A. Hrennikoff, Solution of problems of elasticity by the framework method, ASME J Appl Mech, vol.8, pp.619-715, 1941.

E. Schlangen and E. J. Garboczi, New method for simulating fracture using an elastically uniform random geometry lattice, Int J Eng Sci, vol.34, pp.1131-1144, 1996.
DOI : 10.1016/0020-7225(96)00019-5

M. Ostoja-starzewski, Lattice models in micromechanics, Appl Mech Rev, vol.55, issue.1, pp.35-60, 2002.
DOI : 10.1115/1.1432990

E. Schlangen and J. Van-mier, Simple lattice model for numerical simulation of fracture of concrete materials and structures, Mater Struct, vol.25, pp.534-542, 1992.

E. Schlangen and J. Van-mier, Experimental and numerical analysis of micromechanisms of fracture of cement-based composites, Cem Concr Compos, vol.14, pp.105-118, 1992.

N. Benkemoun, M. Hautefeuille, J. B. Colliat, and A. Ibrahimbegovic, Failure of heterogeneous materials: 3D meso-scale FE models with embedded discontinuities, Int J Numer Methods Eng, vol.82, pp.1671-1688, 2010.
URL : https://hal.archives-ouvertes.fr/hal-02023915

N. Benkemoun, A. Ibrahimbegovic, and J. B. Colliat, Anisotropic constitutive model of plasticity capable of accounting for details of meso-structure of two-phase composite material, Comput Struct, vol.90, pp.153-162, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01380346

M. Nikolic, A. Ibrahimbegovic, and P. Miscevic, Brittle and ductile failure of rocks: embedded discontinuity approach for representing mode I and mode II failure mechanisms, Int J Numer Methods Eng, vol.102, pp.1507-1526, 2015.

M. Nikolic and A. Ibrahimbegovic, Rock mechanics model capable of representing initial heterogeneities and full set of 3D failure mechanisms, Comput Methods Appl Mech Eng, vol.290, pp.209-227, 2015.

M. Vassaux, B. Richard, F. Ragueneau, A. Millard, and A. Delaplace, Lattice models applied to cyclic behavior description of quasi-brittle materials: advantages of implicit integration, Int J Numer Anal Meth Geomech, vol.39, pp.775-798, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01177051

M. Vassaux, C. Oliver-leblond, B. Richard, and F. Ragueneau, Beam-particle approach to model cracking and energy dissipation in concrete: identification strategy and validation, Cem Concr Compos, vol.70, pp.1-14, 2016.
DOI : 10.1016/j.cemconcomp.2016.03.011

URL : https://hal.archives-ouvertes.fr/hal-01297333

G. Cusatis, D. Pelessone, and A. Mencarelli, Lattice discrete particle model (LDPM) for failure behavior of concrete. I: theory, Cem Concr Compos, vol.33, pp.881-890, 2011.

G. Cusatis, A. Mencarelli, D. Pelessone, and J. Baylot, Lattice discrete particle model (LDPM) for failure behavior of concrete. I: calibration and validation, Cem Concr Compos, vol.33, pp.891-905, 2011.

M. Nikolic, A. Ibrahimbegovic, and P. Miscevic, Discrete element model for the analysis of fluid-saturated fractured poro-plastic medium based on sharp crack representation with embedded strong discontinuities, Comput Methods Appl Mech Eng, vol.298, pp.407-427, 2016.

M. Nikolic, A. Ibrahimbegovic, and P. Miscevic, Modelling of internal fluid flow in cracks with embedded strong discontinuities. In: Ibrahimbegovic A (ed) Computational methods for solids and fluids-multiscale analysis, probability aspects and model reduction, pp.315-341, 2016.

