Z. Quan, Z. Larimore, A. Wu, J. Yu, X. Qin et al., Microstructural design and additive manufacturing and characterization of 3D orthogonal short carbon fiber/acrylonitrile-butadiene-styrene preform and composite, Composites Science and Technology, vol.126, pp.139-148, 2016.
DOI : 10.1016/j.compscitech.2016.02.021

J. Cadman, S. Zhou, Y. Chen, and Q. Li, On design of multi-functional microstructural materials, Journal of Materials Science, vol.5, issue.656, pp.51-66, 2013.
DOI : 10.1002/lpor.201000014

F. Fritzen, L. Xia, M. Leuschner, and P. Breitkopf, Topology optimization of multiscale elastoviscoplastic structures, International Journal for Numerical Methods in Engineering, vol.2, issue.2, pp.430-453, 2016.
DOI : 10.1088/0965-0393/2/3A/011

G. Gu, L. Dimas, Z. Qin, and M. Buehler, Optimization of Composite Fracture Properties: Method, Validation, and Applications, Journal of Applied Mechanics, vol.83, issue.7, pp.71-77, 2016.
DOI : 10.1115/1.4033381

URL : http://dspace.mit.edu/bitstream/1721.1/110212/1/Buehler_Optimization%20of%20composite.pdf

B. San and H. Waisman, Optimization of Carbon Black Polymer Composite Microstructure for Rupture Resistance, Journal of Applied Mechanics, vol.84, issue.2, pp.21-26, 2016.
DOI : 10.1115/1.4035050

L. Xia, D. Da, and J. Yvonnet, Topology optimization for maximizing the fracture resistance of quasi-brittle composites, Computer Methods in Applied Mechanics and Engineering, vol.332, pp.234-254, 2018.
DOI : 10.1016/j.cma.2017.12.021

URL : https://hal.archives-ouvertes.fr/hal-01674145

J. Lamon, N. Carrere, and E. Martin, The influence of the interphase and associated interfaces on the deflection of matrix cracks in ceramic matrix composites, Composites A, vol.31, pp.1179-1190, 2000.

V. Tvergaard, Model studies of fibre breakage and debonding in a metal reinforced by short fibres, Journal of the Mechanics and Physics of Solids, vol.41, issue.8, pp.1309-1326, 1993.
DOI : 10.1016/0022-5096(93)90081-P

T. Nguyen, J. Yvonnet, M. Bornert, and C. Chateau, Initiation and propagation of complex 3D networks of cracks in heterogeneous quasi-brittle materials: Direct comparison between in situ testing-microCT experiments and phase field simulations, Journal of the Mechanics and Physics of Solids, vol.95, pp.320-350, 2016.
DOI : 10.1016/j.jmps.2016.06.004

URL : https://hal.archives-ouvertes.fr/hal-01331213

F. Narducci and S. Pinho, Exploiting nacre-inspired crack deflection mechanisms in CFRP via micro-structural design, Composites Science and Technology, vol.153, 2017.
DOI : 10.1016/j.compscitech.2017.08.023

N. Moes, J. Dolbow, and T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.8, issue.1, pp.131-150, 1999.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J

URL : https://hal.archives-ouvertes.fr/hal-01004829

N. Sukumar and M. Moran, Extended finite element method for three-dimensional crack modelling, International Journal for Numerical Methods in Engineering, vol.15, issue.11, pp.1549-1570, 2000.
DOI : 10.1016/0020-7683(79)90062-3

URL : https://hal.archives-ouvertes.fr/hal-01006859

P. Bernard, N. Moes, and N. Chevaugeon, Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings, Computer Methods in Applied Mechanics and Engineering, vol.233, issue.236, pp.11-27, 2012.
DOI : 10.1016/j.cma.2012.02.020

URL : https://hal.archives-ouvertes.fr/hal-01006715

F. Cazes and N. Moes, 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

G. Francfort and 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

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.45-48, pp.45-482765, 2010.
DOI : 10.1016/j.cma.2010.04.011

