T. Abinandanan and F. Haider, An extended cahn-hilliard model for interfaces with cubic anisotropy. Philosophical Magazine A 81, pp.2457-2479, 2001.

M. Adda-bedia and Y. Pomeau, Crack instabilities of a heated glass strip, Physical Review E, vol.52, p.4105, 1995.

M. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet et al., The fenics project version 1.5. Archive of Numerical Software, vol.3, pp.9-23, 2015.

L. Ambrosio, Existence theory for a new class of variational problems, Archive for Rational Mechanics and Analysis, vol.111, pp.291-322, 1990.

L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems, 2000.

L. Ambrosio and V. M. Tortorelli, Approximation of functional depending on jumps by elliptic functional via Gamma-convergence, Communications on Pure and Applied Mathematics, vol.43, pp.999-1036, 1990.

M. Amestoy and J. Leblond, Crack paths in plane situations-II. detailed form of the expansion of the stress intensity factors, International Journal of Solids and Structures, vol.29, pp.465-501, 1992.

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, pp.1209-1229, 2009.

A. Azhdari, S. Nemat-nasser, and J. Rome, Experimental observations and computational modeling of fracturing in an anisotropic brittle crystal (sapphire), International Journal of Fracture, vol.94, pp.251-266, 1998.

S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune et al., PETSc Users Manual, 2016.

A. Ball and B. Payne, The tensile fracture of quartz crystals, Journal of Materials Science, vol.11, pp.731-740, 1976.

J. Bleyer and R. Alessi, Phase-field modeling of anisotropic brittle fracture including several damage mechanisms, Computer Methods in Applied Mechanics and Engineering, vol.336, pp.213-236, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01736465

M. J. Borden, T. J. Hughes, C. M. Landis, and C. V. Verhoosel, A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework, Computer Methods in Applied Mechanics and Engineering, vol.273, pp.100-118, 2014.

R. De-borst and L. Chen, The role of bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement, International journal for numerical methods in engineering, vol.113, pp.999-1019, 2018.

B. Bourdin, Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces and Free Boundaries 9, pp.411-430, 2007.

B. Bourdin, G. Francfort, and J. J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, vol.48, pp.797-826, 2000.

B. Bourdin, G. Francfort, and J. J. Marigo, The variational approach to fracture, Journal of Elasticity, vol.91, pp.5-148, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00551079

M. Burger, T. Esposito, and C. I. Zeppieri, Second-order edge-penalization in the ambrosio-tortorelli functional, Multiscale Modeling & Simulation, vol.13, pp.1354-1389, 2015.

A. Chambolle, G. Francfort, and J. J. Marigo, When and how do cracks propagate, Journal of the Mechanics and Physics of Solids, vol.57, pp.1614-1622, 2009.

M. Chandler, P. Meredith, N. Brantut, and B. Crawford, Fracture toughness anisotropy in shale, Journal of Geophysical Research: Solid Earth, vol.121, pp.1706-1729, 2016.

D. Chapelle and K. J. Bathe, The Finite Element Analysis of Shells-Fundamentals, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00839738

J. Clayton and J. Knap, A geometrically nonlinear phase field theory of brittle fracture, International Journal of Fracture, vol.189, pp.139-148, 2014.

F. Corson, M. Adda-bedia, H. Henry, and E. Katzav, Thermal fracture as a framework for quasi-static crack propagation, International journal of fracture, vol.158, pp.1-14, 2009.

B. Cotterell and J. Rice, Slightly curved or kinked cracks, International Journal of Fracture, vol.16, pp.155-169, 1980.

R. D. Deegan, S. Chheda, L. Patel, M. Marder, H. L. Swinney et al., Wavy and rough cracks in silicon, Physical Review E, vol.67, p.66209, 2003.

D. Carlo, A. Gurtin, M. E. Podio-guidugli, and P. , A regularized equation for anisotropic motion-by-curvature, SIAM Journal on Applied Mathematics, vol.52, pp.1111-1119, 1992.

R. Durán and E. Liberman, On mixed finite element methods for the reissner-mindlin plate model, Mathematics of Computation, vol.58, pp.561-573, 1992.

F. Ebrahimi and S. Hussain, Crack path in single crystals, Scripta Metallurgica et Materialia, vol.32, pp.1507-1511, 1995.

F. Ebrahimi and L. Kalwani, Fracture anisotropy in silicon single crystal, Materials Science and Engineering: A, vol.268, pp.116-126, 1999.

