]. A. Leó+13a and . Baldelli, A variational model for fracture and debonding of thin films under in-plane loadings, Papers in peer reviewed journals, 2013.

]. A. Leó+13d and . Baldelli, Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model, Continuum Mechanics and Thermodynamics 25.2-4, pp.243-268, 2013.

]. A. Leó+11 and . Baldelli, ´ Etude de la multifissuration e délamination par l'approche variationnellè a la mécanique de la fracture, Contributions in peer reviewed conference proceed- ings 10e Colloque National en Calcul des Structures. Giens, pp.1-8, 2011.

]. A. Leó+12 and . Baldelli, Multifissuration and Debonding of Thin Films Analytic and Numeric 1D Solutions Via a Variational Approach, The 23rd International Congress of Theoretical and Applied Mechanics, 2012.

]. A. Leó+13b and . Baldelli, Complex crack patterns: transverse fractures and delamination in thin film systems, Third International Conference on Computational Modeling of Fracture and Failure of Materials and Structures, 2013.

]. A. Leó+13c and . Baldelli, Delamination and fracture of thin films: a variational approach In: Direct and variational methods for nonsmooth problems in mechanics, 2013.

]. B. Ab08a, A. Audoly, and . Boudaoud, Buckling of a stiff film bound to a compliant substrate?Part I: Formulation, linear stability of cylindrical patterns, secondary bifurcations, Bibliography Journal of the Mechanics and Physics of Solids, vol.567, pp.2401-2421, 2008.

]. B. Ab08b, A. Audoly, and . Boudaoud, Buckling of a stiff film bound to a compliant substrate?Part II: A Global Scenario for the Formation of the Herringbone pattern, Journal of the Mechanics and Physics of Solids, vol.567, pp.2422-2443, 2008.

]. B. Ab08c, A. Audoly, and . Boudaoud, Buckling of a stiff film bound to a compliant substrate?Part III: Herringbone solutions at large buckling parameter, Journal of the Mechanics and Physics of Solids, vol.567, pp.2422-2443, 2008.

J. [. Ansini, C. I. Babadjian, and . Zeppieri, THE NEUMANN SIEVE PROBLEM AND DIMENSIONAL REDUCTION: A MULTISCALE APPROACH, Mathematical Models and Methods in Applied Sciences 17.05, pp.681-735, 2007.
DOI : 10.1142/S0218202507002078

URL : https://hal.archives-ouvertes.fr/hal-00265690

[. Ambrosio, A. Coscia, and G. D. Maso, Fine Properties of Functions with Bounded Deformation, Archive for Rational Mechanics and Analysis, vol.139, issue.3, pp.201-238, 1997.
DOI : 10.1007/s002050050051

[. Ambrosio, N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_2

E. [. Ambrico, M. R. Jones, and . Begley, Cracking in thin multi-layers with finite-width and periodic architectures, International Journal of Solids and Structures, vol.39, issue.6, pp.1443-1462, 2002.
DOI : 10.1016/S0020-7683(01)00235-9

]. G. All91a and . Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes, In: Archive for Rational Mechanics and Analysis, vol.1133, pp.261-298, 1991.

]. G. All91b and . Allaire, Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes I. abstract framework, a volume distribution of holes, In: Archive for Rational Mechanics and Analysis, vol.1133, pp.209-259, 1991.

J. [. Abdelmoula and . Marigo, The effective behavior of a fiber bridged crack, Journal of the Mechanics and Physics of Solids, vol.48, issue.11, pp.2419-2444, 2000.
DOI : 10.1016/S0022-5096(00)00003-X

]. L. Amb89 and . Ambrosio, A compactness theorem for a new class of functions of bounded variation, Boll. Un. Mat. Ital. B, vol.7, issue.4, pp.857-881, 1989.

R. Alessi, J. Marigo, and S. Vidoli, Gradient Damage Models Coupled with Plasticity and Nucleation of Cohesive Cracks, Archive for Rational Mechanics and Analysis, vol.110, issue.1
DOI : 10.1007/s00205-014-0763-8

]. N. Ans04 and . Ansini, The nonlinear sieve problem and applications to thin films, Asymptotic Analysis, vol.39, pp.113-145, 2004.