C. Kuhn and R. Müller, A continuum phase field model for fracture, Engineering Fracture Mechanics, vol.77, issue.18, pp.3625-3634, 2010.
DOI : 10.1016/j.engfracmech.2010.08.009

B. Bourdin, G. Francfort, and J. Marigo, The Variational Approach to Fracture, Journal of Elasticity, vol.125, issue.8, pp.5-148, 2008.
DOI : 10.1016/S1874-5717(06)80009-5

URL : https://hal.archives-ouvertes.fr/hal-00551079

K. Pham and J. Marigo, Approche variationnelle de l'endommagement : I. Les concepts fondamentaux, Comptes Rendus M??canique, vol.338, issue.4, pp.191-198, 2010.
DOI : 10.1016/j.crme.2010.03.009

URL : https://hal.archives-ouvertes.fr/hal-00490518

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

D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989.
DOI : 10.1109/TPAMI.1984.4767596

URL : https://dash.harvard.edu/bitstream/handle/1/3637121/Mumford_OptimalApproxPiece.pdf?sequence=1

L. Ambrosio and V. Tortorelli, Approximation of functional depending on jumps by elliptic functional via t-convergence, Communications on Pure and Applied Mathematics, vol.17, issue.8, pp.999-1036, 1990.
DOI : 10.1080/01621459.1987.10478393

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.55, issue.10, pp.1273-1311, 2010.
DOI : 10.1007/978-94-017-1957-5

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.
DOI : 10.1016/j.cma.2015.10.007

URL : https://hal.archives-ouvertes.fr/hal-01213943

M. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, vol.71, issue.2, pp.197-224, 1988.
DOI : 10.1016/0045-7825(88)90086-2

M. Bendsøe and S. O. , Topology Optimization: Theory, Methods and Applications, 2003.

H. Nguyen-xuan, A polytree-based adaptive polygonal finite element method for topology optimization, International Journal for Numerical Methods in Engineering, vol.44, issue.4, pp.972-1000, 2017.
DOI : 10.1007/s00158-011-0650-y

K. Chau, K. Chau, T. Ngo, K. Hackl, and H. Nguyen-xuan, A polytree-based adaptive polygonal finite element method for multi-material topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.332, 2018.
DOI : 10.1016/j.cma.2017.07.035

Y. Xie and G. Steven, A simple evolutionary procedure for structural optimization, Computers & Structures, vol.49, issue.5, pp.885-896, 1993.
DOI : 10.1016/0045-7949(93)90035-C

X. Huang and Y. Xie, Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method, Finite Elements in Analysis and Design, vol.43, issue.14, pp.1039-1049, 2007.
DOI : 10.1016/j.finel.2007.06.006

J. Sethian and A. Wiegmann, Structural Boundary Design via Level Set and Immersed Interface Methods, Journal of Computational Physics, vol.163, issue.2, pp.489-528, 2000.
DOI : 10.1006/jcph.2000.6581

URL : http://www.math.berkeley.edu/~sethian/Publications/../Papers/sethian.optimal_design.ps.gz

M. Wang, X. Wang, and D. Guo, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.1-2, pp.227-246, 2003.
DOI : 10.1016/S0045-7825(02)00559-5

G. Allaire, F. Jouve, and A. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004.
DOI : 10.1016/j.jcp.2003.09.032

L. Xia, F. Fritzen, and P. Breitkopf, Evolutionary topology optimization of elastoplastic structures. Structural and Multidisciplinary Optimization 2017, pp.569-581
DOI : 10.1007/s00158-016-1523-1

L. Xia, Q. Xia, X. Huang, and Y. Xie, Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review, Archives of Computational Methods in Engineering, vol.69, issue.2, pp.10-1007, 2017.
DOI : 10.1016/j.commatsci.2012.12.006

