Bibliography

[cma]

Cmake - cross platform make. URL: \url{http://www.cmake.org/}.

[dia]

Diana User's Manual. URL: https://dianafea.com/manuals/d105/Diana.html (visited on 2021-06-16).

[spa]

Mumps : a parallel sparse direct solver. URL: \url{http://graal.ens-lyon.fr/MUMPS/}.

[num]

Numpy - fundamental package for scientific computing with python. URL: \url{http://www.numpy.org/}.

[par]

Paraview - open source scientific visualization. URL: \url{http://www.paraview.org/}.

[sco]

Scotch: static mapping, graph, mesh and hypergraph partitioning. URL: \url{http://www.labri.fr/perso/pelegrin/scotch/}.

[may]

The mayavi data visualizer. URL: \url{http://mayavi.sourceforge.net/}.

[vis]

Visit visualization tool. URL: \url{http://wci.llnl.gov/codes/visit/}.

[Aif84]

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

[AragonM14]

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: http://dx.doi.org/10.1016/j.cma.2013.10.001, doi:10.1016/j.cma.2013.10.001.

[Bavzant76]

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

[Bavzant86]

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

[BavzantB85]

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

[BavzantPC88]

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

[BCXZ03]

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.

[CO96]

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.

[Cau60]

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

[CFL56]

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.

[Cur92]

A. Curnier. Méthodes numériques en mécanique des solides. EPFL, 1992. URL: http://books.google.ch/books?id=-Z2zygAACAAJ.

[dBvdB94]

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: https://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399%281994%29120%3A12%282519%29 (visited on 2021-06-16), doi:10.1061/(ASCE)0733-9399(1994)120:12(2519).

[dVBvG95]

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.

[DHB10]

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

[FJ09]

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: http://books.google.fr/books?id=bCBtQgAACAAJ.

[GR09]

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: http://dx.doi.org/10.1002/nme.2579, doi:10.1002/nme.2579.

[GDM11]

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

[GD13]

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: https://hal.archives-ouvertes.fr/hal-02535143, doi:10.1002/9781118562086.ch3.

[HB83]

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.

[Jirasek98]

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

[Jirasek07a]

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

[Jirasek07b]

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

[JirasekRG04]

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.

[JirasekR03]

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.

[Lad92]

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

[Lau02]

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.

[Lem96]

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

[Lev10]

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

[Mar81]

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.

[Maz84]

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.

[Nee88]

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

[New59]

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

[NROR01]

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.

[Omo89]

Stephen M. Omohundro. Five balltree construction algorithms. Technical Report TR-89-063, International Computer Science Institute, University of California at Berkeley, 1989. URL: http://ftp.icsi.berkeley.edu/ftp/pub/techreports/1989/tr-89-063.pdf.

[OP99a]

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.

[OP99b]

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.

[PO12]

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

[PatzakRB01]

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

[Pie97]

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.

[PCBavzant87]

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

[Ric76]

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.

[SF96]

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

[Sil00]

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.

[SH92]

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

[SM13]

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.

[TB00]

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

[VRM15]

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

[WRM14]

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

[ZM04]

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.

[HughesBelytschko83]

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.