J. Bleyer, C. Roux-langlois, and J. Molinari, Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms, International Journal of Fracture, vol.72, issue.9, p.270, 2016.
DOI : 10.1016/j.engfracmech.2004.10.011

URL : https://hal.archives-ouvertes.fr/hal-01390233

K. Ravi-chandar, Dynamic Fracture, 2004.
DOI : 10.1016/B0-08-043749-4/02120-0

URL : https://hal.archives-ouvertes.fr/hal-01305640

A. Sagy, G. Cohen, Z. Reches, and J. Fineberg, Dynamic fracture of granular material under quasi-static loading, Journal of Geophysical Research, vol.88, issue.1, 2006.
DOI : 10.1017/CBO9780511623127

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

G. Albertini and D. Kammer, Supershear transition of dynamic mode II fracture in heterogeneous elastic media, Journal of Mechanics and Physics of Solids, 2017.

D. Fisher, K. Dahmen, S. Ramanathan, and Y. Ben-zion, Statistics of Earthquakes in Simple Models of Heterogeneous Faults, Physical Review Letters, vol.101, issue.25, pp.78-4885, 1997.
DOI : 10.1029/95JB03534

Y. Ben-zion, Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes, Reviews of Geophysics, vol.104, issue.1???2, 2008.
DOI : 10.1016/S0065-2687(07)49002-1

B. Shen and A. Inoue, Wavy cleavage fracture of bulk metallic glass, Applied Physics Letters, vol.89, p.251917, 2006.

P. Murali, T. Guo, Y. Zhang, R. Narasimhan, Y. Li et al., Atomic Scale Fluctuations Govern Brittle Fracture and Cavitation Behavior in Metallic Glasses, Physical Review Letters, vol.11, issue.21, pp.215501-290, 2011.
DOI : 10.1038/nmat3024

F. Zhou, Study on the macroscopic behavior and the microscopic process of dynamic crack propagation, 1996.

F. Zhou, J. Molinari, and T. Shioya, A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials, Engineering 295 Fracture Mechanics, pp.72-1383, 2005.

A. Livne, G. Cohen, and J. Fineberg, Universality and Hysteretic Dynamics in Rapid Fracture, Physical Review Letters, vol.59, issue.22, 2005.
DOI : 10.1016/0022-5096(96)00038-5

T. Goldman, A. Livne, J. Fineberg, C. Wolff, N. Richart et al., Acquisition of inertia by a moving crack A non-local continuum damage approach to model dynamic crack branching, Physical Review Letters International Journal for Numerical Methods in Engineering, vol.104, issue.101, pp.933-949, 2010.

D. Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, issue.2, pp.100-104, 1960.
DOI : 10.1016/0022-5096(60)90013-2

]. G. Barenblatt, The Mathematical Theory of Equilibrium Cracks in Brittle Fracture, Advances in Applied Mechanics, vol.7, pp.305-55, 1962.
DOI : 10.1016/S0065-2156(08)70121-2

G. Camacho and M. Ortiz, Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, vol.33, issue.20-22, pp.2899-2938, 1996.
DOI : 10.1016/0020-7683(95)00255-3

M. Ortiz and A. Pandolfi, Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, International Journal for Numerical Methods in Engineering, vol.142, issue.9, pp.1267-1282, 1999.
DOI : 10.1007/BF00033830

URL : http://aero.caltech.edu/~ortiz/Pubs/1999/OrtizPandolfi1999.pdf

W. Chen and G. Ravichandran, Static and Dynamic Compressive Behavior of Aluminum Nitride under Moderate Confinement, Journal of the American Ceramic Society, vol.133, issue.3, pp.579-584, 1996.
DOI : 10.1111/j.1151-2916.1996.tb07913.x

G. Ruiz, M. Ortiz, and A. Pandolfi, Three-dimensional finite-element simulation of the dynamic Brazilian tests on concrete cylinders, International Journal for Numerical Methods in Engineering, vol.25, issue.7, pp.963-994, 2000.
DOI : 10.1051/jp4:1996616

A. Livne, E. Bouchbinder, and J. Fineberg, Breakdown of linear elastic fracture 320 mechanics near the tip of a rapid crack, Physical Review Letters, vol.101, 2008.

