P. Alart and A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution methods, Computer Methods in Applied Mechanics and Engineering, vol.92, issue.3, p.353375, 1991.
DOI : 10.1016/0045-7825(91)90022-X

F. Armero and E. Petocz, Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems, Computer Methods in Applied Mechanics and Engineering, vol.158, issue.3-4, pp.3-4269, 1998.
DOI : 10.1016/S0045-7825(97)00256-9
URL : https://hal.archives-ouvertes.fr/hal-01435615

J. Aubin and H. Frankowska, Set-valued analysis, volume 2 of Systems & Control: Foundations & Applications, Birkhäuser Boston Inc, 1990.

Y. Ayyad, M. Barboteu, and J. Fernandez, A frictionless viscoelastodynamic contact problem with energy consistent properties: Numerical analysis and computational aspects, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.5-8, pp.5-8669, 2009.
DOI : 10.1016/j.cma.2008.10.004

P. Ballard and S. Basseville, Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.1, p.5977, 2005.
DOI : 10.1051/m2an:2005004
URL : https://hal.archives-ouvertes.fr/hal-00088184

G. Barenblatt, The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks, Journal of Applied Mathematics and Mechanics, vol.23, issue.3, p.12731282, 1959.
DOI : 10.1016/0021-8928(59)90157-1

G. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture Advances in applied mechanics, p.55129, 1962.

K. J. Bathe and F. Brezzi, Stability of nite element mixed interpolations for contact problems, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl, vol.12, issue.9, p.167183, 2001.

T. Belytschko and M. Neal, Contact-impact by the pinball algorithm with penalty and Lagrangian methods, International Journal for Numerical Methods in Engineering, vol.42, issue.3, pp.547-572, 1991.
DOI : 10.1002/nme.1620310309

D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods, Athena Scientic, 1982.

D. P. Bertsekas, Nonlinear Programming, Athena Scientic, 1999.

B. Bourdin, G. A. Francfort, and J. Marigo, The variational approach to fracture, J. Elasticity, vol.91, issue.1-3, p.5148, 2008.
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, 2009.
DOI : 10.1007/s10704-010-9562-x

H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, 1973.

H. Brezis, Analyse fonctionnelle: théorie et applications, 1983.

H. Brézis and J. Lions, Sur certains problèmes unilatéraux hyperboliques, C. R. Acad. Sci. Paris Sér. A-B, vol.264, pp.928-931, 1967.

K. Broberg, Cracks and fracture. Academic Pr, 1999.

B. Brogliato, Nonsmooth impact mechanics, Models, dynamics and control, 1996.
DOI : 10.1007/978-1-4471-0557-2

H. Bui and P. Germain, Mécanique de la rupture fragile, 1978.

F. Cagnetti, A VANISHING VISCOSITY APPROACH TO FRACTURE GROWTH IN A COHESIVE ZONE MODEL WITH PRESCRIBED CRACK PATH, Mathematical Models and Methods in Applied Sciences, vol.18, issue.07, p.10271071, 2008.
DOI : 10.1142/S0218202508002942

G. T. Camacho and M. Ortiz, Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, vol.33, issue.20-22, pp.20-222899, 1996.
DOI : 10.1016/0020-7683(95)00255-3

N. Carpenter, R. Taylor, and M. Katona, Lagrange constraints for transcient nite element surface contact, Int. J. Numer. Meth. Engng, vol.32, p.103128, 1991.

L. Champaney, J. Cognard, and P. Ladevèze, Modular analysis of assemblages of three-dimensional structures with unilateral contact conditions, Computers & Structures, vol.73, issue.1-5, pp.249-266, 1999.
DOI : 10.1016/S0045-7949(98)00285-5

Z. Chen, On the augmented Lagrangian approach to Signorini elastic contact problem, Numerische Mathematik, vol.88, issue.4, p.641659, 2001.
DOI : 10.1007/PL00005453

F. H. Clarke, Optimization and nonsmooth analysis, Classics in Applied Mathematics . Society for Industrial and Applied Mathematics (SIAM), vol.5, 1990.
DOI : 10.1137/1.9781611971309

M. Cocou, Existence of solutions of a dynamic Signorini's problem with nonlocal friction in viscoelasticity, Zeitschrift f??r angewandte Mathematik und Physik, vol.53, issue.6, p.10991109, 2002.
DOI : 10.1007/PL00012615

G. Cohen, P. Joly, J. Roberts, and N. Tordjman, Higher order triangular nite elements with mass lumping for the wave equation, SIAM Journal on Numerical Analysis, vol.38, issue.6, p.20472078, 2001.

