Extended Finite Element Method for Crack Propagation

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.

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

• Foreword xiAcknowledgements xiiiList of Symbols xvIntroduction xviiChapter 1. Elementary Concepts of Fracture Mechanics 11.1. Introduction 11.2. Superposition principle 31.3. Modes of crack straining 41.4. Singular fields at cracking point 51.5. Crack propagation criteria 10Chapter 2. Representation of Fixed and Moving Discontinuities 212.1. Geometric representation of a crack: a scale problem 222.2. Crack representation by level sets 292.3. Simulation of the geometric propagation of a crack 522.4. Prospects of the geometric representation of cracks 66Chapter 3. Extended Finite Element Method X-FEM 693.1. Introduction 693.2. Going back to discretization methods 703.3. X-FEM discontinuity modeling 793.4. Technical and mathematical aspects 943.5. Evaluation of the stress intensity factors 98Chapter 4. Non-linear Problems, Crack Growth by Fatigue 1094.1. Introduction 1094.2. Fatigue and non-linear fracture mechanics 1144.3. eXtended constitutive law 1374.4. Applications 164Chapter 5. Applications: Numerical Simulation of Crack Growth 1735.1. Energy conservation: an essential ingredient 1735.2. Examples of crack growth by fatigue simulations 1825.3. Dynamic fracture simulation 1925.4. Simulation of ductile fracture 207Conclusions and Open Problems 227Summary 233Bibliography 235Index 253