A. [. Allaire and . Raphael, Homogenization of a convection???diffusion model with reaction in a porous medium, Comptes Rendus Mathematique, vol.344, issue.8, pp.523-528, 2007.
DOI : 10.1016/j.crma.2007.03.008

[. Ambrosio and V. M. 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 : 10.1002/cpa.3160430805

[. Ambrosio and V. M. Tortorelli, On the approximation of Free Discontinuity Problems, Bollettino dell'Unione Matematica Italiana, pp.6-105, 1992.

J. Babadjian, Quasistatic evolution of a brittle thin film, Calculus of Variations and Partial Differential Equations, vol.74, issue.1, pp.69-118, 2006.
DOI : 10.1007/s00526-005-0369-y

URL : https://hal.archives-ouvertes.fr/hal-00265687

]. S. Bal+12 and . Balay, PETSc Users Manual, 2012.

]. G. Bar62 and . Barenblatt, The Mathematical Theory of Equilibrium Cracks in Brittle Fracture Advances in Applied Mechanics, pp.55-129, 1962.

V. Balbi and P. Ciarletta, Morpho-elasticity of intestinal villi, Journal of The Royal Society Interface, vol.55, issue.6, pp.20130109-1742, 2013.
DOI : 10.1115/1.2979869

URL : https://hal.archives-ouvertes.fr/hal-01460019

A. [. Bellettini and . Coscia, Discrete approximation of a free discontinuity problem, Numerical Functional Analysis and Optimization, vol.1, issue.3-4, pp.3-4, 1994.
DOI : 10.1007/978-1-4612-1015-3

A. [. Bellettini, G. Coscia, and . Dal-maso, Compactness and lower semicontinuity properties in $SBD(\Omega)$, Mathematische Zeitschrift, vol.228, issue.2, pp.337-351, 1998.
DOI : 10.1007/PL00004617

G. [. Braides, A. Dal-maso, and . Garroni, Variational Formulation of Softening Phenomena in Fracture Mechanics: The One-Dimensional Case " . In: Archive for Rational Mechanics and Analysis 146, pp.23-58, 1999.

]. O. Ber+02 and . Bernard, Mechanical and microstructural characterisation of oxide films damage, In: Materials Science and Engineering A, vol.3351, issue.2, pp.32-42, 2002.

]. J. Beu92, . Beuth, and . Fonseca, Cracking of thin bonded films in residual tension Brittle Thin Films, International Journal of Solids and Structures In: Applied Mathematics and Optimization, vol.29133, issue.44, pp.1657-1675, 1992.

I. [. Bhattacharya, G. Fonseca, and . Francfort, An Asymptotic Study??of the Debonding of Thin Films, Archive for Rational Mechanics and Analysis, vol.161, issue.3, pp.205-229, 2002.
DOI : 10.1007/s002050100177

I. [. Bouchitte, G. Fonseca, and . Leoni, A Global Method for Relaxation in W 1,p and in SBV p, Archive for Rational Mechanics and Analysis, vol.165, issue.3, pp.187-242, 2002.
DOI : 10.1007/s00205-002-0220-y

G. [. Bourdin, J. Francfort, and . Marigo, The Variational Approach to Fracture, Journal of Elasticity, vol.91, pp.1-3, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00551079

M. B. Amar and A. Goriely, Growth and instability in elastic tissues, Journal of the Mechanics and Physics of Solids, vol.5310, pp.2284-2319, 2005.

N. [. Beuth and . Klingbeil, Cracking of thin films bonded to elastic-plastic substrates, Journal of the Mechanics and Physics of Solids, vol.44, issue.9, pp.1411-1428, 1996.
DOI : 10.1016/0022-5096(96)00042-7

Z. [. Bialas and . Mroz, Crack patterns in thin layers under temperature loading. Part I: Monotonic loading, In: Engineering Fracture Mechanics, vol.737, pp.917-938, 2006.

Z. [. Bialas and . Mroz, An energy model of segmentation cracking of thin films, Mechanics of Materials, vol.399, pp.845-864, 2007.

]. B. Bou00 and . Bourdin, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, vol.48, issue.4, pp.797-826, 2000.

]. B. Bou02 and . Bourdin, Image segmentation with a finite element method, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.2, pp.229-244, 2002.

]. B. Bou07 and . Bourdin, Numerical implementation of the variational formulation for quasi-static brittle fracture, Interfaces and Free Boundaries, pp.411-430, 2007.

]. A. Bibliography-[-bra98 and . Braides, Approximation of free-discontinuity problems, Analyse fonctionelle. Masson, 1983.

