D. H. Allen and C. R. Searcy, A micromechanical model for a viscoelastic cohesive zone, International Journal of Fracture, vol.107, issue.2, pp.159-176, 2001.

M. Ambati, D. Lorenzis, and L. , Phase-field modeling of brittle and ductile fracture in shells with isogeometric NURBS-based solid-shell elements, Computer Methods in Applied Mechanics and Engineering, vol.312, pp.351-373, 2016.

M. Ambati, T. Gerasimov, D. Lorenzis, and L. , Phasefield modeling of ductile fracture, Computational Mechanics, vol.55, issue.5, pp.1017-1040, 2015.

M. Ambati, R. Kruse, D. Lorenzis, and L. , A phasefield model for ductile fracture at finite strains and its experimental verification, Computational Mechanics, vol.57, issue.1, pp.149-167, 2016.

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.

A. Pires, F. De-souza-neto, E. Owen, and D. , On the finite element prediction of damage growth and fracture initiation in finitely deforming ductile materials, Computer Methods in Applied Mechanics and Engineering, vol.193, pp.5223-5256, 2004.

T. Antretter and F. Fischer, Particle cleavage and ductile crack growth in a two-phase composite on a microscale, Computational Materials Science, vol.13, issue.1-3, pp.1-7, 1998.

A. M. Aragón and A. Simone, The discontinuityenriched finite element method, International Journal for Numerical Methods in Engineering, vol.112, issue.11, pp.1589-1613, 2017.

P. Areias, -. Dias, D. Costa, J. Alfaiate, and E. Júlio, Arbitrary bi-dimensional finite strain cohesive crack propagation, Computational Mechanics, vol.45, issue.1, pp.61-75, 2009.

P. Areias, N. Van-goethem, and E. B. Pires, A damage model for ductile crack initiation and propagation, Computational Mechanics, vol.47, issue.6, pp.641-656, 2011.

P. Areias, -. Dias, D. Costa, J. M. Sargado, and T. Rabczuk, Element-wise algorithm for modeling ductile fracture with the Rousselier yield function, Computational Mechanics, vol.52, issue.6, pp.1429-1443, 2013.

P. Areias, J. Reinoso, P. Camanho, and T. Rabczuk, A constitutive-based element-by-element crack propagation algorithm with local mesh refinement, Computational Mechanics, vol.56, issue.2, pp.291-315, 2015.

M. Arriaga, C. Mcauliffe, and H. Waisman, Onset of shear band localization by a local generalized eigenvalue analysis, Computer Methods in Applied Mechanics and Engineering, vol.289, pp.179-208, 2015.
DOI : 10.1016/j.cma.2015.02.010

URL : https://manuscript.elsevier.com/S0045782515000511/pdf/S0045782515000511.pdf

I. Babuska and J. M. Melenk, University of Maryland-Institute for Physical Science and Technology Banerjee A, Manivasagam R (2009) Triaxiality dependent cohesive zone model, Engineering Fracture Mechanics, vol.76, issue.12, pp.1761-1770, 1995.

G. I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, Advances in applied mechanics, vol.7, pp.55-129, 1962.

Z. P. Ba?ant and M. Jirásek, Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress, Journal of Engineering Mechanics, vol.128, issue.11, p.11, 1119.

M. Shakoor,

E. Béchet, H. Minnebo, N. Moës, B. Burgardt, B. Bourdin et al., Numerical Improved implementation and robustness study of the x-fem for stress analysis around cracks, International Journal for Numerical Methods in Engineering, vol.64, issue.8, pp.1033-1056, 2000.

T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, International journal for numerical methods in engineering, vol.45, issue.5, pp.601-620, 1999.

T. Belytschko, N. Moës, S. Usui, and C. Parimi, Arbitrary discontinuities in finite elements, International Journal for Numerical Methods in Engineering, vol.50, issue.4, pp.993-1013, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01005275

T. Belytschko, S. Loehnert, and J. H. Song, Multiscale aggregating discontinuities: a method for circumventing loss of material stability, International Journal for Numerical Methods in Engineering, vol.73, issue.6, pp.869-894, 2008.

