G. I. Barenblatt, The Mathematical Theory of Equilibrium Cracks in Brittle Fracture, Adv. Appl. Mech, vol.7, pp.55-129, 1962.
DOI : 10.1016/S0065-2156(08)70121-2

D. Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, issue.2, pp.100-104, 1960.
DOI : 10.1016/0022-5096(60)90013-2

X. P. Xu and A. Needleman, Numerical simulations of fast crack growth in brittle solids, Journal of the Mechanics and Physics of Solids, vol.42, issue.9, pp.1397-1434, 1994.
DOI : 10.1016/0022-5096(94)90003-5

G. T. Camacho and M. Ortiz, Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, vol.33, issue.20-22, pp.2899-2938, 1996.
DOI : 10.1016/0020-7683(95)00255-3

A. Needleman and V. Tvergaard, Finite element analysis of localization in plasticity Finite elements, Special problems in solid mechanics, pp.94-157, 1984.

A. Needleman, Some Issues in Cohesive Surface Modeling, Procedia IUTAM, vol.10, pp.221-246, 2014.
DOI : 10.1016/j.piutam.2014.01.020

G. Francfort and J. J. Marigo, Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, vol.46, issue.8, pp.1319-1342, 1998.
DOI : 10.1016/S0022-5096(98)00034-9

B. Bourdin, G. Francfort, and J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, vol.48, issue.4, pp.797-826, 2000.
DOI : 10.1016/S0022-5096(99)00028-9

H. Amor, J. J. Marigo, and C. Maurini, Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, Journal of the Mechanics and Physics of Solids, vol.57, issue.8, pp.1209-1229, 2009.
DOI : 10.1016/j.jmps.2009.04.011

J. Vignollet, S. May, R. De-borst, and C. V. Verhoosel, Phase-field models for brittle and cohesive fracture, Meccanica, vol.96, issue.9, pp.2587-2601, 2014.
DOI : 10.1002/nme.4553

URL : https://pure.tue.nl/ws/files/3747223/844842115995143.pdf

S. May, J. Vignollet, and R. De-borst, A numerical assessment of phase-field models for brittle and cohesive fracture: ??-Convergence and stress oscillations, European Journal of Mechanics - A/Solids, vol.52, pp.72-84, 2015.
DOI : 10.1016/j.euromechsol.2015.02.002

F. Cazes and N. Moës, Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture, International Journal for Numerical Methods in Engineering, vol.339, issue.1, pp.114-143, 2015.
DOI : 10.1016/j.crme.2010.10.010

D. Leguillon, Strength or toughness? A criterion for crack onset at a notch, European Journal of Mechanics - A/Solids, vol.21, issue.1, pp.61-72, 2002.
DOI : 10.1016/S0997-7538(01)01184-6

Z. Yosibash, A. Bussiba, and I. Gilad, Failure criteria for brittle elastic materials, International Journal of Fracture, vol.125, issue.3/4, pp.307-333, 2004.
DOI : 10.1023/B:FRAC.0000022244.31825.3b

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.7500

L. M. Nguyen, D. Leguillon, O. Gillia, and E. Riviere, Bond failure of a SiC/SiC brazed assembly, Mechanics of Materials, vol.50, pp.1-8, 2012.
DOI : 10.1016/j.mechmat.2012.03.001

URL : https://hal.archives-ouvertes.fr/hal-01562899

V. Manti?, Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion, International Journal of Solids and Structures, vol.46, issue.6, pp.287-1304, 2009.
DOI : 10.1016/j.ijsolstr.2008.10.036

D. Leguillon, D. Quesada, C. Putot, and E. Martin, Prediction of crack initiation at blunt notches and cavities ??? size effects, Engineering Fracture Mechanics, vol.74, issue.15, pp.74-2420, 2007.
DOI : 10.1016/j.engfracmech.2006.11.008

