The Variational Approach to Fracture Book

Introduction     1
Going variational     9
Griffith's theory     10
The 1-homogeneous case - A variational equivalence     14
Smoothness - The soft belly of Griffith's formulation     18
The non 1-homogeneous case - A discrete variational evolution     21
Functional framework - A weak variational evolution     22
Cohesiveness and the variational evolution     27
Stationarity versus local or global minimality - A comparison     31
1d traction     31
The Griffith case - Soft device     31
The Griffith case - Hard device     33
Cohesive case - Soft device     34
Cohesive case - Hard device     38
A tearing experiment     42
Initiation     47
Initiation - The Griffith case     48
Initiation - The Griffith case - Global minimality     48
Initiation - The Griffith case - Local minimality     55
Initiation - The cohesive case     58
Initiation - The cohesive 1d case - Stationarity     58
Initiation - The cohesive 3d case - Stationarity     61
Initiation - The cohesive case - Global minimality     67
Irreversibility     70
Irreversibility - The Griffith case - Well-posedness of the variational evolution     70
Irreversibility - The Griffith case - Discrete evolution     70
Irreversibility - The Griffith case - Global minimality in the limit     74
Irreversibility - The Griffith case - Energy balance in the limit     78
Irreversibility - The Griffith case - The time-continuous evolution     80
Irreversibility - The cohesive case     83
Path     90
Griffith vs. Barenblatt     103
Numerics and Griffith     107
Numerical approximation of the energy     108
The first time step     109
Quasi-static evolution     114
Minimization algorithm     115
The alternate minimizations algorithm     116
The backtracking algorithm     117
Numerical experiments     119
The 1D traction (hard device)     119
The tearing experiment     122
Revisiting the 2D traction experiment on a fiber reinforced matrix     132
Fatigue     135
Peeling evolution     137
The limit fatigue law when d [characters not reproducible] 0     139
A variational formulation for fatigue     147
Peeling revisited      147
Generalization     149
Appendix     151
Glossary     156
References     160