P. Grassl, A lattice approach to model flow in cracked concrete, Cem Concr Compos, vol.31, pp.454-460, 2009.
DOI : 10.1016/j.cemconcomp.2009.05.001

URL : http://arxiv.org/pdf/0809.2758

P. Grassl, C. Fahy, D. Gallipoli, and S. J. Wheeler, On a 2D hydro-mechanical lattice approach for modelling hydraulic fracture, J Mech Phys Solids, vol.75, pp.104-118, 2015.
DOI : 10.1016/j.jmps.2014.11.011

URL : https://hal.archives-ouvertes.fr/hal-02153527

J. G. Kirkwood, The skeletal modes of vibration of long chain molecules, J Chem Phys, vol.7, pp.506-509, 1939.

P. N. Keating, Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure, Phys Rev, vol.145, pp.637-645, 1966.

G. N. Hassold and D. J. Srolovitz, Brittle fracture in materials with random defects, Phys Rev, vol.39, pp.9273-9281, 1989.
DOI : 10.1103/physrevb.39.9273

G. Cusatis, Z. Bazant, and L. Cedolin, Confinement-shear lattice CSL model for fracture propagation in concrete, Comput Methods Appl Mech Eng, vol.195, pp.7154-7171, 2006.

C. S. Chang, T. K. Wang, L. J. Sluys, and J. Van-mier, Fracture modeling using a micro-structural mechanics approach I. Theory and formulation, Eng Fract Mech, vol.69, pp.1941-1958, 2002.
DOI : 10.1016/s0013-7944(02)00070-x

B. L. Karihaloo, P. F. Shao, and Q. Z. Xiao, Lattice modelling of the failure of particle composites, Eng Fract Mech, vol.70, pp.2385-2406, 2003.

J. Bolander and S. Saito, Fracture analyses using spring networks with random geometry, Eng Fract Mech, vol.61, pp.569-591, 1998.
DOI : 10.1016/s0013-7944(98)00069-1

P. J. Green and R. Sibson, Computing Dirichlet tessellations in the plane, Comput J, vol.21, pp.168-173, 1978.

J. Bolander and N. Sukumar, Irregular lattice model for quasistatic crack propagation, Phys Rev, vol.71, pp.94106-94107, 2005.
DOI : 10.1103/physrevb.71.094106

URL : https://cloudfront.escholarship.org/dist/prd/content/qt9qn7n4sb/qt9qn7n4sb.pdf?t=lnqgpp

S. Berton and J. Bolander, Crack band model of fracture in irregular lattices, Comput Methods Appl Mech Eng, vol.195, pp.7172-7181, 2006.

P. Grassl and M. Jirasek, Meso-scale approach to modelling the fracture process zone of concrete subjected to uniaxial tension, Int J Solids Struct, vol.47, pp.957-968, 2010.

P. Grassl, D. Gregoire, L. R. Solano, and G. Pijaudier-cabot, Meso-scale modelling of the size effect on the fracture process zone of concrete, Int J Solids Struct, vol.49, pp.1818-1827, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00737096

D. Gregoire, L. Verdon, V. Lefort, P. Grassl, J. Saliba et al., Mesoscale analysis of failure in quasi-brittle materials: comparison between lattice model and acoustic emission data, Int J Numer Anal Meth Geomech, vol.39, pp.1639-1664, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01157977

A. Griffith, The phenomena of rupture and flow in solids, Phil Trans R Soc A, vol.221, pp.163-198, 1921.

G. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate, J Appl Mech, vol.24, pp.361-364, 1957.

E. Orowan, Fracture and strength of solids, Rep Prog Phys, vol.12, p.185, 1948.
DOI : 10.1088/0034-4885/12/1/309

J. R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, J Appl Mech, vol.35, pp.379-386, 1968.

H. J. Herrmann and S. Roux, Statistical models for the fracture of disordered media, pp.159-188, 1990.

A. Ibrahimbegovic, Nonlinear solid mechanics: theoretical formulations and finite element solution methods, 2009.

Z. P. Bazant and F. B. Lin, Non-local yield limit degradation, Int J Numer Methods Eng, vol.26, pp.1805-1823, 1988.

Z. P. Bazant and G. Pijaudier-cabot, Non linear continuous damage, localization instability and convergence, J Appl Mech, vol.55, pp.287-293, 1988.

