J. D. Achenbach and H. Zhu, Effect of interfacial zone on mechanical behavior and failure of fiber-reinforced composites, Journal of the Mechanics and Physics of Solids, vol.37, issue.1, pp.381-393, 1989.

R. F. Gibson, Principles of composite material mechanics, 2011.

P. Chhapadia, P. Mohammadi, and P. Sharma, Curvature-dependent surface energy and implications for nanostructures, Journal of the Mechanics and Physics of Solids, vol.59, issue.1, pp.2103-2115, 2011.

H. Lee, S. M. Dellatore, V. M. Miller, and P. B. Messersmith, Mussel-inspired surface chemistry for multifunctional coatings, Science, vol.318, issue.1, pp.426-430, 2007.

J. Karger-kocsis, H. Mahmood, and A. Pegoretti, Recent advances in fiber/matrix interphase engineering for polymer composites, Progress in Materials Science, issue.1, pp.1-43, 2015.

S. Gao and E. Mäder, Characterisation of interphase nanoscale property variations in glass fibre reinforced polypropylene and epoxy resin composites, Composites Part A: Applied Science and Manufacturing, vol.33, issue.1, pp.559-576, 2002.

J. Jancar, Review of the role of the interphase in the control of composite performance on micro-and nano-length scales, Journal of Materials Science, vol.43, issue.1, pp.6747-6757, 2008.

D. Givoli, Finite element modeling of thin layers, Computer Modeling in Engineering & Sciences, vol.5, issue.1, pp.497-514, 2004.

H. Eslami and F. Müller-plathe, How thick is the interphase in an ultrathin polymer film? coarse-grained molecular dynamics simulations of polyamide-6,6 on graphene, The Journal of Physical Chemistry C, vol.117, issue.1, pp.5249-5257, 2013.

Z. Wang, Q. Lv, S. Chen, C. Li, S. Sun et al., Effect of interfacial bonding on interphase properties in SiO2/epoxy nanocomposite: a molecular dynamics simulation study, ACS Applied Materials & Interfaces, vol.8, issue.1, pp.7499-7508, 2016.

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

A. Klarbring and A. B. Movchan, Asymptotic modelling of adhesive joints, Mechanics of Materials, vol.28, issue.1, pp.137-145, 1998.

D. Bigoni, S. K. Serkov, M. Valentini, and A. B. Movchan, Asymptotic models of dilute composites with imperfectly bonded inclusions, International Journal of Solids and Structures, vol.35, issue.1, pp.3239-3258, 1998.

Z. Hashin, Thin interphase/imperfect interface in elasticity with application to coated fiber composites, Journal of the Mechanics and Physics of Solids, vol.50, issue.1, pp.2509-2537, 2002.

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.1, pp.1413-1426, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00692839

Y. Benveniste, The effective mechanical behaviour of composite materials with imperfect contact between the constituents, Mechanics of Materials, vol.4, issue.1, pp.197-208, 1985.

Z. Hashin, Thermoelastic properties of fiber composites with imperfect interface, Mechanics of Materials, vol.8, issue.1, pp.333-348, 1990.

Z. Hashin, The spherical inclusion with imperfect interface, Journal of Applied Mechanics, vol.58, issue.1, pp.444-449, 1991.

D. Bigoni and A. B. Movchan, Statics and dynamics of structural interfaces in elasticity, International Journal of Solids and Structures, vol.39, issue.1, pp.4843-4865, 2002.

H. L. Duan, J. Wang, Z. P. Huang, and Z. Y. Luo, Stress concentration tensors of inhomogeneities with interface effects, Mechanics of Materials, vol.37, issue.1, pp.723-736, 2005.

J. Wang, H. L. Duan, Z. Zhang, and Z. P. Huang, An anti-interpenetration model and connections between interphase and interface models in particle-reinforced composites, International Journal of Mechanical Sciences, vol.47, issue.1, pp.701-708, 2005.

Y. Benveniste and T. Miloh, Imperfect soft and stiff interfaces in two-dimensional elasticity, Mechanics of Materials, vol.33, pp.309-323, 2001.