F. [. Ciarlet and . Bourquin, Modeling and justification of eigenvalue problems for junctions between elastic structures, Journal of Functional Analysis, vol.87, issue.2, pp.392-427, 1989.

R. [. Crosby and . Bradley, Fragmentation of thin films bonded to solid substrates: Simulations and a mean-field theory, Physical Review E, vol.55, issue.5, pp.6084-6091, 1997.
DOI : 10.1103/PhysRevE.55.6084

Z. [. Cotterell and . Chen, Buckling and cracking of thin films on compliant substrates under compression, International Journal of Fracture, pp.169-179, 2000.

]. H. Cdr93, . Colina, L. De-arcangelis, and S. Roux, Model for surface cracking, In: Physical review. B, Condensed matter, vol.48, issue.6, pp.3666-3676, 1993.

[. Chiu and F. Erdogan, Debonding of graded coatings under in-plane compression, International Journal of Solids and Structures, vol.40, issue.25, pp.7155-7179, 2003.
DOI : 10.1016/S0020-7683(03)00360-3

G. [. Chambolle, J. Francfort, and . Marigo, When and how do cracks propagate?, Journal of the Mechanics and Physics of Solids, vol.57, issue.9, pp.1614-1622, 2009.
DOI : 10.1016/j.jmps.2009.05.009

G. [. Chambolle, J. Francfort, and . Marigo, Revisiting Energy Release Rates in Brittle Fracture, Journal of Nonlinear Science, vol.187, issue.11, pp.395-424, 2010.
DOI : 10.1007/s00332-010-9061-2

URL : https://hal.archives-ouvertes.fr/hal-00490537

M. Charlotte, Revisiting brittle fracture as an energy minimization problem: comparison of Griffith and Barenblatt surface energy models, Damage and Fracture, 2000.

]. A. Cha03 and . Chambolle, A Density Result in Two-Dimensional Linearized Elasticity, and Applications, In: Archive for Rational Mechanics and Analysis, vol.1673, pp.211-233, 2003.

]. P. Cia78 and . Ciarlet, The Finite Element Method for Elliptic Problems. Classics i, Philadelphia: SIAM, 1978.

]. P. Cia88 and . Ciarlet, Mathematical Elasticity Volume I: Three-Dimensional Elasticity, p.451, 1988.

]. P. Cia90 and . Ciarlet, A new class of variational problems arising in the modeling of elastic multi-structures, Numerische Mathematik, vol.57, issue.1, pp.547-560, 1990.

]. P. Cia97 and . Ciarlet, Mathematical Elasticity Volume II: Theory of Plates, 1997.

K. [. Choi and . Kim, Analysis of the spontaneous interfacial decohesion of a thin surface film, Journal of the Mechanics and Physics of Solids, vol.40, issue.1, pp.75-103, 1992.
DOI : 10.1016/0022-5096(92)90254-Y

V. [. Ciarlet and . Lods, Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations, Archive for Rational Mechanics and Analysis, vol.69, issue.18, pp.119-161, 1996.
DOI : 10.1007/BF02316975

V. [. Ciarlet, B. Lods, and . Miara, Asymptotic analysis of linearly elastic shells. II. Justification of flexural shell equations, Archive for Rational Mechanics and Analysis, vol.311, issue.2, pp.163-190, 1996.
DOI : 10.1007/BF02316976

J. [. Cohen, I. Mathiesen, and . Procaccia, Drying patterns: Sensitivity to residual stresses, Physical Review E, vol.79, issue.4, pp.46109-1539, 2009.
DOI : 10.1103/PhysRevE.79.046109

H. L. Cox, The elasticity and strength of paper and other fibrous materials, British Journal of Applied Physics, vol.3, issue.3, pp.72-79, 1952.
DOI : 10.1088/0508-3443/3/3/302

]. B. Dac04 and . Dacorogna, Introduction to the Calculus of Variations, p.486673669, 2004.

]. B. Dac92 and . Dacorogna, Direct Methods in the Calculus of Variations, pp.239-239, 1992.

