Cmake - cross platform make. URL: \url{}.


Diana User's Manual. URL: (visited on 2021-06-16).


Mumps : a parallel sparse direct solver. URL: \url{}.


Numpy - fundamental package for scientific computing with python. URL: \url{}.


Paraview - open source scientific visualization. URL: \url{}.


Scotch: static mapping, graph, mesh and hypergraph partitioning. URL: \url{}.


The mayavi data visualizer. URL: \url{}.


Visit visualization tool. URL: \url{}.


E. C. Aifantis. On the microstructural origin of certain inelastic models. Journal of Engineering Materials and Technology, 106:326 – 330, 1984.


Alejandro M. Aragón and Jean-François Molinari. A hierarchical detection framework for computational contact mechanics. Computer Methods in Applied Mechanics and Engineering, 268(0):574 – 588, 2014. URL:, doi:10.1016/j.cma.2013.10.001.


Zdeněk P. Bažant. Instability, ductility, and size effect in strain-softening concrete. Journal of the Engineering Mechanics Division, 102(5):331 – 344, 1976.


Zdeněk P. Bažant. Mechanics of distributed cracking. Applied Mechanics Reviews, 39(5):675 – 705, 1986.


Zdeněk P. Bažant and Ted Belytschko. Wave propagation in a strain-softening bar: exact solution. Journal of Engineering Mechanics, 111(3):381 – 389, 1985.


Zdeněk P. Bažant and Gilles Pijaudier-Cabot. Nonlocal Continuum Damage, Localization Instability and Convergence. Journal of Applied Mechanics, 55(2):287–293, 1988.


T Belytschko, H Chen, J Xu, and G Zi. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. International Journal for Numerical Methods in Engineering, 58:1875–1905, 2003.


G.T. Camacho and M. Ortiz. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures, 33(20–22):2899–2938, August 1996.


TK Caughey. Classical normal modes in damped linear dynamic systems. Journal of Applied Mechanics, 27(2):269–271, 1960.


Richard Courant, Kurt Otto Friedrichs, and H. Lewy. On the partial difference equations of mathematical physics. Courant Institute of Mathematical Sciences, New York University, New York, 1956.


A. Curnier. Méthodes numériques en mécanique des solides. EPFL, 1992. URL:


René de Borst and A. H. van den Boogaard. Finite‐Element Modeling of Deformation and Cracking in Early‐Age Concrete. Journal of Engineering Mechanics, 120(12):2519–2534, December 1994. Publisher: American Society of Civil Engineers. URL: (visited on 2021-06-16), doi:10.1061/(ASCE)0733-9399(1994)120:12(2519).


J.H.P. de Vree, W.A.M. Brekelmans, and M.A.J. van Gils. Comparison of nonlocal approaches in continuum damage mechanics. Computers &; Structures, 55(4):581 – 588, 1995.


Youn Doh-Ha and Florin Bobaru. Studies of dynamic crack propagation and crack branching with peridynamics. International Journal of Fracture, 162:229–1244, 2010.


F. Frey and J. Jirousek. Méthodes des éléments finis: Analyse des structures et milieux continus. Traité de génie civil de l'Ecole Polytechnique Fédérale de Lausanne. PPUR, 2009. ISBN 9782880748524. URL:


Christophe Geuzaine and Jean-François Remacle. Gmsh: a 3-d finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11):1309–1331, 2009. URL:, doi:10.1002/nme.2579.


C. Giry, F. Dufour, and J. Mazars. Stress-based nonlocal damage model. International Journal of Solids and Structures, 48:3431 – 3443, 2011.


Cédric GIRY and Frédéric Dufour. Stress-based Non-local Damage Model. In Damage Mechanics of Cementitious Materials and Structures, pages 51–88. John Wiley & Sons, Inc., March 2013. URL:, doi:10.1002/9781118562086.ch3.


T.J.R. Hughes and T. Belytschko. A precis of developments in computational methods for transient analysis. Journal. of Applied Mechanics (ASME), 50:1033–1041, 1983.


Milan Jirásek. Nonlocal models for damage and fracture: comparison of approaches. International Journal of Solids and Structures, 35:4133 – 4145, 1998.


Milan Jirásek. Mathematical analysis of strain localization. Revue Europeenne de Genie Civil, 11:977 – 991, 2007.


Milan Jirásek. Nonlocal damage mechanics. Revue Europeenne de Genie Civil, 11:993 – 1021, 2007.