M. E. Gurtin and A. I. Murdoch, A continuum theory of elastic material surfaces, Archives for Rational Mechanics and Analysis, vol.57, pp.291-323, 1975.

M. E. Gurtin and A. I. Murdoch, Surface stress in solids, International Journal of Solids and Structures, vol.14, pp.431-440, 1978.

M. E. Gurtin, J. Weissmüller, and F. Larché, A general theory of curved deformable interfaces in solids at equilibrium, Philosophical Magazine A, vol.78, issue.1, pp.1093-1109, 1998.

D. J. Steigmann and R. W. Ogden, Plain deformations of elastic solids with intrinsic boundary elasticity, Proceedings of the Royal Society of London A, vol.453, pp.853-877, 1997.

D. J. Steigmann and R. W. Ogden, Elastic surface-substrate interactions, Proceedings of the Royal Society of London A, vol.455, pp.437-474, 1999.

A. Javili, F. Dell'-isola, and P. Steinmann, Geometrically nonlinear higher-gradient elasticity with energetic boundaries, Journal of the Mechanics and Physics of Solids, vol.61, issue.1, pp.2381-2401, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00838679

A. Javili, A. Mcbride, P. Steinmann, and B. D. Reddy, A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology, Computational Mechanics, vol.54, issue.1, pp.745-762, 2014.

H. L. Duan and B. L. Karihaloo, Thermo-elastic properties of heterogeneous materials with imperfect interfaces: Generalized levin's formula and hill's connections, Journal of the Mechanics and Physics of Solids, vol.55, issue.1, pp.1036-1052, 2007.

S. G. Mogilevskaya, S. L. Crouch, and H. K. Stolarski, Multiple interacting circular nano-inhomogeneities with surface/interface effects, Journal of the Mechanics and Physics of Solids, vol.56, pp.2298-2327, 2008.

A. Y. Zemlyanova and S. G. Mogilevskaya, Circular inhomogeneity with Steigmann-Ogden interface: Local fields, neutrality, and Maxwell's type approximation formula, International Journal of Solids and Structures, vol.135, pp.85-98, 2002.

Z. Han, S. G. Mogilevskaya, and D. Schillinger, Local fields and overall transverse properties of unidirectional composite materials with multiple nanofibers and Steigmann-Ogden interfaces, International Journal of Solids and Structures, vol.147, pp.166-182

Y. Capdeville and J. J. Marigo, Shallow layer correction for spectral element like methods, Geophysical Journal International, vol.172, issue.1, pp.1135-1150, 2008.
URL : https://hal.archives-ouvertes.fr/insu-01399903

G. Strang and G. J. Fix, An Analysis of the Finite Element Method, 1973.

C. Sussmann, D. Givoli, and Y. Benveniste, Combined asymptotic finite-element modeling of thin layers for scalar elliptic problems, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.1, pp.3265-3269, 2011.

S. Dumont, F. Lebon, and R. Rizzoni, An asymptotic approach to the adhesion of thin stiff films, Mechanics Research Communications, vol.58, issue.1, pp.24-35, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00825708

J. Yvonnet, H. L. 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.42, issue.1, pp.119-131, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00692238

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

E. Benvenuti, G. Ventura, N. Ponara, and A. Tralli, Variationally consistent eXtended FE model for 3D planar and curved imperfect interfaces, Computer Methods in Applied Mechanics and Engineering, vol.267, issue.1, pp.434-457, 2013.

A. Javili, F. F. Dell'-isola, and P. Steinmann, Geometrically nonlinear higher-gradient elasticity with energetic boundaries, Journal of the Mechanics and Physics of Solids, vol.61, issue.1, pp.2381-2401, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00838679

A. Javili, A. Mcbride, P. Steinmann, and B. D. Reddy, A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology, Computational Mechanics, vol.54, issue.1, pp.745-762, 2014.

T. J. Hughes, J. A. Cottrell, and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.1, pp.4135-4195, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01513346

J. A. Cottrell, T. J. Hughes, and Y. Bazilevs, Isogeometric analysis: Towards Integration of CAD and FEA, vol.1, 2009.

D. Schillinger and M. Ruess, The Finite Cell Method: A review in the context of higher-order structural analysis of CAD and image-based geometric models, Archives of Computational Methods in Engineering, vol.22, issue.3, pp.391-455, 2015.