J. Eggleston, G. Mcfadden, and P. Voorhees, A phase-field model for highly anisotropic interfacial energy, Physica D: Nonlinear Phenomena, vol.150, pp.91-103, 2001.

F. Erdogan and G. Sih, On the crack extension in plates under plane loading and transverse shear, Journal of Basic Engineering, vol.85, pp.519-527, 1963.

P. Farrell and C. Maurini, Linear and nonlinear solvers for variational phase-field models of brittle fracture, International Journal for Numerical Methods in Engineering, vol.109, pp.648-667, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01326326

M. Focardi, On the variational approximation of free-discontinuity problems in the vectorial case, Mathematical Models and Methods in Applied Sciences, vol.11, pp.663-684, 2001.

I. Fonseca, Lower semicontinuity of surface energies, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol.120, pp.99-115, 1992.

G. Francfort and J. J. Marigo, Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, vol.46, pp.1319-1342, 1998.

S. Ghosh, A. Choudhury, M. Plapp, S. Bottin-rousseau, G. Faivre et al., Interphase anisotropy effects on lamellar eutectics: A numerical study, Physical Review E, vol.91, p.22407, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01472474

R. Gol'dstein and R. Salganik, Brittle fracture of solids with arbitrary cracks, International Journal of Fracture, vol.10, pp.507-523, 1974.

A. Griffith, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.221, pp.163-198, 1921.

M. Gurtin, Configurational forces as basic concepts of continuum physics, vol.137, 2008.

M. Gurtin and P. Podio-guidugli, Configurational forces and a constitutive theory for crack propagation that allows for kinking and curving, Journal of the Mechanics and Physics of Solids, vol.46, pp.1343-1378, 1998.

M. E. Gurtin, Thermomechanics of evolving phase boundaries in the plane, 1993.

M. E. Gurtin and M. E. Jabbour, Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films, Archive for Rational Mechanics and Analysis, vol.163, pp.171-208, 2002.

V. Hakim and A. Karma, Crack path prediction in anisotropic brittle materials, Physical Review Letters, vol.95, p.235501, 2005.

V. Hakim and A. Karma, Laws of crack motion and phase-field models of fracture, Journal of the Mechanics and Physics of Solids, vol.57, pp.342-368, 2009.

J. S. Hale, M. Brunetti, S. P. Bordas, and C. Maurini, Simple and extensible plate and shell finite element models through automatic code generation tools, Computers & Structures, vol.209, pp.163-181, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01763370

E. Hamm, P. Reis, M. Leblanc, B. Roman, and E. Cerda, Tearing as a test for mechanical characterization of thin adhesive films, Nature materials, vol.7, pp.386-390, 2008.

C. Herring, Some theorems on the free energies of crystal surfaces, Physical Review, vol.82, 1951.

G. A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering, 2000.

M. Hussain, S. Pu, and J. Underwood, Strain energy release rate for a crack under combined mode I and mode II, Fracture Analysis: Proceedings of the 1973 National Symposium on Fracture Mechanics, Part II, pp.2-28, 1974.

A. Ibarra, B. Roman, and F. Melo, The tearing path in a thin anisotropic sheet from two pulling points: Wulff's view, Soft Matter, vol.12, pp.5979-5985, 2016.

M. Ichikawa and S. Tanaka, A critical analysis of the relationship between the energy release rate and the stress intensity factors for non-coplanar crack extension under combined mode loading, International journal of Fracture, vol.18, pp.19-28, 1982.

P. Judt, A. Ricoeur, and G. Linek, Crack path prediction in rolled aluminum plates with fracture toughness orthotropy and experimental validation, Engineering Fracture Mechanics, vol.138, pp.33-48, 2015.

P. O. Judt, J. C. Zarges, A. Ricoeur, and H. P. Heim, Anisotropic fracture properties and crack path prediction in glass and cellulose fiber reinforced composites, Engineering Fracture Mechanics, vol.188, pp.344-360, 2018.

A. Khan and J. Vincent, Anisotropy in the fracture properties of apple flesh as investigated by crack-opening tests, Journal of Materials Science, vol.28, pp.45-51, 1993.

M. Klinsmann, D. Rosato, M. Kamlah, and R. M. Mcmeeking, An assessment of the phase field formulation for crack growth, Computer Methods in Applied Mechanics and Engineering, vol.294, pp.313-330, 2015.

R. Kobayashi and Y. Giga, On anisotropy and curvature effects for growing crystals, Japan Journal of Industrial and Applied Mathematics, vol.18, pp.207-230, 2001.

