFEM

3.2.1 A review of XFEM development

3.2.2 A review of XFEM composite analysis

3.3 Enriched approximations

3.3.1 Partition of unity

3.3.2 Intrinsic and extrinsic enrichments

3.3.3 Partition of unity finite element method

3.3.4 MLS enrichment

3.3.5 Generalised finite element method

3.3.6 Extended finite element method

3.5.7 Generalised PU enrichment

3.4 XFEM formulation

3.4.1 Basic XFEM approximation

3.4.2 Signed distance function

3.4.3 Modelling the crack

3.4.4 Governing equation

3.4.5 XFEM discretisation

3.4.6 Evaluation of derivatives of enrichment functions

3.4.7 Selection of nodes for discontinuity enrichment

3.4.8 Numerical integration

3.5 XFEM strong discontinuity enrichments

3.5.1 A modified FE shape function

3.5.2 The Heaviside function

3.5.3 The sign function

3.5.4 Strong tangential discontinuity

3.5.5 Crack intersection

3.6 XFEM weak discontinuity enrichments

3.7 XFEM crack tip enrichments

3.7.1 Isotropic enrichment

3.7.2 Orthotropic enrichment functions

3.7.3 Bimaterial enrichments

3.7.4 Orthotropic bimaterial enrichments

3.7.5 Dynamic enrichment

3.7.6 Orthotropic dynamic enrichments for moving cracks

3.7.7 Bending plates

3.7.8 Crack tip enrichments in shells

3.7.9 Electro-mechanical enrichment

3.7.10 Dislocation enrichment

3.7.11 Hydraulic fracture enrichment

3.7.12 Plastic enrichment

3.7.13 Viscoelastic enrichment

3.7.14 Contact corner enrichment

3.7.15 Modification for large deformation problems

3.7.16 Automatic enrichment

3.8 Transition from standard to enriched approximation

3.8.1 Linear blending

3.8.2 Hierarchical transition domain

3.9 Tracking moving boundaries

3.9.1 Level set method

3.9.2 Alternative methods

3.10 Numerical simulations

3.10.1 A central crack in an infinite tensile plate
3.10.2 An edge crack in a finite plate
3.10.3 Tensile plate with a central inclined crack
3.10.4 A bending plate in fracture mode III
3.10.5 Crack propagation in a shell
3.10.6 Shear band simulation
3.10.7 Fault simulation
3.10.8 Sliding contact stress singularity by PUFEM
3.10.9 Hydraulic fracture
3.10.10 Dislocation dynamics Chapter 4 Static Fracture Analysis of Composites