L. Xia and P. Breitkopf, Concurrent topology optimization design of material and structure within <mml:math altimg="si25.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msup><mml:mrow><mml:mstyle mathvariant="normal"><mml:mi>FE</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> nonlinear multiscale analysis framework, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.524-542, 2014.
DOI : 10.1016/j.cma.2014.05.022

L. Xia and P. Breitkopf, Multiscale structural topology optimization with an approximate constitutive model for local material microstructure, Computer Methods in Applied Mechanics and Engineering, vol.286, pp.147-167, 2015.
DOI : 10.1016/j.cma.2014.12.018

N. Vermaak, G. Michailidis, G. Parry, R. Estevez, G. Allaire et al., Material interface effects on the topology optimziation of multi-phase structures using a level set method, Structural and Multidisciplinary Optimization, vol.doi, pp.10-1007, 2014.
DOI : 10.1007/s00158-014-1074-2

M. Lawry and K. Maute, Level set topology optimization of problems with sliding contact interfaces, Structural and Multidisciplinary Optimization, vol.82, issue.5, pp.1107-1119, 2015.
DOI : 10.1002/nme.2777

P. Liu, Y. Luo, and Z. Kang, Multi-material topology optimization considering interface behavior via XFEM and level set method, Computer Methods in Applied Mechanics and Engineering, vol.308, pp.113-133, 2016.
DOI : 10.1016/j.cma.2016.05.016

R. Behrou, M. Lawry, and K. Maute, Level set topology optimization of structural problems with interface cohesion, International Journal for Numerical Methods in Engineering, vol.132, issue.11
DOI : 10.1061/(ASCE)0733-9399(2006)132:11(1215)

URL : https://doi.org/10.1002/nme.5540

P. Duysinx and M. Bendsøe, Topology optimization of continuum structures with local stress constraints, International Journal for Numerical Methods in Engineering, vol.10, issue.8, pp.1453-1478, 1998.
DOI : 10.1007/978-94-015-7862-2

URL : http://orbit.dtu.dk/en/publications/topology-optimization-of-continuum-structures-with-local-stress-constraints(47c96145-46b9-4d6f-8e60-f97dccd77541).html

X. Guo, W. Zhang, M. Wang, and P. Wei, Stress-related topology optimization via level set approach, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.47-48, pp.47-483439, 2011.
DOI : 10.1016/j.cma.2011.08.016

Q. Xia, T. Shi, S. Liu, and M. Wang, A level set solution to the stress-based structural shape and topology optimization, Computers & Structures, vol.90, issue.91, pp.90-9155, 2012.
DOI : 10.1016/j.compstruc.2011.10.009

M. Bruggi and P. Duysinx, Topology optimization for minimum weight with compliance and stress constraints. Structural and Multidisciplinary Optimization 2012, pp.369-384
DOI : 10.1007/s00158-012-0759-7

Y. Luo, M. Wang, and Z. Kang, An enhanced aggregation method for topology optimization with local stress constraints, Computer Methods in Applied Mechanics and Engineering, vol.254, pp.31-41, 2013.
DOI : 10.1016/j.cma.2012.10.019

S. Cai, W. Zhang, J. Zhu, and T. Gao, Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.361-387, 2014.
DOI : 10.1016/j.cma.2014.06.007

S. Cai and W. Zhang, Stress constrained topology optimization with free-form design domains, Computer Methods in Applied Mechanics and Engineering, vol.289, pp.267-290, 2015.
DOI : 10.1016/j.cma.2015.02.012

Z. Sun, D. Li, W. Zhang, S. Shi, and X. Guo, Topological optimization of biomimetic sandwich structures with hybrid core and CFRP face sheets, Composites Science and Technology, vol.142, pp.79-90, 2017.
DOI : 10.1016/j.compscitech.2017.01.029

V. Challis, A. Roberts, and A. Wilkins, Fracture resistance via topology optimization, Structural and Multidisciplinary Optimization, vol.35, issue.2, pp.263-271, 2008.
DOI : 10.1080/01630563.1980.10120631