E. Burman, S. Claus, P. Hansbo, M. Larson, and A. Massing, CutFEM: discretizing geometry and partial differential equations, International Journal for Numerical Methods in Engineering, vol.104, issue.7, pp.472-501, 2015.

A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsche's method, for elliptic interface problems, Computer Methods in Applied Mechanics and Engineering, vol.191, pp.537-552, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01352903

D. N. Arnold, F. Brezzi, B. Cockburn, and D. L. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM Journal on Numerical Analysis, vol.39, issue.5, pp.1749-1779, 2002.

Y. Benveniste, Exact results for the local fields and the effective moduli of fibrous composites with thickly coated fibers, Journal of the Mechanics and Physics of Solids, vol.71, issue.2, pp.219-238, 2014.

D. Schillinger, M. Ruess, N. Zander, Y. Bazilevs, A. Düster et al., Small and large deformation analysis with the p-and B-spline versions of the Finite Cell Method, Computational Mechanics, vol.50, issue.4, pp.445-478, 2012.

D. Schillinger, L. Dede, &. , M. A. Scott, J. A. Evans et al., An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces, Computer Methods in Applied Mechanics and Engineering, issue.3, pp.116-150, 2012.

H. Gomez, V. M. Calo, Y. Bazilevs, and T. J. Hughes, Isogeometric analysis of the Cahn-Hilliard phase-field model, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.1, pp.4333-4352, 2008.

C. V. Verhoosel, M. A. Scott, T. J. Hughes, and R. Borst, An isogeometric analysis approach to gradient damage models, International Journal for Numerical Methods in Engineering, vol.86, issue.1, pp.115-134, 2011.

J. Kiendl, F. Auricchio, T. J. Hughes, and A. Reali, Single-variable formulations and isogeometric discretizations for shear deformable beams, Computer Methods in Applied Mechanics and Engineering, vol.284, issue.1, pp.988-1004, 2015.

Y. Zhao, D. Schillinger, and B. Xu, Variational boundary conditions based on the Nitsche method for fitted and unfitted isogeometric discretizations of the mechanically coupled Cahn-Hilliard equation, Journal of Computational Physics, vol.340, issue.1, pp.177-199, 2017.

L. Piegl and W. Tiller, The NURBS Book, vol.3, 1997.

T. Martin, E. Cohen, and R. M. Kirby, Volumetric parameterization and trivariate b-spline fitting using harmonic functions, Computer Aided Geometric Design, vol.26, issue.6, pp.648-664, 2009.

E. Cohen, T. Martin, R. M. Kirby, T. Lyche, and R. F. Riesenfeld, Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.2, pp.334-356, 2010.

M. Haberleitner, B. Jãoettler, M. A. Scott, and D. C. Thomas, Isogeometric Analysis: Representation of Geometry, vol.3, 2018.

B. Müller, F. Kummer, and M. Oberlack, Highly accurate surface and volume integration on implicit domains by means of moment-fitting, International Journal for Numerical Methods in Engineering, vol.96, issue.8, pp.512-528, 2013.

T. Fries and S. Omerovic, Higher-order accurate integration of implicit geometries, International Journal for Numerical Methods in Engineering, vol.106, issue.1, pp.323-371, 2016.

L. Kudela, N. Zander, T. Bog, S. Kollmannsberger, and E. Rank, Efficient and accurate numerical quadrature for immersed boundary methods. Advanced Modeling and Simulation in Engineering Sciences, vol.2, pp.1-22, 2015.

A. Stavrev, L. H. Nguyen, R. Shen, V. Varduhn, M. Behr et al., Geometrically accurate, efficient, and flexible quadrature techniques for the tetrahedral finite cell method, Computer Methods in Applied Mechanics and Engineering, vol.310, pp.646-673, 2016.

C. Lehrenfeld, High order unfitted finite element methods on level set domains using isoparametric mappings, Computer Methods in Applied Mechanics and Engineering, vol.300, pp.716-733, 2016.