R. Courant and D. Hilbert, Methods of mathematical physics, 1953.

G. , D. Maso, and C. Zanini, Quasi-static crack growth for a cohesive zone model with prescribed crack path, Proc. Roy. Soc. Edinburgh Sect. A, vol.137, issue.2, p.253279, 2007.

K. Deimling, Multivalued dierential equations, volume 1 of de Gruyter Series in Nonlinear Analysis and Applications, 1992.

Z. Denkowski, S. Migórski, and N. S. Papageorgiou, An introduction to nonlinear analysis: applications, 2003.
DOI : 10.1007/978-1-4419-9156-0

P. Deuhard, R. Krause, and S. Ertel, A contact-stabilized Newmark method for dynamical contact problems, Int. J. Numer. Methods Engrg, vol.73, issue.9, p.12741290, 2008.

D. Doyen and A. Ern, Analysis of the modied mass method for the dynamic Signorini problem with Coulomb friction

D. Doyen and A. Ern, Convergence of a space semi-discrete modied mass method for the dynamic Signorini problem, Commun. Math. Sci, vol.7, issue.4, p.10631072, 2009.

D. Doyen, A. Ern, and S. Piperno, Time-integration schemes for the nite element dynamic Signorini problem

D. Doyen, A. Ern, and S. Piperno, A three-eld augmented Lagrangian formulation of unilateral contact problems with cohesive forces, ESAIM, Math. Model. Numer. Anal, vol.44, issue.2, p.323346, 2010.

D. Doyen, A. Ern, and S. Piperno, A semi-explicit modied mass method for dynamic contact problems. Lectures Notes in Applied and Computational Mechanics, 2010.

D. S. 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. Duvaut and J. Lions, Inequalities in mechanics and physics, Translated from the French by C. W. John, Grundlehren der Mathematischen Wissenschaften, 1976.

C. Eck, J. Jaru²ek, and M. Krbec, Unilateral contact problems, Variational methods and existence theorems, 2005.
DOI : 10.1201/9781420027365

I. Ekeland and R. Témam, Convex analysis and variational problems, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.28, 1999.
DOI : 10.1137/1.9781611971088

M. Elices, G. Guinea, J. Gomez, and J. Planas, The cohesive zone model: advantages, limitations and challenges, Engineering Fracture Mechanics, vol.69, issue.2, p.137163, 2002.
DOI : 10.1016/S0013-7944(01)00083-2

A. Ern and J. Guermond, Theory and Practice of Finite Elements, Applied Mathematical Sciences, vol.159, 2004.
DOI : 10.1007/978-1-4757-4355-5

L. C. Evans and R. F. Gariepy, Measure theory and ne properties of functions, Studies in Advanced Mathematics, 1992.

M. Falk, A. Needleman, and J. Rice, A critical evaluation of cohesive zone models of dynamic fractur, Le Journal de Physique IV, vol.11, issue.PR5, p.11, 2001.
DOI : 10.1051/jp4:2001506

G. Fichera, Problemi elastostatici con vincoli unilaterali: Il problema di Signorini con ambigue condizioni al contorno, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. I, vol.7, issue.8, p.91140, 1963.
DOI : 10.1007/978-3-642-11033-7_3

A. F. Filippov, Dierential equations with discontinuous righthand sides, volume 18 of Mathematics and its Applications (Soviet Series), 1988.

M. Fortin and R. Glowinski, Augmented Lagrangian methods, Mathematics and its Applications, 1983.

M. Frémond, Contact with adhesion, Topics in nonsmooth mechanics, p.157185, 1988.

L. B. Freund, Dynamic fracture mechanics. Cambridge Monographs on Mechanics and Applied Mathematics, 1990.

R. Glowinski and P. L. Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.9, 1989.
DOI : 10.1137/1.9781611970838

R. Glowinski, J. Lions, and R. Trémolières, Numerical analysis of variational inequalities, of Studies in Mathematics and its Applications, 1981.

R. Glowinski, L. Shiau, Y. M. Kuo, and G. Nasser, The numerical simulation of friction constrained motions (I): one degree of freedom models, Applied Mathematics Letters, vol.17, issue.7, p.801807, 2004.
DOI : 10.1016/j.aml.2004.06.008

R. Glowinski, L. Shiau, Y. M. Kuo, and G. Nasser, The numerical simulation of friction constrained motions (II): Multiple degrees of freedom models, Applied Mathematics Letters, vol.18, issue.10, pp.1108-1115, 2005.
DOI : 10.1016/j.aml.2004.10.008

E. Grosu and I. Harari, Stability of semidiscrete formulations for elastodynamics at small time steps. Finite Elements in Analysis and Design, pp.6-7533, 2007.