Milan Jirásek, S Rolshoven, and P Grassl. Size effect on fracture energy induced by non-locality. International Journal for numerical and analytical methods in geomechanics, 28:653 – 670, 2004.


Milan Jirásek and Simon Rolshoven. Comparison of integral-type nonlocal plasticity models for strain-softening materials. International Journal of Engineering Science, 41:1553–1602, 2003.


P. Ladeveze. A damage computational method for composite structures. Computational & Structures, 44:79–87, 1992.


T.A. Laursen. Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Engineering online library. Springer, 2002. ISBN 9783540429067.


Jean Lemaitre. A Course on Damage Mechanics. Springer Berlin Heidelberg, 1996. ISBN 978-3-540-60980-3.


Sarah Levy. Exploring the Physics behind Dynamic Fragmentation through Parallel Simulations. PhD thesis, ENAC, Lausanne, 2010.


Jean-Jacques Marigo. Formulation d'une loi d'endommagement d'un matériau élastique. C. R. Acad. Sci., Paris, Sér. II, 292(19):1309–1312, 1981.


Jacky Mazars. Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure. PhD thesis, Université Paris 6, 1984.


A. Needleman. Material rate dependence and mesh sensitivity in localization problems. Computer Methods in Applied Mechanics and Engineering, 67(1):69 – 85, 1988.


Nathan M. Newmark. A Method of Computation for Structural Dynamics. Journal of the Engineering Mechanics Division, 85(3):67–94, July 1959.


O. Nguyen, E. A. Repetto, M. Ortiz, and R. A. Radovitzky. A cohesive model of fatigue crack growth. International Journal of Fracture, 110(4):351–369, August 2001. doi:10.1023/A:1010839522926.


Stephen M. Omohundro. Five balltree construction algorithms. Technical Report TR-89-063, International Computer Science Institute, University of California at Berkeley, 1989. URL:


M Ortiz and A Pandolfi. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering, 44:1267–1282, 1999.


M. Ortiz and A. Pandolfi. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering (IJNME), 44:1267–1282, 1999.


A Pandolfi and M Ortiz. An eigenerosion approach to brittle fracture. International Journal for Numerical Methods in Engineering, 92:694–714, 2012.


B. Patzák, D. Rypl, and Z. Bittnar. Parallel explicit finite element dynamics with nonlocal constitutive models. Computers & Structures, 79(26–28):2287 – 2297, 2001.


Grzegorz Pietrzak. Continuum mechanics modelling and augmented Lagrangian formulation of large deformation frictional contact problems. PhD thesis, École Polytechnique Fédérale de Lausanne, 1997. doi:10.5075/epfl-thesis-1656.


Gilles Pijaudier-Cabot and Zdeněk P. Bažant. Nonlocal damage theory. Journal of Engineering Mechanics, 113(10):1512 – 1533, 1987.


James R. Rice. The localisation of plastic deformation. Theoretical and Applied Mechanics (14th International Congress on Theoretical and Applied Mechanics, Delft, 1976, ed. W.T. Koiter), 1:207 – 220, 1976.


Eran Sharon and Jay Fineberg. Microbranching instability and the dynamic fracture of brittle materials. Physical Review B, 54(10):7128 – 7139, 1996.


S A Silling. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids, 48:175–209, 2000.


J.C. Simo and T.J.R. Hughes. Computational Inelasticity. Springer, 1992.


Leonardo Snozzi and Jean-Francois Molinari. A cohesive element model for mixed mode loading with frictional contact capability. International Journal for Numerical Methods in Engineering, 93(5):510–526, February 2013.


Brian Moran Ted Belytschko, Wing Kam Liu. Nonlinear Finite Elements for Continua and Structures. Wiley, 2000.


M. Vocialta, N. Richart, and J.-F. Molinari. 3d dynamic fragmentation with parallel dynamic insertion of cohesive elements. Submitted to IJNME, 2015.


C. Wolff, N. Richart, and J.-F. Molinari. A non-local continuum damage approach to model dynamic crack branching. Submitted to IJNME, 2014.


F. Zhou and J. F. Molinari. Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency. International Journal for Numerical Methods in Engineering, 2004.


T. J. R. Hughes and T. Belytschko. A Précis of Developments in Computational Methods for Transient Analysis. Journal of Applied Mechanics, 50:1033, December 1983.