A. Embar, J. Dolbow, and I. Harari, Imposing Dirichlet boundary conditions with Nitsche's method and splinebased finite elements, International Journal for Numerical Methods in Engineering, vol.83, issue.2, pp.877-898, 2010.

E. Burman and P. Hansbo, Fictitious domain finite element methods using cut elements: Ii. a stabilized Nitsche method, Applied Numerical Mathematics, vol.62, issue.4, pp.328-341, 2012.

W. Jiang, C. Annavarapu, J. E. Dolbow, and I. Harari, A robust Nitsche's formulation for interface problems with spline-based finite elements, International Journal for Numerical Methods in Engineering, vol.104, issue.7, pp.676-696, 2015.

D. Schillinger, I. Harari, M. Hsu, D. Kamensky, K. F. Stoter et al., The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements, Computer Methods in Applied Mechanics and Engineering, vol.309, pp.625-652, 2016.

F. De-prenter, C. Verhoosel, and H. Van-brummelen, Preconditioning immersed isogeometric finite element methods with application to flow problems, vol.3, 2017.

A. Massing, B. Schott, and W. A. Wall, A stabilized Nitsche cut finite element method for the Oseen problem, Computer Methods in Applied Mechanics and Engineering, vol.3, issue.2, 2017.

A. Düster, J. Parvizian, Z. Yang, and E. Rank, The finite cell method for three-dimensional problems of solid mechanics, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.3768-3782, 2001.

M. Joulaian, S. Hubrich, and A. Düster, Numerical integration of discontinuities on arbitrary domains based on moment fitting, Computational Mechanics, vol.57, issue.6, pp.979-999, 2001.

R. Bouclier and J. Passieux, A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis, Computer Methods in Applied Mechanics and Engineering, vol.340, issue.4, pp.253-277, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01816443

B. Rivière, Linear elasticity, Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations, chapter 5, pp.109-115, 2008.

S. Soon, B. Cockburn, and H. K. Stolarski, A hybridizable discontinuous Galerkin method for linear elasticity, International Journal for Numerical Methods in Engineering, vol.80, issue.8, pp.1058-1092, 2009.

F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, vol.4, 1991.

P. Hansbo and M. G. Larson, Discontinuous galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.17, pp.1895-1908, 2002.

C. Annavarapu, M. Hautefeuille, and J. E. Dolbow, A robust Nitsche's formulation for interface problems, Computer Methods in Applied Mechanics and Engineering, vol.225, issue.3, pp.44-54, 2012.

I. Harari and E. Grosu, A unified approach for embedded boundary conditions for fourth-order elliptic problems, International Journal for Numerical Methods in Engineering, vol.104, issue.7, pp.655-675, 2015.

U. Langer, A. Mantzaflaris, S. Moore, and I. Toulopoulos, Multipatch discontinuous Galerkin isogeometric analysis, Isogeometric Analysis and Applications, pp.1-32, 2015.

R. E. Miller and V. B. Shenoy, Size-dependent elastic properties of nanosized structural elements, Nanotechnology, vol.11, issue.3, p.139, 2000.

P. Sharma and S. Ganti, Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies, Journal of Applied Mechanics, vol.71, issue.5, pp.663-671, 2004.

A. Javili, P. Steinmann, and J. Mosler, Micro-to-macro transition accounting for general imperfect interfaces, Computer Methods in Applied Mechanics and Engineering, vol.317, issue.6, pp.274-317, 2017.

M. Cenanovic, P. Hansbo, and M. G. Larson, Cut finite element modeling of linear membranes, Computer Methods in Applied Mechanics and Engineering, vol.310, issue.6, pp.98-111, 2016.

D. Schillinger, T. Gangwar, A. Gilmanov, J. D. Heuschele, and H. K. Stolarski, Embedded shell finite elements: Solid-shell interaction, surface locking, and application to image-based bio-structures, Computer Methods in Applied Mechanics and Engineering, vol.335, issue.6, pp.298-326, 2018.

Y. Guo, J. Heller, T. J. Hughes, M. Ruess, and D. Schillinger, Variationally consistent isogeometric analysis of trimmed thin shells at finite deformations, based on the step exchange format, Computer Methods in Applied Mechanics and Engineering, vol.336, issue.6, pp.39-79, 2018.