A. Livne, E. Bouchbinder, I. Svetlizky, and J. Fineberg, The Near-Tip Fields of Fast Cracks, Science, vol.103, issue.16, pp.1359-1363, 2010.
DOI : 10.1103/PhysRevLett.103.164301

M. Ramulu and A. Kobayashi, Mechanics of crack curving and branching -a 325 dynamic fracture analysis, Dynamic fracture, pp.61-75, 1985.

J. Fineberg, S. Gross, M. Marder, and H. Swinney, Instability in dynamic fracture, Physical Review Letters, vol.67, issue.457, 1991.
DOI : 10.1103/physrevlett.67.457

URL : http://chaos.ph.utexas.edu/~marder/fracture/physics_reports.ps.gz

E. Sharon, S. Gross, J. Fineberg, E. Sharon, and J. Fineberg, Local crack branching as a mechanism for instability in dynamic fracture Confirming the continuum theory of dynamic brittle fracture for fast cracks, Physical Review Letters Nature, vol.74, issue.397, pp.333-335, 1995.

X. Xu and A. Needleman, Numerical simulations of fast crack growth in brittle solids, Journal of the Mechanics and Physics of Solids, vol.42, issue.9, pp.1397-1434, 1994.
DOI : 10.1016/0022-5096(94)90003-5

J. Song, H. Wang, and T. Belytschko, A comparative study on finite element methods for dynamic fracture, Computational Mechanics, vol.67, issue.13, pp.239-250, 2008.
DOI : 10.1007/s00466-007-0210-x

Y. Ha and F. Bobaru, Studies of dynamic crack propagation and crack branching with peridynamics, International Journal of Fracture, vol.76, issue.13, pp.229-340, 2010.
DOI : 10.1007/s10704-010-9442-4

T. Belytschko, W. K. Liu, B. Moran, and K. Elkhodary, Nonlinear finite elements for continua and structures, 2014.

R. Courant, K. Friedrichs, and H. Lewy, On the partial difference equations of mathematical physics, IBM Journal of Research and Development, vol.11, pp.345-215, 1967.

A. Palmer and J. Rice, The Growth of Slip Surfaces in the Progressive Failure of Over-Consolidated Clay, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.332, issue.1591, pp.527-548, 1973.
DOI : 10.1098/rspa.1973.0040

A. Hillerborg, M. Modeer, and P. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research, vol.6, issue.6, pp.773-782, 1976.
DOI : 10.1016/0008-8846(76)90007-7

L. Snozzi, A. Caballero, and J. Molinari, Influence of the meso-structure in dynamic fracture simulation of concrete under tensile loading, Cement and Concrete Research, vol.41, issue.11, pp.1130-1142, 2011.
DOI : 10.1016/j.cemconres.2011.06.016

J. Fineberg, S. Gross, M. Marder, and H. Swinney, Instability in the propagation of fast cracks, Physical Review B, vol.26, issue.10, 1992.
DOI : 10.1007/BF01140627

J. Molinari, G. Gazonas, R. Raghupathy, A. Rusinek, and F. Zhou, The cohesive element approach to dynamic fragmentation: the question of energy convergence, International Journal for Numerical Methods in Engineering, vol.61, issue.3, pp.69-484, 2007.
DOI : 10.1007/BF00033830

URL : https://hal.archives-ouvertes.fr/hal-00123064

M. Marder, New dynamical equation for cracks, Physical Review Letters, vol.8, issue.19, p.2484, 1991.
DOI : 10.1007/BF00042404

M. Marder, Adiabatic equation for cracks, Philosophical Magazine Part B, vol.78, issue.2, pp.203-214, 1998.
DOI : 10.1103/PhysRevLett.66.2484

URL : http://chaos.utexas.edu/manuscripts/1078264057.pdf

]. E. Yoffe, The moving griffith crack, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol.42, pp.365-739, 1951.
DOI : 10.1080/14786445108561302

T. Seelig and D. Gross, On the interaction and branching of fast running cracks???a numerical investigation, Journal of the Mechanics and Physics of Solids, vol.47, issue.4, pp.935-952, 1999.
DOI : 10.1016/S0022-5096(98)00069-6

K. Ravi-chandar and W. Knauss, An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching, International Journal of Fracture, vol.7, issue.No. 1, pp.141-154, 1984.
DOI : 10.1007/BF01157550

N. Fleck, V. Deshpande, and M. Ashby, Micro-architectured materials: past, present and future, Proceedings of the Royal Society of, p.375
DOI : 10.1098/rspa.2008.0328