C. Hager, S. Hüeber, and B. I. Wohlmuth, A stable energy-conserving approach for frictional contact problems based on quadrature formulas, International Journal for Numerical Methods in Engineering, vol.40, issue.2, p.205225, 2008.
DOI : 10.1002/nme.2069

C. Hager and B. I. Wohlmuth, Analysis of a Space-Time Discretization for Dynamic Elasticity Problems Based on Mass-Free Surface Elements, SIAM Journal on Numerical Analysis, vol.47, issue.3, p.18631885, 2009.
DOI : 10.1137/080715627

E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration, of Springer Series in Computational Mathematics, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01403326

W. Han and M. Sofonea, Quasistatic contact problems in viscoelasticity and viscoplasticity, AMSIP Studies in Advanced Mathematics, vol.30, 2002.

J. Haslinger, I. Hlavá£ek, and J. Ne£as, Numerical methods for unilateral problems in solid mechanics, Handbook of numerical analysis, p.313485, 1996.
DOI : 10.1016/S1570-8659(96)80005-6

P. Hauret, Mixed interpretation and extensions of the Khenous-Laborde-Renard mass lumping approach for elastodynamics with contact, 2010.

P. Hauret and P. L. Tallec, Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.37-40, pp.37-4048904916, 2006.
DOI : 10.1016/j.cma.2005.11.005
URL : https://hal.archives-ouvertes.fr/hal-00111458

P. Hauret and P. L. Tallec, A discontinuous stabilized mortar method for general 3D elastic problems, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.49-52, p.48814900, 2007.
DOI : 10.1016/j.cma.2007.06.014
URL : https://hal.archives-ouvertes.fr/hal-00175620

P. Hild and P. Laborde, Quadratic nite element methods for unilateral contact problems, Appl. Numer. Math, vol.41, issue.3, p.401421, 2002.

P. Hild and Y. Renard, Local uniqueness and continuation of solutions for the discrete Coulomb friction problem in elastostatics, Quarterly of Applied Mathematics, vol.63, issue.3, p.553573, 2005.
DOI : 10.1090/S0033-569X-05-00974-0
URL : https://hal.archives-ouvertes.fr/hal-00690592

J. Hiriart-urruty and C. Lemaréchal, Fundamentals of convex analysis. Grundlehren Text Editions, 2001.

S. Hüeber and B. I. Wohlmuth, An optimal a priori error estimate for nonlinear multibody contact problems, SIAM J. Numer. Anal, vol.43, issue.1, p.156173, 2005.

T. J. Hughes-arthur and M. Raefsky, The nite element method Linear static and dynamic nite element analysis, With the collaboration of Robert M, 1987.

P. Jaillet, D. Lamberton, and B. Lapeyre, Variational inequalities and the pricing of American options, Acta Applicandae Mathematicae, vol.60, issue.3, pp.263289-263299, 1990.
DOI : 10.1007/BF00047211

C. Kane, E. A. Repetto, M. Ortiz, and J. E. Marsden, Finite element analysis of nonsmooth contact, Computer Methods in Applied Mechanics and Engineering, vol.180, issue.1-2, p.126, 1999.
DOI : 10.1016/S0045-7825(99)00034-1

H. Khenous, Problèmes de contact unilatéral avec frottement de Coulomb en élastostatique et élastodynamique. Etude mathématique et résolution numérique, 2005.

H. B. Khenous, P. Laborde, and Y. Renard, Comparison of two approaches for the discretization of elastodynamic contact problems, Comptes Rendus Mathematique, vol.342, issue.10, pp.791-796, 2006.
DOI : 10.1016/j.crma.2006.03.011
URL : https://hal.archives-ouvertes.fr/hal-00690583

H. B. Khenous, P. Laborde, and Y. Renard, Mass redistribution method for nite element contact problems in elastodynamics, Eur. J. Mech. A Solids, vol.27, issue.5, p.918932, 2008.

N. Kikuchi and J. T. Oden, Contact problems in elasticity: a study of variational inequalities and nite element methods, SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.8, 1988.
DOI : 10.1137/1.9781611970845

D. Kinderlehrer, Remarks about Signorini's problem in linear elasticity, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.8, issue.44, p.605645, 1981.

D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Society for Industrial Mathematics, 2000.
DOI : 10.1137/1.9780898719451

C. Klapproth, A. Schiela, and P. Deuhard, Consistency results for the contact-stabilized Newmark method, Numer. Math, vol.116, issue.1, p.6594, 2010.