M. [. Destuynder and . Djaoua, Sur une Interpr??tation Math??matique de l'Int??grale de Rice en Th??orie de la Rupture Fragile, Mathematical Methods in the Applied Sciences, vol.III, issue.1, pp.70-87, 1981.
DOI : 10.1002/mma.1670030106

J. [. David, C. Marigo, and . Pideri, Homogenized Interface Model Describing Inhomogeneities Located on a Surface, Journal of Elasticity, vol.4, issue.1, pp.153-187, 2012.
DOI : 10.1007/s10659-012-9374-5

URL : https://hal.archives-ouvertes.fr/hal-00655496

[. Piero and D. R. Owen, Multiscale Modeling in Continuum Mechanics and Structured Deformations, 2004.
DOI : 10.1007/978-3-7091-2770-4

[. Piero and L. Truskinovsky, Macro-and micro-cracking in onedimensional elasticity, International Journal of Solids and Structures, vol.38, pp.6-7, 2001.

]. G. Dt02a, R. Dal-maso, and . Toader, A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results " . In: Archive for Rational Mechanics and Analysis 162, pp.101-135, 2002.

]. G. Dt02b, R. Dal-maso, and . Toader, A Model for the Quasi-Static Growth of Brittle Fractures: Existence and Approximation Results " . In: Archive for Rational Mechanics and Analysis 162, pp.101-135, 2002.

M. [. Drory, A. Thouless, and . Evans, On the decohesion of residually stressed thin films, Acta Metallurgica, vol.36, issue.8, pp.2019-2028, 1960.
DOI : 10.1016/0001-6160(88)90303-3

J. Dundurs, Edge-bonded dissimilar orthogonal elastic wedges, Journal of Applied Mechanics, vol.36, 1969.

M. [. Evans, M. S. Drory, and . Hu, The cracking and decohesion of thin films, Journal of Materials Research, vol.3, pp.5-1043, 1988.

A. [. Efendiev and . Mielke, On the Rate-Independent Limit of Systems with Dry Friction and Small Viscosity, Journal of Convex Analysis, vol.131, pp.151-167, 2006.

]. H. Eva89 and . Evans, Cracking and spalling of protective oxide layers, In: Materials Science and Engineering, pp.120-121, 1989.

F. [. Focardi and . Iurlano, Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity, pp.1-16, 2013.

R. [. Friesecke, S. James, and . Müller, A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence, Archive for Rational Mechanics and Analysis, vol.180, issue.2, pp.183-236, 2006.
DOI : 10.1007/s00205-005-0400-7

C. [. Francfort and . Larsen, Existence and convergence for quasi-static evolution in brittle fracture, Communications on Pure and Applied Mathematics, vol.120, issue.10, pp.1465-1500, 2003.
DOI : 10.1002/cpa.3039

J. [. Francfort and . 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

S. [. Freund and . Suresh, Thin Film Materials. Stress, Defect Formation and Surface Evolution, pp.770-9780521529778, 2009.

]. N. Fuk+99 and . Fukugami, Density measurement of thin glass layers for gas barrier films, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, vol.174, pp.1840-07342101, 1999.

[. Giorgi, M. Carriero, and A. Leaci, Existence theorem for a minimum problem with free discontinuity set, Archive for Rational Mechanics and Analysis, vol.107, issue.4, pp.195-218, 1989.
DOI : 10.1007/BF01052971

]. A. Gia05 and . Giacomini, Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures, In: Calc. Var. Partial Dif, vol.22, issue.2, pp.129-172, 2005.

E. [. Groisman and . Kaplan, An Experimental Study of Cracking Induced by Desiccation, Europhysics Letters (EPL), vol.25, issue.6, pp.415-420, 1994.
DOI : 10.1209/0295-5075/25/6/004

L. Goehring, L. Mahadevan, and S. W. Morris, Nonequilibrium scale selection mechanism for columnar jointing, Proceedings of the National Academy of Sciences, vol.106, issue.2, pp.387-92, 2009.
DOI : 10.1073/pnas.0805132106

]. L. Goe+10 and . Goehring, Evolution of mud-crack patterns during repeated drying cycles, In: Soft Matter, vol.615, pp.3562-1744, 2010.

]. A. Gri21 and . Griffith, The Phenomena of Rupture and Flow in Solids, In: Philosophical Transactions of the Royal Society of London, vol.221, pp.163-198, 1921.

]. U. Han02 and . Handge, Analysis of a shear-lag model with nonlinear elastic stress transfer for sequential cracking, Journal of Materials Science, vol.37, pp.4775-4782, 2002.