T. Belytschko, W. K. Liu, B. Moran, and E. Khalil, Nonlinear Finite Elements for Continua and Structures, 2013.

J. Besson, Continuum Models of Ductile Fracture: A Review, International Journal of Damage Mechanics, vol.19, issue.1, pp.3-52, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00550957

H. J. Böhm, Mechanics of Microstructured Materials, 2004.

M. J. Borden, T. J. Hughes, C. M. Landis, A. Anvari, and I. J. Lee, A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects, Computer Methods in Applied Mechanics and Engineering, vol.312, pp.130-166, 2016.

H. Borouchaki, P. Laug, A. Cherouat, and K. Saanouni, Adaptive remeshing in large plastic strain with damage, International Journal for Numerical Methods in Engineering, vol.63, issue.1, pp.1-36, 2005.

E. Bosco, V. G. Kouznetsova, and M. Geers, Multiscale computational homogenization-localization for propagating discontinuities using X-FEM, International Journal for Numerical Methods in Engineering, vol.102, issue.3-4, pp.496-527, 2015.

P. O. Bouchard, F. Bay, Y. Chastel, and I. Tovena, Crack propagation modelling using an advanced remeshing technique, Computer Methods in Applied Mechanics and Engineering, vol.189, issue.3, pp.723-742, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00677709

P. O. Bouchard, L. Bourgeon, S. Fayolle, and K. Mocellin, An enhanced Lemaitre model formulation for materials processing damage computation, experiments in revisited brittle fracture, vol.4, pp.797-826, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00521625

P. Broumand and A. Khoei, X-FEM modeling of dynamic ductile fracture problems with a nonlocal damage-viscoplasticity model. Finite Elements in, Analysis and Design, vol.99, pp.49-67, 2015.

B. J. Carter, P. A. Wawrzynek, and A. R. Ingraffea, Automated 3-D crack growth simulation, International Journal for Numerical Methods in Engineering, vol.47, issue.1-3, pp.229-253, 2000.

J. César-de-sá, P. Areias, and C. Zheng, Damage modelling in metal forming problems using an implicit non-local gradient model, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.6646-6660, 2006.

N. Chandra, H. Li, C. Shet, and H. Ghonem, Some issues in the application of cohesive zone models for metal-ceramic interfaces, International Journal of Solids and Structures, vol.39, issue.10, pp.2827-2855, 2002.

J. Chen and H. Yuan, A micro-mechanical damage model based on gradient plasticity: algorithms and applications, International Journal for Numerical Methods in Engineering, vol.54, issue.3, pp.399-420, 2002.
DOI : 10.1002/nme.431

J. P. Crété, P. Longère, and J. M. Cadou, Numerical modelling of crack propagation in ductile materials combining the gtn model and x-fem, Computer Methods in Applied Mechanics and Engineering, vol.275, pp.204-233, 2014.

T. Drabek and H. Böhm, Damage models for studying ductile matrix failure in composites, Computational Materials Science, vol.32, issue.3-4, pp.329-336, 2005.
DOI : 10.1016/j.commatsci.2004.09.035

C. Duarte, O. Hamzeh, T. Liszka, and W. Tworzydlo, A generalized finite element method for the simulation of three-dimensional dynamic crack propagation, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.15, pp.2227-2262, 2001.