B. Li, D. Millán, A. Torres-sáncheza, B. Roman, and M. Arroyo, A variational model of fracture for tearing brittle thin sheets, Journal of the Mechanics and Physics of Solids, vol.119, pp.334-348, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01851214

B. Li, C. Peco, D. Millán, I. Arias, and M. Arroyo, Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy, International Journal for Numerical Methods in Engineering, vol.102, pp.711-727, 2015.

M. Marder, Cracks cleave crystals, vol.66, p.364, 2004.

J. J. Marigo, C. Maurini, and K. Pham, An overview of the modelling of fracture by gradient damage models, Meccanica, vol.51, pp.3107-3128, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01374814

N. P. Mitchell, V. Koning, V. Vitelli, and W. T. Irvine, Fracture in sheets draped on curved surfaces, Nature Materials, vol.16, pp.89-93, 2017.

F. Mouhat and F. X. Coudert, Necessary and sufficient elastic stability conditions in various crystal systems, Physical Review B, vol.90, p.224104, 2014.

P. Müller and J. Métois, Anisotropy of the surface thermodynamic properties of silicon, Thin Solid Films, vol.517, pp.65-68, 2008.

D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.42, pp.577-685, 1989.

K. H. Nam, I. H. Park, and S. H. Ko, Patterning by controlled cracking, Nature, vol.485, pp.221-224, 2012.

M. Nasseri and B. Mohanty, Fracture toughness anisotropy in granitic rocks, International Journal of Rock Mechanics and Mining Sciences, vol.45, pp.167-193, 2008.

T. T. Nguyen, J. Réthoré, and M. C. Baietto, Phase field modelling of anisotropic crack propagation, European Journal of Mechanics-A/Solids, vol.65, pp.279-288, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01519161

K. Palaniswamy and W. Knauss, On the problem of crack extension in brittle solids under general loading, Mechanics Today, vol.4, pp.87-184, 1978.

K. Pham, H. Amor, J. J. Marigo, and C. Maurini, Gradient damage models and their use to approximate brittle fracture, International Journal of Damage Mechanics, vol.20, pp.618-652, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00549530

R. T. Rockafellar, Convex Analysis, 1997.

B. Roman, Fracture path in brittle thin sheets: a unifying review on tearing, International Journal of Fracture, vol.182, pp.209-237, 2013.

V. Romero, B. Roman, E. Hamm, and E. Cerda, Spiral tearing of thin films, Soft Matter, vol.9, pp.8282-8288, 2013.

R. A. Schultz and R. C. Bradt, Cleavage of ceramic and mineral single crystals, in: Fracture Mechanics of Ceramics, pp.135-153, 1992.

R. F. Sekerka, Analytical criteria for missing orientations on three-dimensional equilibrium shapes, Journal of Crystal Growth, vol.275, pp.77-82, 2005.

Y. Sumi, Mathematical and Computational Analyses of Cracking Formation, vol.2, 2014.

A. Takei, B. Roman, J. Bico, E. Hamm, and F. Melo, Forbidden directions for the fracture of thin anisotropic sheets: an analogy with the wulff plot, Physical Review Letters, vol.110, 2013.

E. Tanné, T. Li, B. Bourdin, J. J. Marigo, and C. Maurini, Crack nucleation in variational phase-field models of brittle fracture, Journal of the Mechanics and Physics of Solids, vol.110, pp.80-99, 2018.

T. C. Ting, Anisotropic elasticity: Theory and Applications, 1996.

S. Torabi and J. Lowengrub, Simulating interfacial anisotropy in thin-film growth using an extended cahn-hilliard model, Physical Review E, vol.85, p.41603, 2012.

S. Torabi, J. Lowengrub, A. Voigt, and S. Wise, A new phase-field model for strongly anisotropic systems, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.465, pp.1337-1359, 2009.

B. Yang and K. Ravi-chandar, Crack path instabilities in a quenched glass plate, Journal of the Mechanics and Physics of Solids, vol.49, pp.91-130, 2001.

A. Yuse and M. Sano, Transition between crack patterns in quenched glass plates, Nature, vol.362, pp.329-331, 1993.

A. Yuse and M. Sano, Instabilities of quasi-static crack patterns in quenched glass plates, Physica D: Nonlinear Phenomena, vol.108, pp.365-378, 1997.

A. Zehnder, Fracture Mechanics (Lecture Notes in Applied and Computational Mechanics), 2012.