Z. [. Hutchinson and . Suo, Mixed Mode Cracking in Layered Materials, In: Advances in Applied Mechanics, vol.29, pp.63-191, 1991.
DOI : 10.1016/S0065-2156(08)70164-9

Z. [. Ho and . Suo, Tunneling Cracks in Constrained Layers, Journal of Applied Mechanics, vol.60, issue.4, pp.890-00218936, 1993.
DOI : 10.1115/1.2900998

I. [. Hornig, A. Sokolov, and . Blumen, Patterns and scaling in surface fragmentation processes, Physical Review E, vol.54, issue.4, pp.4293-4298, 1996.
DOI : 10.1103/PhysRevE.54.4293

]. Hsu01 and . Hsueh, Analyses of Multiple Film Cracking in Film/Substrate Systems, Journal of the American Ceramic Society, vol.8412, pp.2955-2961, 2001.

]. R. Hua+03 and . Huang, Channel-cracking of thin films with the extended finite element method, In: Engineering Fracture Mechanics, vol.7018, pp.2513-2526, 2003.

]. J. Hut96 and . Hutchinson, Stresses and Failure Modes in Thin Films and Multilayers, 1996.

J. [. Jensen, K. Hutchinson, and . Kyung-suk, Decohesion of a cut prestressed film on a substrate, International Journal of Solids and Structures, vol.26, issue.9-10, pp.1099-1114, 1990.
DOI : 10.1016/0020-7683(90)90018-Q

]. S. Kit11 and . Kitsunezaki, Crack growth in drying paste, Advanced Powder Technology, vol.223, pp.311-318, 2011.

]. S. Kit99 and . Kitsunezaki, Fracture patterns induced by desiccation in a thin layer, pp.6449-64, 1999.

M. Kocvara, A. Mielke, and T. Rubicek, A Rate-Independent Approach to the Delamination Problem, Mathematics and Mechanics of Solids, pp.423-447, 2005.
DOI : 10.1177/1081286505046482

]. Y. Let+04 and . Leterrier, Mechanical integrity of transparent conductive oxide films for flexible polymer-based displays, In: Thin Solid Films, vol.4601, issue.2, pp.156-166, 2004.

Y. Leterrier, Models for saturation damage state and interfacial shear strengths in multilayer coatings, Mechanics of Materials, vol.42, issue.3, pp.326-334, 2010.
DOI : 10.1016/j.mechmat.2009.11.006

M. [. Leung, A. He, and . Evans, The cracking resistance of nanoscale layers and films, Journal of Materials Research, vol.41, issue.07, pp.7-1693, 1995.
DOI : 10.1557/JMR.1995.1693

]. J. Lia03 and . Liang, Evolving crack patterns in thin films with the extended finite element method, International Journal of Solids and Structures, vol.4010, pp.2343-2354, 2003.

Z. [. Leung and . Néda, Pattern Formation and Selection in Quasistatic Fracture, Physical review letters, pp.662-667, 2000.
DOI : 10.1103/PhysRevLett.85.662

[. Lazarus and L. Pauchard, From craquelures to spiral crack patterns: influence of layer thickness on the crack patterns induced by desiccation, Soft Matter, vol.48, issue.6, pp.2552-1744, 2011.
DOI : 10.1039/c0sm00900h

]. J. Mar+ and . Marthelot, Crescent and spiral cracks paths in thin films: when delamination cooperates with crack propagation

J. Marthelot, Ruine de films minces par coopération entre rupture et délaminage, pp.1-3

A. Mesgarnejad, B. Bourdin, and M. Khonsari, A variational approach to the fracture of brittle thin films subject to out-of-plane loading, Journal of the Mechanics and Physics of Solids, vol.61, issue.11, pp.1-32, 2013.
DOI : 10.1016/j.jmps.2013.05.001

]. P. Mea87 and . Meakin, A simple model for elastic fracture in thin films, In: Thin Solid Films, vol.151, issue.2, pp.165-190, 1987.