R. El-khaoulani and P. O. Bouchard, An anisotropic mesh adaptation strategy for damage and failure in ductile materials, Finite Elements in Analysis and Design, vol.59, pp.1-10, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00702193

R. El-khaoulani and P. O. Bouchard, Efficient numerical integration of an elastic-plastic damage law within a mixed velocity-pressure formulation, Mathematics and Computers in Simulation, vol.94, pp.145-158, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00845444

T. Elguedj, A. Gravouil, and A. Combescure, Appropriate extended functions for x-fem simulation of plastic fracture mechanics, Computer Methods in Applied Computational methods for ductile fracture modeling at the microscale, p.39, 2006.
DOI : 10.1016/j.cma.2005.02.007

URL : https://hal.archives-ouvertes.fr/hal-00373830

, Mechanics and Engineering, vol.195, issue.7, pp.501-515

F. Payet, S. Chiaruttini, V. Besson, J. Feyel, and F. , Amorçage et propagation de fissures dans les milieux ductiles non locaux. PhD thesis, Ecole Nationale Supérieure des Mines de Paris Feld, vol.71, pp.57-69, 2010.

S. Forest, Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage, Journal of Engineering Mechanics, vol.135, issue.3, pp.117-131, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00368014

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.

T. P. Fries and T. Belytschko, The extended/generalized finite element method: an overview of the method and its applications, International Journal for Numerical Methods in Engineering, vol.84, issue.3, pp.253-304, 2010.

M. Geers, V. Kouznetsova, and W. Brekelmans, Gradient-enhanced computational homogenization for the micro-macro scale transition, Le Journal de Physique IV, vol.11, issue.PR5, pp.5-145, 2001.

M. G. Geers, V. G. Kouznetsova, and W. Brekelmans, Multi-scale computational homogenization: Trends and challenges, Journal of computational and applied mathematics, vol.234, issue.7, pp.2175-2182, 2010.

N. A. Giang, M. Kuna, and G. Hütter, Influence of carbide particles on crack initiation and propagation with competing ductile-brittle transition in ferritic steel. Theoretical and Applied Fracture Mechanics in press, 2017.

M. Gologanu, J. B. Leblond, and J. Devaux, Approximate models for ductile metals containing non-spherical voids-Case of axisymmetric prolate ellipsoidal cavities, Journal of the Mechanics and Physics of Solids, vol.41, issue.11, p.90029, 1993.

A. Gravouil, N. Moës, and T. Belytschko, Non-planar 3d crack growth by the extended finite element and level sets-part ii: Level set update, International Journal for Numerical Methods in Engineering, vol.53, issue.11, pp.2569-2586, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01007111

C. Gruau and T. Coupez, 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.4951-4976, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00517639

A. L. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I-Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, vol.99, issue.1, 1977.

C. Hirt and B. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, vol.39, issue.1, pp.201-225, 1981.

A. Hosokawa, D. S. Wilkinson, J. Kang, M. Kobayashi, and H. Toda, Void growth and coalescence in model materials investigated by high-resolution x-ray microtomography, International Journal of Fracture, vol.181, issue.1, pp.51-66, 2013.

C. Hu and S. Ghosh, Locally enhanced Voronoi cell finite element model (LE-VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions, International Journal for Numerical Methods in Engineering, vol.76, issue.12, pp.1955-1992, 2008.

J. W. Hutchinson, Generalizing J 2 flow theory: Fundamental issues in strain gradient plasticity, Acta Mechanica Sinica, vol.28, issue.4, pp.1078-1086, 2012.

D. 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.

E. Ibijola, On some fundamental concepts of Continuum Damage Mechanics, Computer Methods in Applied Mechanics and Engineering, vol.191, pp.1505-1520, 2002.

J. Jackiewicz and M. Kuna, Non-local regularization for FE simulation of damage in ductile materials, Computational Materials Science, vol.28, issue.3-4, pp.684-695, 2003.

J. R. Jain and S. Ghosh, Damage evolution in composites with a homogenization-based continuum damage mechanics model, International Journal of Damage Mechanics, vol.18, issue.6, pp.533-568, 2009.

M. Jirásek, Comparative study on finite elements with embedded discontinuities, Computer methods in applied mechanics and engineering, vol.188, issue.1, pp.307-330, 2000.

L. Kachanov, Time of the Rupture Process under Creep Conditions, Bull SSR Acad Sci, Division of Technical Sciences, vol.8, pp.26-31, 1958.