E. Martin, D. Leguillon, and N. Carrère, A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates, International Journal of Solids and Structures, vol.47, issue.9, pp.47-1297, 2010.
DOI : 10.1016/j.ijsolstr.2010.01.018

D. Leguillon, Determination of the length of a short crack at a v-notch from a full field measurement, International Journal of Solids and Structures, vol.48, issue.6, pp.884-892, 2011.
DOI : 10.1016/j.ijsolstr.2010.11.020

P. Weissgraeber, D. Leguillon, and W. Becker, A review of Finite Fracture Mechanics: crack initiation at singular and non-singular stress raisers, Archive of Applied Mechanics, vol.141, issue.1???2, pp.86-375, 2016.
DOI : 10.1007/s10704-006-0083-6

URL : https://hal.archives-ouvertes.fr/hal-01563116

B. Lawn, Fracture of Brittle Solids, 1993.
DOI : 10.1017/CBO9780511623127

V. Mantic, Prediction of initiation and growth of cracks in composites. Coupled stress and energy criterion of the finite fracture mechanics, Proceedings of the 16th European Conference on Composite Materials, 2014.

L. Vincent and P. Soille, Watersheds in digital spaces: an efficient algorithm based on immersion simulations, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.6, pp.583-598, 1991.
DOI : 10.1109/34.87344

B. T. Roerdink and A. Meijster, The Watershed Transform: Definitions, Algorithms and Parallelization Strategies, Fundamenta Informaticae, pp.41-187, 2001.

J. Li, F. Song, and C. Jiang, A non-local approach to crack process modeling in ceramic materials subjected to thermal shock, Engineering Fracture Mechanics, vol.133, pp.85-98, 2015.
DOI : 10.1016/j.engfracmech.2014.11.007

P. Bouchard, F. Bay, and Y. , Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.35-36, pp.3887-3908, 2003.
DOI : 10.1016/S0045-7825(03)00391-8

URL : https://hal.archives-ouvertes.fr/hal-00677710

N. Moës, J. Dolbow, and T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131-150, 1999.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A

J. Li and X. B. Zhang, A criterion study for non-singular stress concentrations in brittle or quasibrittle materials, Engng Fract, Mech, vol.74, pp.505-523, 2006.

D. Leguillon and Z. Yosibash, Crack onset at a v-notch. Influence of the notch tip radius, International Journal of Fracture, vol.122, issue.1/2, pp.1-21, 2003.
DOI : 10.1023/B:FRAC.0000005372.68959.1d

V. X. Tran, D. Leguillon, A. Krishnan, and L. Xu, Interface crack initiation at V-notches along adhesive bonding in weakly bonded polymers subjected to mixed-mode loading, International Journal of Fracture, vol.141, issue.1, pp.176-65, 2012.
DOI : 10.1023/B:FRAC.0000022244.31825.3b

URL : https://hal.archives-ouvertes.fr/hal-01562935

G. Sih, Handbook of stress-intensity factors, 1973.

P. Judt and A. Ricoeur, Crack growth simulation of multiple cracks systems applying remote contour interaction integrals, Theoretical and Applied Fracture Mechanics, vol.75, pp.75-78, 2015.
DOI : 10.1016/j.tafmec.2014.11.001

L. Ma and A. Korsunsky, On The Use Of Vector J-Integral In Crack Growth Criteria For Brittle Solids, International Journal of Fracture, vol.45, issue.4, pp.39-46, 2005.
DOI : 10.1115/1.3424360

A. Parvizi, K. Garrett, and J. Bailey, Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates, Journal of Materials Science, vol.8, issue.1, pp.195-201, 1978.
DOI : 10.1007/BF00739291

S. R. Kim and J. Nairn, Fracture mechanics analysis of coating/substrate systems, Part II: Experiments in bending, Engng. Fract. Mech, pp.65-595, 2000.

