K. K. Chawla, Composite materials: science and engineering, 2012.

J. W. Hutchinson and Z. Suo, Mixed mode cracking in layered materials, Advances in Applied Mechanics, vol.29, pp.63-191, 1991.

M. Y. He, F. E. Heredia, D. J. Wissuchek, M. C. Shaw, and A. G. Evans, The mechanics of crack growth in layered materials, Acta Metallurgica et Materialia, vol.41, issue.4, pp.1223-1228, 1993.

A. G. Evans, M. Rühle, B. J. Dalgleish, and P. G. Charalambides, The fracture energy of bimaterial interfaces, Metallurgical Transactions A, vol.21, issue.9, pp.2419-2429, 1990.

M. Y. He and J. W. Hutchinson, Crack deflection at an interface between dissimilar elastic materials, International Journal of Solids and Structures, vol.25, issue.9, pp.1053-1067, 1989.

D. Leguillon, C. Lacroix, and E. Martin, Interface debonding ahead of a primary crack, Journal of the Mechanics and Physics of Solids, vol.48, issue.10, pp.2137-2161, 2000.

E. Martin, D. Leguillon, and C. Lacroix, A revisited criterion for crack deflection at an interface in a brittle bimaterial, Composites science and technology, vol.61, issue.12, pp.1671-1679, 2001.

D. S. Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, pp.100-104, 1960.

G. I. Barenblatt, The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. axially-symmetric cracks, Journal of Applied Mathematics and Mechanics, vol.23, issue.3, pp.622-636, 1959.

X. Xu and A. Needleman, Void nucleation by inclusion debonding in a crystal matrix, Modelling and Simulation in Materials Science and Engineering, vol.1, issue.2, p.111, 1993.

Z. Jin, G. H. Paulino, and R. H. Dodds, Cohesive fracture modeling of elastic-plastic crack growth in functionally graded materials, Engineering Fracture Mechanics, vol.70, issue.14, pp.1885-1912, 2003.

P. P. Camanho, C. G. Davila, and M. F. De-moura, Numerical simulation of mixed-mode progressive delamination in composite materials, Journal of Composite Materials, vol.37, issue.16, pp.1415-1438, 2003.

A. Esmaeili, A. Javili, and P. Steinmann, Coherent energetic interfaces accounting for in-plane degradation, International Journal of Fracture, vol.202, issue.2, pp.135-165, 2016.

A. Esmaeili, P. Steinmann, and A. Javili, Non-coherent energetic interfaces accounting for degradation, Computational Mechanics, vol.59, issue.3, pp.361-383, 2017.

O. Allix and P. Ladevèze, Interlaminar interface modelling for the prediction of delamination, Composite structures, vol.22, issue.4, pp.235-242, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01745254

O. Allix and A. Corigliano, Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens, International Journal of Fracture, vol.77, issue.2, pp.111-140, 1996.
URL : https://hal.archives-ouvertes.fr/hal-01745236

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.

G. T. Camacho and M. Ortiz, Computational modelling of impact damage in brittle materials, International Journal of solids and structures, vol.33, issue.20, pp.2899-2938, 1996.

M. Elices, G. V. Guinea, J. Gomez, and J. Planas, The cohesive zone model: advantages, limitations and challenges, Engineering fracture mechanics, vol.69, issue.2, pp.137-163, 2002.

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.131-156, 1999.

T. Nagashima, Y. Omoto, and S. Tani, Stress intensity factor analysis of interface cracks using X-FEM, International Journal for Numerical Methods in Engineering, vol.56, issue.8, pp.1151-1173, 2003.

X. Y. Liu, Q. Z. Xiao, and B. L. Karihaloo, XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials, International Journal for Numerical Methods in Engineering, vol.59, issue.8, pp.1103-1118, 2004.

N. Sukumar, Z. Y. Huang, J. Prévost, and Z. Suo, Partition of unity enrichment for bimaterial interface cracks, International Journal for Numerical Methods in Engineering, vol.59, issue.8, pp.1075-1102, 2004.