V. Kouznetsova, M. Geers, and W. Brekelmans, Size of a representative volume element in a second-order computational homogenization framework, International Journal for Multiscale Computational Engineering, vol.2, issue.4, 2004.

P. Laborde, J. Pommier, Y. Renard, and M. Salaün, High-order extended finite element method for cracked domains, International Journal for Numerical Methods in Engineering, vol.64, issue.3, pp.354-381, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00815711

M. Shakoor,

R. A. Lebensohn, J. P. Escobedo, E. K. Cerreta, D. Denniskoller, C. A. Bronkhorst et al., Modeling void growth in polycrystalline materials, Acta Materialia, vol.61, issue.18, pp.6918-6932, 2013.

J. Lemaitre and J. L. Chaboche, Phenomenological approach of damage rupture, Journal de Mécanique Appliquée, vol.2, issue.3, pp.317-365, 1978.

J. Lemaitre, R. Desmorat, and M. Sauzay, Anisotropic damage law of evolution, European Journal of Mechanics-A/Solids, vol.19, issue.2, pp.187-208, 2000.

S. Li and S. Ghosh, Debonding in composite microstructures with morphological variations, International Journal of computational methods, vol.1, issue.01, pp.121-149, 2004.

Y. Liang and P. Sofronis, Micromechanics and numerical modelling of the hydrogen-particle-matrix interactions in nickel-base alloys. Modelling and Simulation in, Materials Science and Engineering, vol.11, issue.4, pp.523-551, 2003.

G. Liu, D. Zhou, Y. Bao, J. Ma, Z. Han et al., Multiscale analysis of interaction between macro crack and microdefects by using multiscale projection method. Theoretical and Applied Fracture Mechanics, Computational Materials Science, vol.16, issue.1-4, pp.197-205, 1999.

Z. Liu, M. Fleming, and W. K. Liu, Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials, Computer Methods in Applied Mechanics and Engineer, 2017.

S. Loehnert and T. Belytschko, A multiscale projection method for macro/microcrack simulations, International Journal for Numerical Methods in Engineering, vol.71, issue.12, pp.1466-1482, 2007.
DOI : 10.1002/nme.2001

E. Lorentz, A mixed interface finite element for cohesive zone models, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.2, pp.302-317, 2008.
DOI : 10.1016/j.cma.2008.08.006

URL : https://hal.archives-ouvertes.fr/hal-00359363

E. Lorentz, J. Besson, and V. Cano, Numerical simulation of ductile fracture with the Rousselier constitutive law, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.21-24, pp.1965-1982, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00268315

T. Massart, R. Peerlings, and M. Geers, An enhanced multi-scale approach for masonry wall computations with localization of damage, International journal for numerical methods in engineering, vol.69, issue.5, pp.1022-1059, 2007.
DOI : 10.1002/nme.1799

URL : http://www.mate.tue.nl/mate/pdfs/6798.pdf

K. Mathur, A. Needleman, and V. Tvergaard, Ductile failure analyses on massively parallel computers, Computer Methods in Applied Mechanics and Engineering, vol.119, issue.3-4, pp.90091-90095, 1994.
DOI : 10.1016/0045-7825(94)90091-4

K. Matou?, M. Geers, V. G. Kouznetsova, and A. Gillman, A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials, Journal of Computational Physics, vol.330, pp.192-220, 2017.

K. Matsui, K. Terada, and K. Yuge, Two-scale finite element analysis of heterogeneous solids with periodic microstructures, Computers & structures, vol.82, issue.7, pp.593-606, 2004.
DOI : 10.1016/j.compstruc.2004.01.004

C. Mcauliffe and H. Waisman, A coupled phase field shear band model for ductile-brittle transition in notched plate impacts, Computer Methods in Applied Mechanics and Engineering, vol.305, pp.173-195, 2016.

P. Mchugh and P. Connolly, Micromechanical modelling of ductile crack growth in the binder phase of WC-Co, Computational Materials Science, vol.27, issue.4, pp.423-436, 2003.

