Fatigue crack propagation theories

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Table of contents

List of figures
List of tables v
List of abbreviations
Introduction
1 Fatigue: an overview
1.1 History of fatigue
1.2 Different forms of fatigue in the engineering world
1.3 Phases of fatigue life
1.4 Different domains of fatigue
1.5 Different types of load fluctuations
1.6 Existing fatigue approaches
1.6.1 Cumulative fatigue damage theories
1.6.2 Fatigue crack propagation theories
1.7 Cyclic elasto-(visco)plasticity
1.8 Concluding remarks
2 Continuum damage mechanics
2.1 Continuum mechanics: an overview
2.1.1 Admissibility conditions
2.1.2 Constitutive relations
2.2 General constitutive behaviour
2.2.1 Concept of plasticity
2.2.2 Rate-independent plasticity
2.2.3 Viscoplasticity
2.2.4 Concept of damage
2.2.5 Damage with elasto-(visco)plasticity
2.3 CDM approaches in fatigue
2.4 Concluding remark
3 Reduced order modelling and large time increment method
3.1 Classical incremental method
3.2 Model reduction techniques
3.2.1 Proper orthogonal decomposition (POD): a posteriori model reduction technique
3.2.2 Proper generalised decomposition (PGD): a priori model reduction technique
3.3 Large time increment (LATIN) method
3.3.1 First principle: separation of difficulties
3.3.2 Second principle: two-step algorithm
3.3.3 Third principle: model reduction method
3.3.4 A note on “normal formulation”
3.3.5 LATIN method in a heuristic nutshell
3.3.6 Newton-Raphson technique in the light of LATIN method
3.4 Concluding remark
4 LATIN-PGD technique for cyclic damage simulation
4.1 The proposed problem
4.2 Initialisation
4.3 Local stage
4.4 Search direction for global stage
4.5 Internal variables at the global stage
4.6 PGD formulation of the global stage
4.6.1 Separable representation of the quantities of interest
4.6.2 Hybrid method to construct the PGD reduced-order basis
4.7 Relaxation of the solution field and convergence criterion
4.8 Numerical examples
4.8.1 Bar under traction
4.8.2 “L” shaped structure
4.8.3 Plate with a hole
4.9 Concluding remarks
5 Multi-scale temporal discretisation approach
5.1 Finite element like time interpolation scheme
5.2 Computation of one “nodal cycle”
5.2.1 Initialisation
5.2.2 Local stage
5.2.3 Global stage
5.3 Numerical examples
5.3.1 Verification with mono-scale LATIN method
5.3.2 Influence of the “training stage”
5.3.3 Simulation of large number of cycles
5.3.4 Pre-damaged structure
5.3.5 Variable amplitude loading
5.3.6 Virtual ε-N curves
5.4 Concluding remark
6 Conclusion and future perspective
Appendices
A Calculation of the finite element operators
B Solution technique of the temporal problem
C Orthonormalisation of the space functions
D Alternative method of incorporating non-linear elastic state law
E Extended summary in French
Reference