Extended Finite Element Method for Crack Propagation

<p>Foreword xi</p>
<p>Acknowledgements xiii</p>
<p>List of Symbols xv</p>
<p>Introduction xvii</p>
<p>Chapter 1. Elementary Concepts of Fracture Mechanics 1</p>
<p>1.1. Introduction 1</p>
<p>1.2. Superposition principle 3</p>
<p>1.3. Modes of crack straining 4</p>
<p>1.4. Singular fields at cracking point 5</p>
<p>1.5. Crack propagation criteria 10</p>
<p>Chapter 2. Representation of Fixed and Moving Discontinuities 21</p>
<p>2.1. Geometric representation of a crack: a scale problem 22</p>
<p>2.2. Crack representation by level sets 29</p>
<p>2.3. Simulation of the geometric propagation of a crack 52</p>
<p>2.4. Prospects of the geometric representation of cracks 66</p>
<p>Chapter 3. Extended Finite Element Method X–FEM 69</p>
<p>3.1. Introduction 69</p>
<p>3.2. Going back to discretization methods 70</p>
<p>3.3. X–FEM discontinuity modeling 79</p>
<p>3.4. Technical and mathematical aspects 94</p>
<p>3.5. Evaluation of the stress intensity factors 98</p>
<p>Chapter 4. Non–linear Problems, Crack Growth by Fatigue 109</p>
<p>4.1. Introduction 109</p>
<p>4.2. Fatigue and non–linear fracture mechanics 114</p>
<p>4.3. eXtended constitutive law 137</p>
<p>4.4. Applications 164<br /><br />Chapter 5. Applications: Numerical Simulation of Crack Growth 173</p>
<p>5.1. Energy conservation: an essential ingredient 173</p>
<p>5.2. Examples of crack growth by fatigue simulations 182</p>
<p>5.3. Dynamic fracture simulation 192</p>
<p>5.4. Simulation of ductile fracture 207</p>
<p>Conclusions and Open Problems 227</p>
<p>Summary 233</p>
<p>Bibliography 235</p>
<p>Index 253</p>