J. Mediavilla, R. Peerlings, and M. Geers, A robust and consistent remeshing-transfer operator for ductile fracture simulations, Computers & Structures, vol.84, issue.8-9, pp.604-623, 2006.
DOI : 10.1016/j.compstruc.2005.10.007

J. Mediavilla, R. Peerlings, and M. Geers, Discrete crack modelling of ductile fracture driven by non-local softening plasticity, International Journal for Numerical Methods in Engineering, vol.66, issue.4, pp.661-688, 2006.
DOI : 10.1002/nme.1572

URL : http://mate.tue.nl/mate/pdfs/5841.pdf

Q. Meng and Z. Wang, Prediction of interfacial strength and failure mechanisms in particle-reinforced metal-matrix composites based on a micromechanical model, Engineering Fracture Mechanics, vol.142, pp.170-183, 2015.

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, issue.45, pp.2765-2778, 2010.
DOI : 10.1016/j.cma.2010.04.011

C. Miehe, F. Welschinger, and M. Hofacker, Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field fe implementations, International Journal for Numerical Methods in Engineering, vol.83, issue.10, pp.1273-1311, 2010.
DOI : 10.1002/nme.2861

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.

N. Moës, A. Gravouil, and T. Belytschko, Non-planar 3d crack growth by the extended finite element Computational methods for ductile fracture modeling at the microscale 41 and level sets-part i: Mechanical model, International Journal for Numerical Methods in Engineering, vol.53, issue.11, pp.2549-2568, 2002.

N. Moës, C. Stolz, P. E. Bernard, and N. Chevaugeon, A level set based model for damage growth: The thick level set approach, International Journal for Numerical Methods in Engineering, vol.86, issue.3, pp.358-380, 2011.

S. Moorthy and S. Ghosh, A Voronoi Cell finite element model for particle cracking in elastic-plastic composite materials, Computer Methods in Applied Mechanics and Engineering, vol.151, issue.3-4, pp.377-400, 1998.
DOI : 10.1016/s0045-7825(97)00160-6

T. Morgeneyer, L. Helfen, I. Sinclair, H. Proudhon, F. Xu et al., Ductile crack initiation and propagation assessed via in situ synchrotron radiation-computed laminogra, 2011.
DOI : 10.1016/j.scriptamat.2011.09.005

, Scripta Materialia, vol.65, issue.11, pp.1010-1013

K. Nahshon and J. Hutchinson, Modification of the Gurson Model for shear failure, European Journal of Mechanics-A/Solids, vol.27, issue.1, pp.1-17, 2008.

N. `-egre, P. Steglich, D. Brocks, W. Koçak, and M. , Numerical simulation of crack extension in aluminium welds, Computational Materials Science, vol.28, issue.3-4, pp.723-731, 2003.

O. Nguyen, E. Repetto, M. Ortiz, and R. Radovitzky, A cohesive model of fatigue crack growth, International Journal of Fracture, vol.110, issue.4, pp.351-369, 2001.

V. P. Nguyen, M. Stroeven, and L. J. Sluys, Multiscale continuous and discontinuous modeling of heterogeneous materials: a review on recent developments, Journal of Multiscale Modelling, vol.3, issue.04, pp.229-270, 2011.

O. 'keeffe, S. C. Tang, S. Kopacz, A. M. Smith, J. Rowenhorst et al., Multiscale ductile fracture integrating tomographic characterization and 3-D simulation, Acta Materialia, vol.82, pp.503-510, 2015.

J. Oliver, A. Huespe, and P. Sanchez, A comparative study on finite elements for capturing strong discontinuities: E-fem vs x-fem, Computer methods in applied mechanics and engineering, vol.195, issue.37, pp.4732-4752, 2006.

M. Ortiz and A. Pandolfi, Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, International Journal for Numerical Methods in Engineering, vol.44, issue.9, pp.1267-1282, 1999.

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.90002-90004, 1988.

