Extended Finite Element Method for Crack Propagation

Novel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided.

Foreword xi

Acknowledgements xiii

List of Symbols xv

Introduction xvii

Chapter 1. Elementary Concepts of Fracture Mechanics 1

1.1. Introduction 1

1.2. Superposition principle 3

1.3. Modes of crack straining 4

1.4. Singular fields at cracking point 5

1.5. Crack propagation criteria 10

Chapter 2. Representation of Fixed and Moving Discontinuities 21

2.1. Geometric representation of a crack: a scale problem 22

2.2. Crack representation by level sets 29

2.3. Simulation of the geometric propagation of a crack 52

2.4. Prospects of the geometric representation of cracks 66

Chapter 3. Extended Finite Element Method X-FEM 69

3.1. Introduction 69

3.2. Going back to discretization methods 70

3.3. X-FEM discontinuity modeling 79

3.4. Technical and mathematical aspects 94

3.5. Evaluation of the stress intensity factors 98

Chapter 4. Non-linear Problems, Crack Growth by Fatigue 109

4.1. Introduction 109

4.2. Fatigue and non-linear fracture mechanics 114

4.3. eXtended constitutive law 137

4.4. Applications 164

Chapter 5. Applications: Numerical Simulation of Crack Growth 173

5.1. Energy conservation: an essential ingredient 173

5.2. Examples of crack growth by fatigue simulations 182

5.3. Dynamic fracture simulation 192

5.4. Simulation of ductile fracture 207

Conclusions and Open Problems 227

Summary 233

Bibliography 235

Index 253

"The book, intended for the solid mechanics community, is concisely written and includes numerous illustrations." (Booknews, 1 June 2011)

Sylvie Pommier is Professor at Ecole Normale Supérieure de Cachan and the LMT-Cachan Laboratory in France. Her main research topics include the development of fatigue crack growth rate predictions and methods accounting for load history effects under complex loading conditions (mixed mode loading, non-isothermal fatigue, variable amplitude, corrosion assisted fatigue).

Anthony Gravouil is Professor at INSA and the LaMCoS Laboratory in Lyon, France. His main research topics include the development of efficient and robust numerical methods (X-FEM) for the simulation of crack growth without remeshing, local multi-grid strategy coupled with X-FEM with a 3D representation of “real” cracks by level sets from 3D imaging and the development of space-time multi-scale methods for transient nonlinear dynamics (simulation of crash and impact phenomena).

Alain Combescure is Professor at INSA in Lyon, France. His specialties include buckling, fracture mechanics, dynamics (mainly computational mechanics).

Nicolas Moës is Professor at Ecole Centrale de Nantes in France. His research interests include computational methods in engineering for fracture and impact, and X-FEM.