D. B. Huynh and T. Belytschko, The extended finite element method for fracture in composite materials, International Journal for Numerical Methods in Engineering, vol.77, issue.2, pp.214-239, 2009.

Y. Wang and H. Waisman, Progressive delamination analysis of composite materials using xfem and a discrete damage zone model, Computational Mechanics, vol.55, issue.1, pp.1-26, 2015.

G. A. 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.

B. Bourdin, G. A. Francfort, and J. J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, vol.48, issue.4, pp.797-826, 2000.

B. Bourdin, G. A. Francfort, and J. J. Marigo, The variational approach to fracture, Journal of Elasticity, vol.91, issue.1-3, pp.5-148, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00551079

B. Bourdin, C. Larsen, and C. Richardson, A time-discrete model for dynamic fracture based on crack regularization, International Journal of Fracture, vol.168, pp.133-143, 2011.

C. Kuhn and R. Müller, A continuum phase field model for fracture, Engineering Fracture Mechanics, vol.77, issue.18, pp.3625-3634, 2010.

C. Miehe, M. Hofacker, and F. Welschinger, A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.2765-2778, 2010.

A. Karma, D. Kessler, and H. Levine, Phase-field model of mode III dynamic fracture, Physical Review Letters, vol.87, issue.4, p.45501, 2001.

T. T. Nguyen, J. Yvonnet, Q. Zhu, M. Bornert, and C. Chateau, A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure, Engineering Fracture Mechanics, vol.139, pp.18-39, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01140963

C. V. Verhoosel and R. Borst, A phase-field model for cohesive fracture, International Journal for Numerical Methods in Engineering, vol.96, issue.1, pp.43-62, 2013.

T. T. Nguyen, J. Yvonnet, Q. Zhu, M. Bornert, and C. Chateau, A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography, Computer Methods in Applied Mechanics and Engineering, vol.312, pp.567-595, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01213943

A. C. Hansen-dörr, R. Borst, P. Hennig, and M. Kästner, Phase-field modelling of interface failure in brittle materials, Computer Methods in Applied Mechanics and Engineering, vol.346, pp.25-42, 2019.

A. Turon, C. G. Davila, P. Camanho, and J. Costa, An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models, Engineering Fracture Mechanics, vol.74, issue.10, pp.1665-1682, 2007.

Y. Li and M. Zhou, Prediction of fracture toughness of ceramic composites as function of microstructure: I. numerical simulations, Journal of the Mechanics and Physics of Solids, vol.61, issue.2, pp.472-488, 2013.

J. P. Parmigiani and M. D. Thouless, The roles of toughness and cohesive strength on crack deflection at interfaces, Journal of the Mechanics and Physics of Solids, vol.54, issue.2, pp.266-287, 2006.

S. A. Ponnusami, S. Turteltaub, and S. Van-der-zwaag, Cohesive-zone modelling of crack nucleation and propagation in particulate composites, Engineering Fracture Mechanics, vol.149, pp.170-190, 2015.

M. Paggi and J. Reinoso, Revisiting the problem of a crack impinging on an interface: a modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone model, Computer Methods in Applied Mechanics and Engineering, vol.321, pp.145-172, 2017.

Y. Benveniste, A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media, Journal of the Mechanics and Physics of Solids, vol.54, issue.4, pp.708-734, 2006.

J. Yvonnet, H. Le, and Q. He, An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites, Computational Mechanics, vol.42, issue.1, pp.119-131, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00692238

S. T. Gu and Q. C. He, Interfacial discontinuity relations for coupled multifield phenomena and their application to the modeling of thin interphases as imperfect interfaces, Journal of the Mechanics and Physics of Solids, vol.59, issue.7, pp.1413-1426, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00692839

Q. Zhu, S. Gu, J. Yvonnet, J. Shao, and Q. He, Three-dimensional numerical modelling by XFEM of spring-layer imperfect curved interfaces with applications to linearly elastic composite materials, International Journal for Numerical Methods in Engineering, vol.88, issue.4, pp.307-328, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00659383

A. Javili, A. Mcbride, and P. Steinmann, Thermomechanics of solids with lower-dimensional energetics: on the importance of surface, interface, and curve structures at the nanoscale. a unifying review, Applied Mechanics Reviews, vol.65, issue.1, p.10802, 2013.