O. ¨-stlund, R. Golling, S. Oldenburg, and M. , Microstructure based modeling of ductile fracture initiation in press-hardened sheet metal structures, Computer Methods in Applied Mechanics and Engineering, vol.302, pp.90-108, 2016.

J. H. Panchal, S. R. Kalidindi, and D. L. Mcdowell, Key computational modeling issues in Integrated Computational Materials Engineering. Computer-Aided Design, vol.45, issue.1, pp.4-25, 2013.

R. Peerlings, D. Borst, R. Brekelmans, W. , D. Vree et al., Gradient enhanced damage for quasi-brittle materials, International Journal for Numerical Methods in Engineering, vol.39, pp.3391-3403, 1996.

K. Perzyn´skiperzyn´ski, A. Wrozyna, R. Kuziak, A. Legwand, and L. Madej, Development and validation of multi scale failure model for dual phase steels, Finite Elements in Analysis and Design, vol.124, pp.7-21, 2016.

A. Pineau, A. Benzerga, and T. Pardoen, Failure of metals I: Brittle and ductile fracture, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01308255

, Acta Materialia, vol.107, pp.424-483

R. Pourmodheji and M. Mashayekhi, Improvement of the extended finite element method for ductile crack growth, Materials Science and Engineering: A, vol.551, pp.255-271, 2012.

T. Rabczuk, S. Bordas, and G. Zi, On threedimensional modelling of crack growth using partition of unity methods, Computers & structures, vol.88, issue.23, pp.1391-1411, 2010.

A. Ramazani, A. Schwedt, A. Aretz, U. Prahl, and W. Bleck, Characterization and modelling of failure initiation in dp steel, Computational materials science, vol.75, pp.35-44, 2013.

W. H. Reed and T. Hill, Triangular mesh methods for the neutron transport equation, 1973.

B. Ren, S. Li, J. Qian, and X. Zeng, Meshfree simulations of spall fracture, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.5-8, pp.797-811, 2011.

J. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of applied mechanics, vol.35, pp.379-386, 1968.

J. R. Rice, Mathematical analysis in the mechanics of fracture. Fracture: an advanced treatise, vol.2, pp.191-311, 1968.

G. Rousselier, Ductile fracture models and their potential in local approach of fracture, Nuclear Engineering and Design, vol.105, issue.1, pp.97-111, 1987.

M. Shakoor,

E. Roux, M. Bernacki, and P. O. Bouchard, A level-set and anisotropic adaptive remeshing strategy for the modeling of void growth under large plastic strain, Computational Materials Science, vol.68, pp.32-46, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00756435

E. Roux, M. Shakoor, M. Bernacki, and P. O. Bouchard, A new finite element approach for modelling ductile damage void nucleation and growth-analysis of loading path effect on damage mechanisms. Modelling and Simulation in, Materials Science and Engineering, vol.22, issue.7, p.1, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01090403

S. Salih, K. Davey, and Z. Zou, Rate-dependent elastic and elasto-plastic cohesive zone models for dynamic crack propagation, International Journal of Solids and Structures, vol.90, pp.95-115, 2016.

M. Samal, M. Seidenfuss, E. Roos, B. Dutta, and H. Kushwaha, Finite element formulation of a new nonlocal damage model, Finite Elements in Analysis and Design, vol.44, issue.6-7, pp.358-371, 2008.

I. Scheider, Derivation of separation laws for cohesive models in the course of ductile fracture, Engineering Fracture Mechanics, vol.76, issue.10, pp.1450-1459, 2009.

F. Scheyvaerts, P. Onck, C. Tekoglu, and T. Pardoen, The growth and coalescence of ellipsoidal voids in plane strain under combined shear and tension, Journal of the Mechanics and Physics of Solids, vol.59, issue.2, pp.373-397, 2011.

M. R. Seabra, J. De-sa, S. ?-u?tari?, P. Rodi?, and T. , Some numerical issues on the use of xfem for ductile fracture, Computational Mechanics, vol.50, issue.5, pp.611-629, 2012.

