This book discusses new techniques for the simulation of cracks in complex conditions required for industrial applications.
The level sets method makes it possible to simulate the presence and evolution of a crack with a complex shape. The extended finite element method (X-FEM) uses a priori knowledge on the problem to resolve it, and makes it possible to take into account the presence of a crack without remeshing. The non-linearity of the material behavior, which is essential in the area of fatigue, is simulated by an extended law of elastic-plastic behavior for the X-FEM element. The extended finite elements also allow us to perfectly control the energy exchanges, which is of benefit for crack simulation in fragile media or in dynamics.
1. Elementary Concepts of Fracture Mechanics.
2. Representation of Fixed and Moving Discontinuities.
3. Extended Finite Element Method X-FEM.
4. Non-linear Problems, Crack Growth by Fatigue.
5. Applications: Numerical Simulation of Crack Growth.
Conclusions and Open Problems.
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