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Table of contents
1 Résumé des travaux de thèse en Français
1.1 Contexte et objectifs de la thèse
1.2 Modèle analytique
1.2.1 Volume Elémentaire Représentatif
1.2.2 Contributions statique et dynamique du tenseur des contraintes
1.3 Résultats
1.4 Conclusion et perspectives
2 Literature review
2.1 Introduction
2.2 Experimental works
2.3 Modeling
2.3.1 Quasi-static analysis on void growth
2.3.1.1 Introduction
2.3.1.2 McClintock Model
2.3.1.3 Gurson model
2.3.1.4 Gurson Tvergaard and Needleman model (GTN model)
2.3.2 Dynamic analysis for porous materials
2.3.2.1 Introduction
2.3.2.2 Carroll and Holt Model
2.3.2.3 Molinari and Mercier Model-2001
2.3.2.4 Leblond and Roy Model
2.3.2.5 Molinari et. al Model
2.3.3 Conclusion
3 Modeling
3.1 Geometry of the RVE and formulation of the velocity field
3.1.1 Formulation of the admissible velocity field
3.2 Formulation of the micro-inertia dependent term dyn
3.2.1 Plane strain case
3.2.2 Uniaxial deformation
3.3 Quasistatic stress tensor static
4 Results
4.1 Introduction
4.2 Axisymmetric loading
4.3 Plane strain
4.4 Hydrostatic loading
4.5 Additional loading cases
4.6 Conclusion
5 Finite element modeling
5.1 Introduction
5.2 Plane strain configuration
5.3 Hydrostatic loading
5.3.1 Boundary conditions inherited from the analytical model
5.3.2 Closed unit-cell
5.3.3 Validation on the reference case
5.3.4 Thin cylinder, l0=10m
5.4 Additional loading cases
5.4.1 Imposed axial strain rate (D33=constant) with combined stress imposed on the lateral surface
5.4.2 Uniaxial loading: Case 1, =1/3
5.4.3 Biaxial loading: Case 2, =2/3
5.5 Influence of the elastic properties
6 Conclusion and perspectives
A Formulation of the macroscopic dynamic stress tensor, dyn.
A.1 General formulation
A.2 Case where = 0 3
A.3 Axisymmetric case
B Analytical relationships for the quasi-static macroscopic stress, static.
C Formulation of the macroscopic dynamic stress tensor (dyn) for 2D approach.
Bibliography