M. Seabra, S. ?-u?tari?, P. , C. De-sa, J. Rodi? et al., Damage driven crack initiation and propagation in ductile metals using XFEM, Computational Mechanics, vol.52, issue.1, pp.161-179, 2013.

M. Shakoor, M. Bernacki, and P. O. Bouchard, A new body-fitted immersed volume method for the modeling of ductile fracture at the microscale: Analysis of void clusters and stress state effects on coalescence, Engineering Fracture Mechanics, vol.147, pp.398-417, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01181257

M. Shakoor, M. Bernacki, and P. O. Bouchard, Ductile fracture of a metal matrix composite studied using 3D numerical modeling of void nucleation and coalescence. Engineering Fracture Mechanics in press, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01629229

M. Shakoor, P. O. Bouchard, and M. Bernacki, An adaptive level-set method with enhanced volume conservation for simulations in multiphase domains, International Journal for Numerical Methods in Engineering, vol.109, issue.4, pp.555-576, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01504468

M. Shakoor, A. Buljac, J. Neggers, F. Hild, T. F. Morgeneyer et al., On the choice of boundary conditions for micromechanical simulations based on 3D imaging, International Journal of Solids and Structures, vol.112, pp.83-96, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01471645

P. Shanthraj, L. Sharma, B. Svendsen, F. Roters, and D. Raabe, A phase field model for damage in elastoviscoplastic materials, Computer Methods in Applied Mechanics and Engineering, vol.312, pp.167-185, 2016.

D. C. Simkins and S. Li, Meshfree simulations of thermo-mechanical ductile fracture, Computational Mechanics, vol.38, issue.3, pp.235-249, 2006.

B. C. Simonsen and S. Li, Mesh-free simulation of ductile fracture, International Journal for Numerical Methods in Engineering, vol.60, issue.8, pp.1425-1450, 2004.

I. Singh, B. Mishra, and S. Bhattacharya, Xfem simulation of cracks, holes and inclusions in functionally graded materials, International Journal of Mechanics and Materials in Design, vol.7, issue.3, p.199, 2011.

S. Soghrati, F. Xiao, and A. Nagarajan, A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems, Computational Mechanics, vol.59, issue.4, pp.667-684, 2017.

D. Steglich, T. Siegmund, and W. Brocks, (99)00083-X Strouboulis T, Babu?ka I, Copps K (2000) The design and analysis of the generalized finite element method, Computer methods in applied mechanics and engineering, vol.16, issue.1-4, pp.43-69, 1999.

N. Sukumar and T. Belytschko, Arbitrary branched and intersecting cracks with the extended finite element method, Int J Numer Meth Eng, vol.48, pp.1741-1760, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01005274

N. Sukumar, N. Moës, B. Moran, and T. Belytschko, Extended finite element method for three-dimensional crack modelling, International Journal for Numerical Methods in Engineering, vol.48, issue.11, pp.1549-1570, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01006859

N. Sukumar, D. Chopp, N. Moës, and T. Belytschko, Modeling holes and inclusions by level sets in the extended finite-element method, Computer Methods in Applied Mechanics and Engineering, vol.190, pp.6183-6200, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01528265

N. Sukumar, J. Dolbow, and N. Moës, Extended finite element method in computational fracture mechanics: a retrospective examination, International Journal of Fracture, vol.196, issue.1-2, pp.189-206, 2015.

, Computational methods for ductile fracture modeling at the microscale 43

E. Svenning, F. Larsson, and M. Fagerström, Twoscale modeling of fracturing solids using a smeared macro-to-micro discontinuity transition, Computational Mechanics pp, pp.1-15, 2017.

C. Teko?-glu, J. W. Hutchinson, and T. Pardoen, On localization and void coalescence as a precursor to ductile fracture, Philosophical transactions Series A, Mathematical, physical, and engineering sciences, vol.373, 2015.

R. Tian, S. Chan, S. Tang, A. M. Kopacz, J. S. Wang et al., A multiresolution continuum simulation of the ductile fracture process, Journal of the Mechanics and Physics of Solids, vol.58, issue.10, pp.1681-1700, 2010.

