F. Barbea, R. Queyc, A. Musienkod, and G. Cailletaud, Three-dimensional characterization of strain localization bands in high-resolution elastoplastic polycrystals, Mechanics Research Communications, vol.36, issue.7, pp.762-768, 2009.
DOI : 10.1016/j.mechrescom.2009.06.002

B. Bary, M. B. Haha, E. Adam, and P. , Numerical and analytical effective elastic properties of degraded cement pastes, Cement and Concrete Research, vol.39, issue.10, pp.902-912, 2009.
DOI : 10.1016/j.cemconres.2009.06.012

E. Béchet, N. Moës, and B. Wohlmuth, A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method, International Journal for Numerical Methods in Engineering, vol.85, issue.1, pp.931-954, 2009.
DOI : 10.1002/nme.2515

T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering, vol.55, issue.5, pp.601-620, 1999.
DOI : 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S

T. Belytschko, C. Parimi, N. Moës, N. Sukumar, and S. Usui, Structured extended finite element methods for solids defined by implicit surfaces, International Journal for Numerical Methods in Engineering, vol.78, issue.1-2, pp.609-635, 2003.
DOI : 10.1002/nme.686

C. Daux, N. Moës, J. Dolbow, N. Sukumar, and T. Belytschko, Arbitrary branched and intersecting cracks with the extended finite element method, International Journal for Numerical Methods in Engineering, vol.32, issue.12, pp.481741-1760, 2000.
DOI : 10.1002/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO;2-L

URL : https://hal.archives-ouvertes.fr/hal-01005274

M. P. Carmo, Differential Geometry of Curves and Surfaces, 1976.

C. Duarte, L. G. Reno, and A. Simone, A high-order generalized FEM for through-the-thickness branched cracks, International Journal for Numerical Methods in Engineering, vol.39, issue.3, pp.325-351, 2007.
DOI : 10.1002/nme.2012

T. P. Fries, A corrected XFEM approximation without problems in blending elements, International Journal for Numerical Methods in Engineering, vol.67, issue.3, pp.503-535, 2008.
DOI : 10.1002/nme.2258

R. Gracie, H. Wang, and T. Belytschko, Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods, International Journal for Numerical Methods in Engineering, vol.59, issue.11, pp.741645-669, 2008.
DOI : 10.1002/nme.2217

H. Ji and J. E. Dolbow, On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method, International Journal for Numerical Methods in Engineering, vol.190, issue.14, pp.2508-2535, 2004.
DOI : 10.1002/nme.1167

T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach, International Journal of Solids and Structures, vol.40, issue.13-14, pp.3647-3679, 2003.
DOI : 10.1016/S0020-7683(03)00143-4

B. L. Karihaloo and Q. Z. Xiao, Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review, Computers & Structures, vol.81, issue.3, pp.119-129, 2003.
DOI : 10.1016/S0045-7949(02)00431-5

J. M. Melenk and I. Babu?-ska, The partition of unity finite element method: Basic theory and applications, Computer Methods in Applied Mechanics and Engineering, vol.139, issue.1-4, pp.289-303, 1996.
DOI : 10.1016/S0045-7825(96)01087-0

R. Merle and J. Dolbow, Solving thermal and phase change problems with the eXtended finite element method, Computational Mechanics, vol.28, issue.5, pp.339-350, 2002.
DOI : 10.1007/s00466-002-0298-y

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.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A

N. Moës, M. Cloirec, P. Cartraud, and J. Remacle, A computational approach to handle complex microstructure geometries, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.3163-3177, 2003.
DOI : 10.1016/S0045-7825(03)00346-3

N. Moës, E. Bechet, and M. Tourbier, Imposing Dirichlet boundary conditions in the extended finite element method, International Journal for Numerical Methods in Engineering, vol.12, issue.12, pp.1641-1669, 2006.
DOI : 10.1002/nme.1675

H. M. Mourad, J. Dolbow, and I. Harari, A bubble-stabilized finite element method for Dirichlet constraints on embedded interfaces, International Journal for Numerical Methods in Engineering, vol.50, issue.4, pp.772-793, 2007.
DOI : 10.1002/nme.1788

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.12-49, 1998.
DOI : 10.1016/0021-9991(88)90002-2

N. Sukumar, D. L. 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, issue.46-47, pp.6183-6200, 2001.
DOI : 10.1016/S0045-7825(01)00215-8

URL : https://hal.archives-ouvertes.fr/hal-01007065

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.15, issue.11, pp.1549-1570, 2000.
DOI : 10.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A

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

J. A. Thorpe, Elementary Topics in Differential Geometry, 1979.
DOI : 10.1007/978-1-4612-6153-7

C. Toulemonde, R. Masson, and J. Gharib, Modeling the effective elastic behavior of composites: a mixed Finite Element and homogenisation approach, Comptes Rendus M??canique, vol.336, issue.3, pp.275-282, 2008.
DOI : 10.1016/j.crme.2007.11.024

J. Yvonnet, H. Le-quang, 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.71, issue.1, pp.119-131, 2008.
DOI : 10.1007/s00466-008-0241-y

URL : https://hal.archives-ouvertes.fr/hal-00692238

J. Yvonnet, Q. He, and C. Toulemonde, Numerical modelling of the effective conductivities of composites with arbitrarily shaped inclusions and highly conducting interface, Composites Science and Technology, vol.68, issue.13, pp.2828-2825, 2008.
DOI : 10.1016/j.compscitech.2008.06.008

URL : https://hal.archives-ouvertes.fr/hal-00692237

J. Yvonnet, Q. He, Q. Zhu, and J. Shao, A general and efficient computational procedure for modelling the Kapitza thermal resistance based on XFEM, Computational Materials Science, vol.50, issue.4, 2010.
DOI : 10.1016/j.commatsci.2010.02.040

URL : https://hal.archives-ouvertes.fr/hal-00559198

T. I. Zohdi and P. Wriggers, Aspects of the computational testing of the mechanical properties of microheterogeneous material samples, International Journal for Numerical Methods in Engineering, vol.36, issue.11, pp.2573-2599, 2001.
DOI : 10.1002/nme.146