R. Krause and M. Walloth, Presentation and comparison of selected algorithms for dynamic contact based on the Newmark scheme, Applied Numerical Mathematics, vol.62, issue.10
DOI : 10.1016/j.apnum.2012.06.014

A. S. Kravchuk and P. J. Neittaanmäki, Variational and quasi-variational inequalities in mechanics, volume 147 of Solid Mechanics and its Applications, 2007.

S. Krenk, Energy conservation in Newmark based time integration algorithms, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.44-47, pp.44-4761106124, 2006.
DOI : 10.1016/j.cma.2005.12.001

K. Kunisch and G. Stadler, Generalized Newton methods for the 2D-Signorini contact problem with friction in function space, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.4, pp.827-854, 2005.
DOI : 10.1051/m2an:2005036
URL : https://hal.archives-ouvertes.fr/hal-01371379

P. Ladevèze, Nonlinear Computational Structural Mechanics -New Approaches and Non- Incremental Methods of Calculation, 1999.

C. J. Larsen, Models for dynamic fracture based on grith's criterion, IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, 2010.

C. J. Larsen, C. Ortner, and E. Süli, EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE, Mathematical Models and Methods in Applied Sciences, vol.20, issue.07, p.10211048, 2010.
DOI : 10.1142/S0218202510004520

T. A. Laursen, Computational contact and impact mechanics Fundamentals of modeling interfacial phenomena in nonlinear nite element analysis, 2002.

T. A. Laursen and V. Chawla, DESIGN OF ENERGY CONSERVING ALGORITHMS FOR FRICTIONLESS DYNAMIC CONTACT PROBLEMS, International Journal for Numerical Methods in Engineering, vol.37, issue.5, p.863886, 1997.
DOI : 10.1002/(SICI)1097-0207(19970315)40:5<863::AID-NME92>3.0.CO;2-V
URL : https://hal.archives-ouvertes.fr/hal-01435617

T. A. Laursen and G. R. Love, Improved implicit integrators for transient impact problemsgeometric admissibility within the conserving framework, Internat. J. Numer. Methods Engrg, vol.53, issue.2, p.245274, 2002.

B. Lawn, Fracture of brittle solids, 1993.
DOI : 10.1017/CBO9780511623127

G. Lebeau and M. Schatzman, A wave problem in a half-space with a unilateral constraint at the boundary, Journal of Differential Equations, vol.53, issue.3, p.309361, 1984.
DOI : 10.1016/0022-0396(84)90030-5
URL : https://hal.archives-ouvertes.fr/hal-01294216

J. Lions and E. Magenes, Non-homogeneous boundary value problems and applications, 1972.
DOI : 10.1007/978-3-642-65161-8

E. Lorentz, A mixed interface nite element for cohesive zone models, Computer Methods in Applied Mechanics and Engineering, vol.198, p.302317, 2008.

M. Marcus and V. J. , Every superposition operator mapping one Sobolev space into another is continuous, Journal of Functional Analysis, vol.33, issue.2, p.217229, 1979.
DOI : 10.1016/0022-1236(79)90113-7
URL : http://doi.org/10.1016/0022-1236(79)90113-7

J. Marigo and L. Truskinovsky, Initiation and propagation of fracture in the models of Grith and Barenblatt, Contin. Mech. Thermodyn, vol.16, issue.4, p.391409, 2004.

J. Mazars, Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure

J. J. Moreau, Numerical aspects of the sweeping process, Computational modeling of contact and friction, p.329349, 1999.
DOI : 10.1016/S0045-7825(98)00387-9
URL : https://hal.archives-ouvertes.fr/hal-01349847

M. Moussaoui and K. Khodja, R??gularit?? des solutions d'un probl??me m??l?? Dirichlet???Signorini dans un domaine polygonal plan, Communications in Partial Differential Equations, vol.60, issue.5-6, pp.5-6805826, 1992.
DOI : 10.1080/03605309208820864

R. H. Nochetto and L. B. Wahlbin, Positivity preserving nite element approximation, Math. Comp, vol.71, issue.240, p.14051419, 2002.
DOI : 10.1090/s0025-5718-01-01369-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.107.1439

N. Nsiampa, J. Ponthot, and L. Noels, Comparative study of numerical explicit schemes for impact problems, International Journal of Impact Engineering, vol.35, issue.12, pp.1688-1694, 2008.
DOI : 10.1016/j.ijimpeng.2008.07.003
URL : https://hal.archives-ouvertes.fr/hal-00542559

A. Pandol, P. R. Guduru, M. Ortiz, and A. J. Rosakis, Three dimensional cohesive-element analysis and experiments of dynamic fracture in C300 steel, International Journal of Solids and Structures, vol.37, issue.27, pp.3733-3760, 2000.
DOI : 10.1016/S0020-7683(99)00155-9

L. Paoli and M. Schatzman, A numerical scheme for impact problems. I. The onedimensional case, SIAM J. Numer. Anal, vol.40, issue.2, p.702733, 2002.