G. [. Maso, R. Francfort, and . Toader, Quasistatic Crack Growth in Nonlinear Elasticity, Archive for Rational Mechanics and Analysis, vol.9, issue.2, pp.165-225, 2005.
DOI : 10.1007/s00205-004-0351-4

A. [. Millet, A. Hamdouni, and . Cimetì-ere, A classification of thin plate models by asymptotic expansion of non-linear three-dimensional equilibrium equations, International Journal of Non-Linear Mechanics, vol.36, issue.1, pp.165-186, 2001.
DOI : 10.1016/S0020-7462(00)00005-6

URL : https://hal.archives-ouvertes.fr/hal-00312262

F. [. Maso and . Iurlano, Fracture models as ?-limits of damage models, In: Communications on Pure and Applied Mathematics, vol.12, issue.4, 2013.

]. B. Mia94 and . Miara, Jusitification of the asymptotic analysis of elastic plates, I. The linear case, In: Asymptotic Analysis, vol.9, pp.47-60, 1994.

]. A. Mie05 and . Mielke, Evolution of rate-independent systems " . In: Handbook of Differential Equations: Evolutionary Differential Equations, 2004.

[. Marigo and N. Meunier, Hierarchy of One-Dimensional Models in Nonlinear Elasticity, Journal of Elasticity, vol.18, issue.2, pp.1-28, 2006.
DOI : 10.1007/s10659-005-9036-y

URL : https://hal.archives-ouvertes.fr/hal-00551082

J. [. Mumford and . 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 : 10.1002/cpa.3160420503

[. Marigo and L. Truskinovsky, Initiation and propagation of fracture in the models of Griffith and Barenblatt, Continuum Mechanics and Thermodynamics, pp.391-409, 2004.
DOI : 10.1007/s00161-003-0164-y

URL : https://hal.archives-ouvertes.fr/hal-00111432

F. [. Mielke, V. I. Theil, and . Levitas, A variational formulation of rateindependent phase transformations using an extremum principle, 2000.

T. Munson, TAO 2.1 Users Manual, Tech. rep. Mathematics and Computer Science Division, 2012.

]. M. Neg99 and . Negri, The anisotropy introduced by the mesh in the finite element approximation of the mumford-shah functional, In: Numerical Functional Analysis and Optimization, vol.209, issue.10, pp.957-982, 1999.

]. Q. Ngu00 and . Nguyen, Stability and nonlinear solid mechanics, pp.978-978, 2000.

R. Nahta and B. Moran, Film cracking and debonding in a coated fiber, International Journal of Fracture, vol.30, issue.15, pp.351-372, 1996.
DOI : 10.1007/BF00018596

K. Pham, Gradient Damage Models and Their Use to Approximate Brittle Fracture, International Journal of Damage Mechanics, vol.30, issue.4, pp.618-652, 2010.
DOI : 10.1016/0029-5493(92)90094-C

URL : https://hal.archives-ouvertes.fr/hal-00549530

]. K. Pm10a, J. Pham, and . Marigo, Approche variationnelle de l'endommagement : I. Les concepts fondamentaux, Comptes Rendus Mécanique, vol.338, issue.4, pp.191-198, 2010.

]. K. Pm10b, J. Pham, and . Marigo, Approche variationnelle de l'endommagement : II. Les modèlesmodèlesà gradient, Comptes Rendus Mécanique, vol.338, issue.4, pp.199-206, 2010.

J. [. Pham, C. Marigo, and . Maurini, The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models, Journal of the Mechanics and Physics of Solids, vol.59, issue.6, pp.1163-1190, 2011.
DOI : 10.1016/j.jmps.2011.03.010

URL : https://hal.archives-ouvertes.fr/hal-00578995

L. [. Del-piero and . Truskinovsky, A one-dimensional model for localized and distributed failure, Le Journal de Physique IV 08.PR8, pp.1155-4339, 1998.
DOI : 10.1051/jp4:1998812

. Rhee, Contact-induced Damage in Ceramic Coatings on Compliant Substrates: Fracture Mechanics and Design, Journal of the American Ceramic Society, vol.10, issue.6, pp.1066-1072, 2001.
DOI : 10.1111/j.1151-2916.2001.tb00791.x

]. J. [-ric68a and . Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, Journal of Applied Mechanics, vol.352, pp.379-386, 1968.

]. J. [-ric68b and . Rice, Mathematical Analysis in the Mechanics of Fracture In: Fracture: an Advanced Treatise, Ed. by H. Liebowitz. B2, vol.107, pp.191-311, 1968.