V. Tomar, J. Zhai, and M. Zhou, Bounds for element size in a variable stiffness cohesive finite element model, International journal for numerical methods in engineering, vol.61, issue.11, pp.1894-1920, 2004.

S. Toro, P. J. Sánchez, J. M. Podestá, P. J. Blanco, A. E. Huespe et al., Cohesive surface model for fracture based on a two-scale formulation: computational implementation aspects, Engineering fracture mechanics, vol.58, issue.4, pp.1665-1682, 2007.

A. Turon, P. Camanho, J. Costa, and J. Renart, Accurate simulation of delamination growth under mixedmode loading using cohesive elements: Definition of interlaminar strengths and elastic stiffness, Composite Structures, vol.92, issue.8, pp.1857-1864, 2010.

V. Tvergaard and A. Needleman, Analysis of the cup-cone fracture in a round tensile bar, 1984.

, Acta Metallurgica, vol.32, issue.1, p.90213

N. Vajragupta, V. Uthaisangsuk, B. Schmaling, S. Münstermann, A. Hartmaier et al., A micromechanical damage simulation of dual phase steels using XFEM, Computational Materials Science, vol.54, issue.1, pp.271-279, 2012.

M. Vaz and D. Owen, Aspects of ductile fracture and adaptive mesh refinement in damaged elasto-plastic materials, International Journal for Numerical Methods in Engineering, vol.50, issue.1, pp.29-54, 2001.

M. Vocialta, N. Richart, and J. F. Molinari, 3d dynamic fragmentation with parallel dynamic insertion of cohesive elements, International Journal for Numerical Methods in Engineering, vol.109, issue.12, pp.1655-1678, 2017.

Z. Wang, T. Yu, T. Q. Bui, N. A. Trinh, N. Luong et al., Numerical modeling of 3-d inclusions and voids by a novel adaptive xfem, Advances in Engineering Software, vol.102, pp.105-122, 2016.

J. Wolf, P. Longère, J. M. Cadou, and J. P. Crété, Numerical modeling of strain localization in engineering ductile materials combining cohesive models and X-FEM, International Journal of Mechanics and Materials in Design, pp.1-17, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02151844

C. Wolff, N. Richart, and J. F. Molinari, A nonlocal continuum damage approach to model dynamic crack branching, International Journal for Numerical Methods in Engineering, vol.101, issue.12, pp.933-949, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01417917

J. Wulf, T. Steinkopff, and H. Fischmeister, Fesimulation of crack paths in the real microstructure of an Al(6061)/SiC composite, Acta Materialia, vol.44, issue.5, pp.1765-1779, 1996.

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

L. Xue, Constitutive modeling of void shearing effect in ductile fracture of porous materials, Engineering Fracture Mechanics, vol.75, issue.11, pp.3343-3366, 2008.

C. Ye, J. Shi, and G. J. Cheng, An extended finite element method (xfem) study on the effect of reinforcing particles on the crack propagation behavior in a metal-matrix composite, International Journal of Fatigue, vol.44, pp.151-156, 2012.

Z. Yuan and J. Fish, Toward realization of computational homogenization in practice, International Journal for Numerical Methods in Engineering, vol.73, issue.3, pp.361-380, 2008.
DOI : 10.1002/nme.2074

Z. Zhang and A. Naga, A New Finite Element Gradient Recovery Method: Superconvergence Property, SIAM Journal on Scientific Computing, vol.26, issue.4, pp.1192-1213, 2005.
DOI : 10.1137/s1064827503402837

URL : http://www.math.wayne.edu/~zzhang/paper/zhang-naga1.pdf

O. C. Zienkiewicz and J. Z. Zhu, A simple error estimator and adaptive procedure for practical engineerng analysis, International Journal for Numerical Methods in Engineering, vol.24, issue.2, pp.337-357, 1987.
DOI : 10.1002/nme.1620240206