M. Adda-bedia, R. Arias, M. B. Amar, and F. Lund, Generalized Griffith criterion for dynamic fracture and the stability of crack motion at high velocities, Physical Review E, vol.60, issue.2, pp.2366-2376, 1999.
DOI : 10.1103/PhysRevE.60.2366

R. Alessi, J. J. Marigo, and S. Vidoli, Gradient damage models coupled with plasticity: Variational formulation and main properties, Mechanics of Materials, vol.80, pp.351-367, 2015.
DOI : 10.1016/j.mechmat.2013.12.005

M. Attigui and C. Petit, Numerical path independent integral in dynamic fracture mechanics, ECF 11 ? Mechanisms and Mechanics of Damage and Failure, 1996.

M. J. Borden, C. V. Verhoosel, M. A. Scott, T. J. Hughes, and C. M. Landis, A phase-field description of dynamic brittle fracture, Computer Methods in Applied Mechanics and Engineering, vol.217, issue.220, pp.77-95, 2012.
DOI : 10.1016/j.cma.2012.01.008

B. Bourdin, G. A. Francfort, and J. J. Marigo, The Variational Approach to Fracture, Journal of Elasticity, vol.125, issue.8, pp.5-148, 2008.
DOI : 10.1007/s10659-007-9107-3

URL : https://hal.archives-ouvertes.fr/hal-00551079

B. Bourdin, C. J. Larsen, and C. L. Richardson, A time-discrete model for dynamic fracture based on crack regularization, International Journal of Fracture, vol.14, issue.1, pp.133-143, 2011.
DOI : 10.1007/s10704-010-9562-x

P. Destuynder and M. 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

F. Freddi and G. Royer-carfagni, Regularized variational theories of fracture: A unified approach, Journal of the Mechanics and Physics of Solids, vol.58, issue.8, pp.1154-1174, 2010.
DOI : 10.1016/j.jmps.2010.02.010

L. B. Freund, Dynamic Fracture Mechanics DOI 10, p.9780511546761, 1017.

A. A. Griffith, The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.221, issue.582-593, pp.163-198, 1921.
DOI : 10.1098/rsta.1921.0006

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, issue.2, pp.342-368, 2009.
DOI : 10.1016/j.jmps.2008.10.012

W. R. Hamilton, On a General Method in Dynamics; By Which the Study of the Motions of All Free Systems of Attracting or Repelling Points is Reduced to the Search and Differentiation of One Central Relation, or Characteristic Function, Philosophical Transactions of the Royal Society of London, vol.124, issue.0, pp.247-308, 1834.
DOI : 10.1098/rstl.1834.0017

M. Hintermüller and V. A. Kovtunenko, From shape variation to topological changes in constrained minimization: a velocity method-based concept, Optimization Methods and Software, vol.26, issue.4-5, pp.4-5, 2011.
DOI : 10.1007/978-3-642-58106-9

A. Khludnev, J. Soko?owski, and K. Szulc, Shape and topological sensitivity analysis in domains with cracks, Applications of Mathematics, vol.55, issue.6, pp.433-469, 2010.
DOI : 10.1007/s10492-010-0018-4

URL : https://hal.archives-ouvertes.fr/hal-00315837

T. Li, J. J. Marigo, D. Guilbaud, and S. Potapov, Gradient damage modeling of brittle fracture in an explicit dynamics context, International Journal for Numerical Methods in Engineering, vol.44, issue.20, 2016.
DOI : 10.1002/nme.5262

URL : https://hal.archives-ouvertes.fr/hal-01248263

E. Lorentz and S. Andrieux, A variational formulation for nonlocal damage models, International Journal of Plasticity, vol.15, issue.2, pp.119-138, 1999.
DOI : 10.1016/S0749-6419(98)00057-6

E. Lorentz and V. Godard, Gradient damage models: Toward full-scale computations DOI http, Computer Methods in Applied Mechanics and Engineering, vol.2002122, pp.1927-1944, 2011.

G. Maugin, On the J-integral and energy-release rates in dynamical fracture, Acta Mechanica, vol.40, issue.1-4, pp.33-47, 1994.
DOI : 10.1007/BF01183940

T. Nishioka and S. N. Atluri, Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics, Engineering Fracture Mechanics, vol.18, issue.1, pp.1-22, 1983.
DOI : 10.1016/0013-7944(83)90091-7

G. E. Oleaga, Remarks on a basic law for dynamic crack propagation, Journal of the Mechanics and Physics of Solids, vol.49, issue.10, pp.2273-2306, 2001.
DOI : 10.1016/S0022-5096(01)00048-5

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.30, issue.4, pp.618-652, 2011.
DOI : 10.1016/0029-5493(92)90094-C

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

K. Pham and J. J. Marigo, Approche variationnelle de l'endommagement : II. Les mod??les ?? gradient, Comptes Rendus M??canique, vol.338, issue.4, pp.199-206, 2010.
DOI : 10.1016/j.crme.2010.03.012

URL : https://hal.archives-ouvertes.fr/hal-00490520

K. Pham and J. J. Marigo, From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models, Continuum Mechanics and Thermodynamics, vol.30, issue.6, pp.2-4, 2013.
DOI : 10.1007/s00161-011-0228-3

URL : https://hal.archives-ouvertes.fr/hal-00647860

K. Pham, J. J. Marigo, and C. 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

E. Sharon and J. Fineberg, Microbranching instability and the dynamic fracture of brittle materials, Physical Review B, vol.54, issue.10, pp.7128-7139, 1996.
DOI : 10.1103/PhysRevB.54.7128

P. Sicsic and J. J. Marigo, From Gradient Damage Laws to Griffith???s Theory of Crack Propagation, Journal of Elasticity, vol.59, issue.6, pp.55-74, 2013.
DOI : 10.1007/s10659-012-9410-5