. Dans-chaque-cas, les résultats numériques sont appuyés par des résultats analytiques ou semi-analytiques

]. H. Références1, J. Amor, C. Marigo, and . 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.

B. Bourdin, G. Francfort, and J. Marigo, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, vol.48, issue.4, pp.787-826, 2000.
DOI : 10.1016/S0022-5096(99)00028-9

B. Bourdin, J. Marigo, C. Maurini, and P. Sicsic, Morphogenesis and Propagation of Complex Cracks Induced by Thermal Shocks, Physical Review Letters, vol.112, issue.1, p.14301, 2014.
DOI : 10.1103/PhysRevLett.112.014301
URL : https://hal.archives-ouvertes.fr/hal-00911118

G. Francfort and J. 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

M. Frémond and B. Nedjar, Damage, gradient of damage and principle of virtual power, International Journal of Solids and Structures, vol.33, issue.8, pp.1083-1103, 1996.
DOI : 10.1016/0020-7683(95)00074-7

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

E. Lorentz and S. Andrieux, Analysis of non-local models through energetic formulations, International Journal of Solids and Structures, vol.40, issue.12, pp.2905-2936, 2003.
DOI : 10.1016/S0020-7683(03)00110-0

E. Lorentz and V. Godard, Gradient damage models: Toward full-scale computations, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.21-22, pp.1927-1944, 2011.
DOI : 10.1016/j.cma.2010.06.025

K. Pham, H. Amor, 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, 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

P. Sicsic and J. Marigo, From Gradient Damage Laws to Griffith???s Theory of Crack Propagation, Journal of Elasticity, vol.59, issue.6, pp.1-20, 2012.
DOI : 10.1007/s10659-012-9410-5

P. Sicsic, J. Marigo, and C. Maurini, Initiation of a periodic array of cracks in the thermal shock problem: A gradient damage modeling, Journal of the Mechanics and Physics of Solids, vol.63, pp.256-284, 2014.
DOI : 10.1016/j.jmps.2013.09.003
URL : https://hal.archives-ouvertes.fr/hal-00843625