R. 1. Barenblatt, The Mathematical Theory of Equilibrium Cracks in Brittle Fracture, Adv. Appl. Mech, vol.7, pp.55-129, 1962.
DOI : 10.1016/S0065-2156(08)70121-2

D. Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, issue.2, pp.100-104, 1960.
DOI : 10.1016/0022-5096(60)90013-2

X. P. Xu and A. Needleman, Numerical simulations of fast crack growth in brittle solids, Journal of the Mechanics and Physics of Solids, vol.42, issue.9, pp.1397-1434, 1994.
DOI : 10.1016/0022-5096(94)90003-5

G. T. Camacho and M. Ortiz, Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, vol.33, issue.20-22, pp.2899-2938, 1996.
DOI : 10.1016/0020-7683(95)00255-3

A. Needleman and V. Tvergaard, Finite element analysis of localization in plasticity Finite elements, Special problems in solid mechanics, pp.94-157, 1984.

A. Needleman, Some Issues in Cohesive Surface Modeling, Procedia IUTAM, vol.10, pp.221-246, 2014.
DOI : 10.1016/j.piutam.2014.01.020

URL : http://doi.org/10.1016/j.piutam.2014.01.020

G. Francfort and J. J. Marigo, Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, vol.46, issue.8, pp.1319-1342, 1998.
DOI : 10.1016/S0022-5096(98)00034-9

B. Bourdin, G. Francfort, and J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, vol.48, issue.4, pp.797-826, 2000.
DOI : 10.1016/S0022-5096(99)00028-9

H. Amor, J. J. Marigo, and C. Maurini, Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, Journal of the Mechanics and Physics of Solids, vol.57, issue.8, pp.1209-1229, 2009.
DOI : 10.1016/j.jmps.2009.04.011

J. Vignollet, S. May, R. De-borst, and C. V. Verhoosel, Phase-field models for brittle and cohesive fracture, Meccanica, vol.96, issue.9, pp.2587-2601, 2014.
DOI : 10.1002/nme.4553

URL : https://pure.tue.nl/ws/files/3747223/844842115995143.pdf

S. May, J. Vignollet, and R. De-borst, A numerical assessment of phase-field models for brittle and cohesive fracture: ??-Convergence and stress oscillations, European Journal of Mechanics - A/Solids, vol.52, pp.72-84, 2015.
DOI : 10.1016/j.euromechsol.2015.02.002

F. Cazes and N. Moës, Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture, International Journal for Numerical Methods in Engineering, vol.339, issue.1, pp.114-143, 2015.
DOI : 10.1016/j.crme.2010.10.010

D. Leguillon, Strength or toughness? A criterion for crack onset at a notch, European Journal of Mechanics - A/Solids, vol.21, issue.1, pp.61-72, 2002.
DOI : 10.1016/S0997-7538(01)01184-6

Z. Yosibash, A. Bussiba, and I. Gilad, Failure criteria for brittle elastic materials, International Journal of Fracture, vol.125, issue.3/4, pp.307-333, 2004.
DOI : 10.1023/B:FRAC.0000022244.31825.3b

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.7500

L. M. Nguyen, D. Leguillon, O. Gillia, and E. Riviere, Bond failure of a SiC/SiC brazed assembly, Mechanics of Materials, vol.50, pp.1-8, 2012.
DOI : 10.1016/j.mechmat.2012.03.001

URL : https://hal.archives-ouvertes.fr/hal-01562899

V. Manti?, Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion, International Journal of Solids and Structures, vol.46, issue.6, pp.287-1304, 2009.
DOI : 10.1016/j.ijsolstr.2008.10.036

D. Leguillon, D. Quesada, C. Putot, and E. Martin, Prediction of crack initiation at blunt notches and cavities ??? size effects, Engineering Fracture Mechanics, vol.74, issue.15, pp.74-2420, 2007.
DOI : 10.1016/j.engfracmech.2006.11.008