P. Bövik, On the modelling of thin interface layers in elastic and acoustic scattering problems, The Quarterly Journal of Mechanics and Applied Mathematics, vol.47, issue.1, pp.17-42, 1994.

Z. Hashin, Thin interphase/imperfect interface in conduction, Journal of Applied Physics, vol.89, issue.4, pp.2261-2267, 2001.

A. Javili, S. Kaessmair, and P. Steinmann, General imperfect interfaces, Computer Methods in Applied Mechanics and Engineering, vol.275, pp.76-97, 2014.

T. T. Nguyen, J. Réthoré, J. Yvonnet, and M. Baietto, Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials, Computational Mechanics, vol.60, pp.289-314, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01499862

K. Pham, H. Amor, J. Marigo, and C. Maurini, Gradient damage models and their use to approximate brittle fracture, International Journal of Damage Mechanics, vol.20, issue.4, pp.618-652, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00549530

C. Miehe, Comparison of two algorithms for the computation of fourth-order isotropic tensor functions, Computers & Structures, vol.66, issue.1, pp.37-43, 1998.

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.

M. J. Borden, C. V. Verhoosel, M. A. Scott, T. J. Hughes, and C. M. Landis, A phase-field description of dynamic brittle fracture, Computer Methods in Applied Mechanics and Engineering, vol.217, pp.77-95, 2012.

T. T. Nguyen, J. Yvonnet, M. Bornert, C. Chateau, K. Sab et al., On the choice of parameters in the phase field method for simulating crack initiation with experimental validation, International Journal of Fracture, vol.197, issue.2, pp.213-226, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01258035

L. Sinien, Y. Lin, Z. Xiaoguang, and Q. Zongneng, Microdamage and interfacial adhesion in glass bead-filled high-density polyethylene, Journal of Materials Science, vol.27, issue.17, pp.4633-4638, 1992.

W. Yang, H. Araki, C. Tang, S. Thaveethavorn, A. Kohyama et al., Singlecrystal sic nanowires with a thin carbon coating for stronger and tougher ceramic composites, Advanced Materials, vol.17, issue.12, pp.1519-1523, 2005.

G. Zhu, S. Dong, J. Hu, Y. Kan, L. Gao et al., Microstructure and mechanical properties of cf/sic composites reinforced with boron nitride nanowires, Journal of Ceramic Science and Technology, vol.08, issue.1, pp.31-38, 2017.

D. Leguillon and E. Martin, The strengthening effect caused by an elastic contrast? part I: the bimaterial case, International Journal of Fracture, vol.179, issue.1-2, pp.157-167, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01667040

T. T. Nguyen, D. Waldmann, and T. Q. Bui, Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures, Journal of Computational Physics, vol.386, pp.585-610, 2019.

A. Krishnan and L. R. Xu, Experimental studies on the interaction among cracks, notches and interfaces of bonded polymers, International Journal of Solids and Structures, vol.50, issue.10, pp.1583-1596, 2013.

J. C. Newman and I. S. Raju, An empirical stress-intensity factor equation for the surface crack, Engineering Fracture Mechanics, vol.15, issue.1, pp.185-192, 1981.

R. A. Smith and J. F. Cooper, A finite element model for the shape development of irregular planar cracks, International Journal of Pressure Vessels and Piping, vol.36, issue.4, pp.315-326, 1989.

M. Kikuchi, Y. Wadaand, and K. Suga, Surface crack growth simulation under mixed mode cyclic loading condition, Procedia Engineering, vol.10, pp.427-432, 2011.