M. [. Roubí?ek and . Kru?ík, Microstructure evolution model in micromagnetics, Zeitschrift für angewandte Mathematik und Physik, pp.159-182, 2004.
DOI : 10.1007/s00033-003-0110-7

T. Roubí?ek, L. Scardia, and C. Zanini, Quasistatic delamination problem, Continuum Mechanics and Thermodynamics, pp.223-235, 2009.
DOI : 10.1007/s00161-009-0106-4

]. E. San+07, . Santanach, and . Carreras, Avoiding " mud " cracks during drying of thin films from aqueous colloidal suspensions, In: Journal of colloid and interface science, vol.313, issue.1, pp.160-168, 2007.

]. E. Sán80 and . Sánchez-palencia, Non-Homogeneous Media and Vibration Theory, 1980.

]. E. San82 and . Sanchez-palencia, On the asymptotics of the fluid flow past an array of fixed obstacles, International Journal of Engineering Science, vol.2012, pp.1291-1301, 1982.

L. [. Stringfellow and . Freund, The effect of interfacial friction on the buckle-driven spontaneous delamination of a compressed thin film, International Journal of Solids and Structures, vol.30, issue.10, pp.1379-1395, 1993.
DOI : 10.1016/0020-7683(93)90219-W

A. [. Szymczak and . Ladd, The initial stages of cave formation: Beyond the one-dimensional paradigm, Earth and Planetary Science Letters, vol.301, issue.3-4, pp.3-4, 2011.
DOI : 10.1016/j.epsl.2010.10.026

P. Sicsic and J. Marigo, From Gradient Damage Laws to Griffith???s Theory of Crack Propagation, Journal of Elasticity, vol.59, issue.6, pp.374-3535, 2012.
DOI : 10.1007/s10659-012-9410-5

E. [. Sánchez-hubert and . Sánchez-palencia, Introduction aux méthodes asympotiques etàetà l'homogénéisation, 1992.

A. [. Shenoy, L. B. Schwartzman, and . Freund, Crack patterns in brittle thin films, pp.1-100, 2000.

]. Z. Suo01 and . Suo, Fracture in Thin Films, Encyclopedia of Materials: Science and Technology, pp.3290-3296, 2001.

K. [. Sendova and . Willis, Spiral and curved periodic crack patterns in sol-gel films, Applied Physics A: Materials Science & Processing, pp.957-959, 2003.
DOI : 10.1007/s00339-002-1757-1

B. [. Toga and . Alaca, Junction formation during desiccation cracking, Physical Review E, vol.74, issue.2, pp.21405-1539, 2006.
DOI : 10.1103/PhysRevE.74.021405

]. M. Tho+11 and . Thouless, Periodic cracking of films supported on compliant substrates, In: Journal of the mechanics and physics of solids, vol.59, issue.9, pp.1927-1937, 2011.

E. [. Thouless, A. Olsson, and . Gupta, Cracking of brittle films on elastic substrates, Acta Metallurgica et Materialia, vol.40, issue.6, pp.1287-1292, 1992.
DOI : 10.1016/0956-7151(92)90429-I

P. [. Tada, G. R. Paris, and . Irwin, The Stress Analysis of Cracks Handbook, Third Edition, pp.10016-5990, 2000.
DOI : 10.1115/1.801535

. G. Vma99-]-a, I. Varias, E. C. Mastorakos, and . Aifantis, Numerical simulation of interface crack in thin films, pp.195-207, 1999.

]. E. Win67 and . Winkler, Die Lehre von der Elasticität und Festigkeit, p.388, 1867.

J. [. Xia and . Hutchinson, Crack patterns in thin films, Journal of the Mechanics and Physics of Solids, vol.48, issue.6-7, pp.1107-1131, 2000.
DOI : 10.1016/S0022-5096(99)00081-2

H. Yu and J. W. Hutchinson, Delamination of thin film strips, Thin Solid Films, vol.423, issue.1, pp.54-63, 2003.
DOI : 10.1016/S0040-6090(02)00973-2

Z. [. Ye, A. Suo, and . Evans, Thin film cracking and the roles of substrate and interface, International Journal of Solids and Structures, vol.29, issue.21, pp.2639-2648, 1992.
DOI : 10.1016/0020-7683(92)90227-K

Y. [. Yanaka, N. Tsukahara, and . Nakaso, Cracking phenomena of brittle films in nanostructure composites analysed by a modified shear lag model with residual strain, Journal of Materials Science, vol.33, issue.8, pp.2111-2119, 1998.
DOI : 10.1023/A:1004371203514