E. Martin, D. Leguillon, and N. Carrère, A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates, International Journal of Solids and Structures, vol.47, issue.9, pp.47-1297, 2010.
DOI : 10.1016/j.ijsolstr.2010.01.018

D. Leguillon, Determination of the length of a short crack at a v-notch from a full field measurement, International Journal of Solids and Structures, vol.48, issue.6, pp.884-892, 2011.
DOI : 10.1016/j.ijsolstr.2010.11.020

P. Weissgraeber, D. Leguillon, and W. Becker, A review of Finite Fracture Mechanics: crack initiation at singular and non-singular stress raisers, Archive of Applied Mechanics, vol.141, issue.1???2, pp.86-375, 2016.
DOI : 10.1007/s10704-006-0083-6

URL : https://hal.archives-ouvertes.fr/hal-01563116

B. Lawn, Fracture of Brittle Solids, 1993.
DOI : 10.1017/CBO9780511623127

V. Mantic, Prediction of initiation and growth of cracks in composites. Coupled stress and energy criterion of the finite fracture mechanics, Proceedings of the 16th European Conference on Composite Materials, 2014.

L. Vincent and P. Soille, Watersheds in digital spaces: an efficient algorithm based on immersion simulations, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.6, pp.583-598, 1991.
DOI : 10.1109/34.87344

URL : http://biometrics.cse.msu.edu/PRIPSeminar/Watershed/91VincentWatershed.pdf

B. T. Roerdink and A. Meijster, The Watershed Transform: Definitions, Algorithms and Parallelization Strategies, Fundamenta Informaticae, pp.41-187, 2001.

J. Li, F. Song, and C. Jiang, A non-local approach to crack process modeling in ceramic materials subjected to thermal shock, Engineering Fracture Mechanics, vol.133, pp.85-98, 2015.
DOI : 10.1016/j.engfracmech.2014.11.007

P. Bouchard, F. Bay, and Y. , Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.35-36, pp.3887-3908, 2003.
DOI : 10.1016/S0045-7825(03)00391-8

URL : https://hal.archives-ouvertes.fr/hal-00677710

N. Moës, J. Dolbow, and T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131-150, 1999.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A

J. Li and X. B. Zhang, A criterion study for non-singular stress concentrations in brittle or quasibrittle materials, Engng Fract, Mech, vol.74, pp.505-523, 2006.

D. Leguillon and Z. Yosibash, Crack onset at a v-notch. Influence of the notch tip radius, International Journal of Fracture, vol.122, issue.1/2, pp.1-21, 2003.
DOI : 10.1023/B:FRAC.0000005372.68959.1d

V. X. Tran, D. Leguillon, A. Krishnan, and L. Xu, Interface crack initiation at V-notches along adhesive bonding in weakly bonded polymers subjected to mixed-mode loading, International Journal of Fracture, vol.141, issue.1, pp.176-65, 2012.
DOI : 10.1023/B:FRAC.0000022244.31825.3b

URL : https://hal.archives-ouvertes.fr/hal-01562935

G. Sih, Handbook of stress-intensity factors, 1973.

P. Judt and A. Ricoeur, Crack growth simulation of multiple cracks systems applying remote contour interaction integrals, Theoretical and Applied Fracture Mechanics, vol.75, pp.75-78, 2015.
DOI : 10.1016/j.tafmec.2014.11.001

L. Ma and A. Korsunsky, On The Use Of Vector J-Integral In Crack Growth Criteria For Brittle Solids, International Journal of Fracture, vol.45, issue.4, pp.39-46, 2005.
DOI : 10.1115/1.3424360

A. Parvizi, K. Garrett, and J. Bailey, Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates, Journal of Materials Science, vol.8, issue.1, pp.195-201, 1978.
DOI : 10.1007/BF00739291

S. R. Kim and J. Nairn, Fracture mechanics analysis of coating/substrate systems, Part II: Experiments in bending, Engng. Fract. Mech, pp.65-595, 2000.