L. Paoli and M. Schatzman, A Numerical Scheme for Impact Problems II: The Multidimensional Case, SIAM Journal on Numerical Analysis, vol.40, issue.2, p.734768, 2002.
DOI : 10.1137/S003614290037873X

L. Q. Qi and J. Sun, A nonsmooth version of Newton's method, Mathematical Programming, vol.264, issue.1-3, p.353367, 1993.
DOI : 10.1007/BF01581275

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, p.141154, 1984.
DOI : 10.1007/BF01157550

P. Raviart and J. Thomas, Introduction à l'analyse numérique des équations aux dérivées partielles, Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree]. Masson, 1983.

Y. Renard, The singular dynamic method for constrained second order hyperbolic equations: Application to dynamic contact problems, Journal of Computational and Applied Mathematics, vol.234, issue.3, p.906923, 2010.
DOI : 10.1016/j.cam.2010.01.058
URL : https://hal.archives-ouvertes.fr/hal-01461799

J. Rice, The mechanics of earthquake rupture, Physics of the Earthï¾½s Interior, p.555649, 1980.

W. Rudin, Real and complex analysis, 1987.

O. Samudrala, Y. Huang, and A. J. Rosakis, Subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone, Journal of the Mechanics and Physics of Solids, vol.50, issue.6, pp.1231-1268, 2002.
DOI : 10.1016/S0022-5096(01)00129-6

M. Schatzman and M. Bercovier, Numerical approximation of a wave equation with unilateral constraints, Mathematics of Computation, vol.53, issue.187, p.5579, 1989.
DOI : 10.1090/S0025-5718-1989-0969491-5
URL : https://hal.archives-ouvertes.fr/hal-01295436

E. Sharon, S. Gross, and J. Fineberg, Energy dissipation in dynamic fracture. Physical review letters, p.21172120, 1996.

L. Slimane, A. Bendali, and P. Laborde, Mixed formulations for a class of variational inequalities, M2AN Math. Model. Numer. Anal, vol.38, issue.1, p.177201, 2004.

G. V. Smirnov, Introduction to the theory of dierential inclusions, Graduate Studies in Mathematics, vol.41, 2002.

M. Sofonea, W. Han, and M. Shillor, Analysis and approximation of contact problems with adhesion or damage, Pure and Applied MathematicsBoca Raton, vol.276, 2006.
DOI : 10.1201/9781420034837

D. E. Stewart, Rigid-Body Dynamics with Friction and Impact, SIAM Review, vol.42, issue.1, p.339, 2000.
DOI : 10.1137/S0036144599360110

C. Talon and A. Curnier, A model of adhesion coupled to contact and friction, European Journal of Mechanics - A/Solids, vol.22, issue.4, pp.545-565, 2003.
DOI : 10.1016/S0997-7538(03)00046-9

R. Taylor and P. Papadopoulos, On a nite element method for dynamic contact/impact problems, Int. J. Numer. Meth. Engng, vol.36, p.21232140, 1993.

R. Temam, Navier Stokes Equations: Theory and Numerical Analysis, Studies in Mathematics and its Applications, 1977.
DOI : 10.1115/1.3424338

M. G. Tijssens, B. L. Sluys, and E. Van-der-giessen, Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces, European Journal of Mechanics - A/Solids, vol.19, issue.5, pp.761-779, 2000.
DOI : 10.1016/S0997-7538(00)00190-X

D. Vola, E. Pratt, M. Jean, and M. Raous, Consistent time discretization for a dynamical frictional contact problem and complementarity techniques, Revue Europ??enne des ??l??ments Finis, vol.7, issue.1-3, pp.149-162, 1998.
DOI : 10.1080/12506559.1998.11690471

T. Warburton and J. S. Hesthaven, On the constants in hp-nite element trace inverse inequalities, Comput. Methods Appl. Mech. Engrg, vol.192, issue.25, p.27652773, 2003.

J. R. Willis, A comparison of the fracture criteria of griffith and barenblatt, Journal of the Mechanics and Physics of Solids, vol.15, issue.3, pp.151-162, 1967.
DOI : 10.1016/0022-5096(67)90029-4

P. Wriggers, Computational Contact Mechanics, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00466790

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

F. Zhou, J. Molinari, and T. Shioya, A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials, Engineering Fracture Mechanics, vol.72, issue.9, pp.1383-1410, 2005.
DOI : 10.1016/j.engfracmech.2004.10.011