4.1 Introduction

4.2 Anisotropic elasticity

4.2.1 Elasticity solution

4.2.2 Anisotropic stress functions

4.3 Analytical solutions for near crack tip

4.3.1 The general solution

4.3.2 Special solutions for different types of composites

4.4 Orthotropic mixed mode fracture

4.4.1 Energy release rate for anisotropic materials

4.4.2 Anisotropic singular elements

4.4.3 SIF calculation by interaction integral

4.4.4 Orthotropic crack propagation criteria

4.5 Anisotropic XFEM

4.5.1 Governing equation

4.5.2 XFEM discretisation

4.5.3 Orthotropic enrichment functions

4.6 Numerical simulations

4.6.1 Plate with a crack parallel to material axis of orthotropy

4.6.2 Edge crack with several orientations of the axes of orthotropy

4.6.3 Inclined edge notched tensile specimen

4.6.4 Central slanted crack

4.6.5 An inclined centre crack in a disk subjected to point loads

4.6.6 Crack propagation in an orthotropic beam

Chapter 5 Dynamic Fracture Analysis of Composites

5.1 Introduction

5.1.1 Dynamic fracture mechanics

5.1.2 Dynamic fracture mechanics of composites

5.1.3 Dynamic fracture by XFEM

5.2 Analytical solutions for near crack tips in dynamic states

5.2.1 Analytical solutions for a propagating crack in isotropic material

5.2.2 Asymptotic solution for a stationary crack in orthotropic media

5.2.3 Analytical solution for near crack tip of a propagating crack in orthotropic material

5.3 Dynamic stress intensity factors

5.3.1 Stationary and moving crack dynamic stress intensity factors

5.3.2 Dynamic fracture criteria

5.3.3 J integral for dynamic problems

5.3.4 Domain integral for orthotropic media

5.3.5 Interaction integral

5.3.6 Crack-axis component of the dynamic J integral

5.3.7 Field decomposition technique

5.4 Dynamic XFEM

5.4.1 Dynamic equations of motion

5.4.2 XFEM discretisation

5.4.3 XFEM enrichment functions

5.4.4 Time integration schemes

5.5 Numerical simulations

5.5.1 Plate with a stationary central crack

5.5.2 Mode I plate with an edge crack

5.5.3 Mixed mode edge crack in composite plates

5.5.4 A composite plate with double edge cracks under impulsive loading

5.5.5 Pre-cracked three point bending beam under impact loading

5.5.6 Propagating central inclined crack in a circular orthotropic plate

Chapter 6 Fracture Analysis of Functionally Graded Materials

6.1 Introduction

6.2 Analytical solution for near crack tip

6.2.1 Average material properties

6.2.2 Mode I near tip fields in FGM composites

6.2.3 Stress and displacement field (similar to homogeneous orthotropic composites)

6.3 Stress intensity factor

6.3.1 J integral

6.3.2 Interaction integral

6.3.3 FGM auxiliary fields

6.3.4 Isoparametric FGM

6.4 Crack propagation in FGM composites

6.5 Inhomogeneous XFEM

6.5.1 Governing equation

6.5.2 XFEM approximation

6.5.3 XFEM discretisation

6.6 Numerical examples

6.6.1 Plate with a centre crack parallel to material gradient

6.6.2 Proportional FGM plate with an inclined centre crack

6.6.3 Non-proportiona FGM plate with a fixed inclined centre crack

6.6.4 Rectangular plate with an inclined crack (non-proportional)

6.6.5 Crack propagation in a four-point FGM beam

Chapter 7 Delamination/Interlaminar Crack Analysis

7.1 Introduction

7.2 Fracture mechanics for bimaterial interface cracks

7.2.1 Isotropic bimaterial interfaces

7.2.2 Orthotropic bimaterial interface cracks

7.2.3 Stress contours for a crack between two dissimilar orthotropic materials

7.3 Stress intensity factors for interlaminar cracks

7.4 Delamination propagation

7.4.1 Fracture energy based criteria

7.4.2 Stress based criteria

7.4.3 Contact based criteria

7.5 Bimaterial XFEM

7.5.1 Governing equation

7.5.2 XFEM discretisation

7.5.3 XFEM enrichment functions for bimaterial problems

7.5.4 Discretisation and integration

7.6 Numerical examples

7.6.1 Central crack in an infinite bimaterial plate

7.6.2 Isotropic-orthotropic bimaterial crack

7.6.3 Orthotropic double cantilever beam

7.6.4 Concrete beams strengthened with fully bonded GFRP

7.6.5 FRP reinforced concrete cantilever beam subjected to edge loadings

7.6.6 Delamination of metallic I beams strengthened by FRP strips

7.6.7 Variable section beam reinforced by FRP

Chapter 8 New Orthotropic Frontiers

8.1 Introduction

8.2 Orthotropic XIGA

8.2.1 NURBS basis function

8.2.2 Extended Isogeometric analysis

8.2.3 XIGA simulations

8.3 Orthotropic dislocation dynamics

8.3.1 Straight dislocations in anisotropic materials

8.3.2 Edge dislocations in anisotropic materials

8.3.3 Curve dislocations in anisotropic materials

8.3.4 Anisotropic dislocation XFEM

8.3.5 Plane strain anisotropic solution

8.3.6 Individual sliding systems s1 and s2 in an infinite domain

8.3.7 Simultaneous sliding systems in an infinite domain

8.4 Other anisotropic applications

8.4.1 Biomechanics

8.4.2 Piezoelectric

References

Index