O. Amir and S. O. , Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization. Structural and Multidisciplinary Optimization 2012, pp.157-174
DOI : 10.1007/s00158-012-0817-1

URL : http://orbit.dtu.dk/en/publications/reinforcement-layout-design-for-concrete-structures-based-on-continuum-damage-and-truss-topology-optimization(ea90a0fb-d546-4767-97bc-e24a9a0c01ae).html

O. Amir, A topology optimization procedure for reinforced concrete structures, Computers & Structures, vol.114, issue.115, pp.46-58, 2013.
DOI : 10.1016/j.compstruc.2012.10.011

M. Jansen, G. Lombaert, M. Schevenels, and S. O. , Topology optimization of fail-safe structures using a simplified local damage model. Structural and Multidisciplinary Optimization 2013, pp.657-666
DOI : 10.1007/s00158-013-1001-y

URL : http://orbit.dtu.dk/en/publications/topology-optimization-of-failsafe-structures-using-a-simplified-local-damage-model(9658b269-613d-49ed-91b0-ab0936dc14fe).html

K. James and H. Waisman, Failure mitigation in optimal topology design using a coupled nonlinear continuum damage model, Computer Methods in Applied Mechanics and Engineering, vol.268, pp.614-631, 2014.
DOI : 10.1016/j.cma.2013.10.022

Z. Kang, P. Liu, and M. Li, Topology optimization considering fracture mechanics behaviors at specified locations, Structural and Multidisciplinary Optimization, vol.49, issue.5, pp.1-18, 2016.
DOI : 10.1016/0045-7949(93)90035-C

C. Verhoosel and R. De-borst, A phase-field model for cohesive fracture, International Journal for Numerical Methods in Engineering, vol.1, issue.220, pp.43-62, 2013.
DOI : 10.1088/0965-0393/1/2/001

URL : http://eprints.gla.ac.uk/87662/1/Rene%20De%20Borst%20-%20Paper.pdf

X. Huang and Y. Xie, Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials, Computational Mechanics, vol.45, issue.1, pp.393-401, 2009.
DOI : 10.1080/08905459708945415

D. Da, X. Cui, K. Long, and G. Li, Concurrent topological design of composite structures and the underlying multi-phase materials, Computers & Structures, vol.179, issue.1, pp.1-14, 2017.
DOI : 10.1016/j.compstruc.2016.10.006

K. Maute, S. Schwarz, and E. Ramm, Adaptive topology optimization of elastoplastic structures, Structural Optimization, vol.10, issue.2, pp.81-91, 1998.
DOI : 10.1007/978-94-010-9577-8_33

S. Schwarz, K. Maute, and E. Ramm, Topology and shape optimization for elastoplastic structural response, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.15-17, pp.15-172135, 2001.
DOI : 10.1016/S0045-7825(00)00227-9

X. Huang and Y. Xie, Topology optimization of nonlinear structures under displacement loading, Engineering Structures, vol.30, issue.7, pp.2057-2068, 2008.
DOI : 10.1016/j.engstruct.2008.01.009

L. Xia and P. Breitkopf, Recent Advances on Topology Optimization of Multiscale Nonlinear Structures, Archives of Computational Methods in Engineering, vol.51, issue.1, p.227249, 2017.
DOI : 10.1016/j.matdes.2013.05.014

O. Sigmund, A 99 line topology optimization code written in Matlab, Structural and Multidisciplinary Optimization, vol.21, issue.2, pp.120-127, 2001.
DOI : 10.1007/s001580050176

URL : http://orbit.dtu.dk/en/publications/a-99-line-topology-optimization-code-written-in-matlab(b0794468-93a9-4cca-87b3-b4224938859a).html

X. Huang and Y. Xie, Topology Optimization of Continuum Structures: Methods and Applications
DOI : 10.1002/9780470689486

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.
DOI : 10.1016/j.engfracmech.2015.03.045

URL : https://hal.archives-ouvertes.fr/hal-01140963