V. P. Nguyen, O. Lloberas-valls, M. Stroeven, and L. J. Sluys, Homogenization-based multiscale crack modelling: from microdiffusive damage to macro-cracks, Comput Methods Appl Mech Engrg, vol.200, pp.1220-1236, 2011.

L. Contrafatto, M. Cuomo, and S. Gazzo, A concrete homogenisation technique at meso-scale level accounting for damaging behaviour of cement paste and aggregates, Comput Struct, vol.173, pp.1-18, 2016.

S. Toro, P. J. Sanchez, P. J. Blanco, . De-souza, E. A. Neto et al., Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales, Int J Plast, vol.76, pp.75-110, 2016.

J. Oliver, M. Caicedo, E. Roubin, A. E. Huespe, and J. A. Hernandez, Continuum approach to computational multiscale modeling of propagating fracture, Comput Methods Appl Mech Engrg, vol.294, pp.384-427, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01876087

J. Fish, Bridging the scales in nano engineering and science, J Nanopart Res, vol.8, pp.577-594, 2006.

A. Ibrahimbegovic, R. Niekamp, C. Kassiotis, D. Markovic, and H. Matthies, Code-coupling strategy for efficient development of computer software in multiscale and multiphysics nonlinear evolution problems in computational mechanics, Adv Eng Softw, vol.72, pp.8-17, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01763305

C. L. Rountree, R. K. Kalia, E. Lidorikis, A. Nakano, L. Van-brutzel et al., Atomistic aspects of crack propagation in brittle materials: multimillion atom molecular dynamics simulations, Ann Rev Mater Res, vol.32, pp.377-400, 2002.

D. Bonamy and E. Bouchaud, Failure of heterogeneous materials: a dynamic phase transition?, Phys Rep, vol.498, pp.1-44, 2011.

R. K. Kalia, A. Nakano, P. Vashishta, C. L. Rountree, L. Van-brutzel et al., Multiresolution atomistic simulations of dynamic fracture in nanostructured ceramics and glasses, Int J Fract, vol.121, pp.71-79, 2003.

G. I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, Adv Appl Mech, vol.7, pp.55-129, 1962.

D. S. Dugdale, Yielding of steel sheets containing slits, J Mech Phys Solids, vol.8, pp.100-104, 1960.

G. Lilliu and J. Van-mier, 3D lattice type fracture model for concrete, Eng Fract Mech, vol.70, p.927941, 2003.

N. Moes, J. Dolbow, and T. Belytschko, A finite element method for crack growth without remeshing, Int J Numer Methods Eng, vol.46, pp.131-150, 1999.
URL : https://hal.archives-ouvertes.fr/hal-01004829

T. P. Fries and T. Belytschko, The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns, Int J Numer Methods Eng, vol.68, pp.1358-1385, 2006.

T. P. Fries and T. Belytschko, The generalized/extended finite element method: an overview of the method and its applications, Int J Numer Methods Eng, vol.84, pp.253-304, 2010.

M. Jirasek, Comparative study on finite elements with embedded discontinuities, Comput Methods Appl Mech Engrg, vol.188, pp.307-330, 2000.

J. Oliver, A. E. Huespe, and P. J. Sanchez, A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM, Comput Methods Appl Mech Engrg, vol.195, pp.4732-4752, 2006.

C. Linder and F. Armero, Finite elements with embedded strong discontinuities for the modeling of failure in solids, Int J Numer Meth Eng, vol.72, pp.1391-1433, 2007.

D. Brancherie and A. Ibrahimbegovic, Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures, Part I: theoretical formulation and numerical implementation, Eng Comput, vol.26, pp.100-127, 2009.

J. Dujc, B. Brank, and A. Ibrahimbegovic, Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids, Int J Numer Meth Eng, vol.94, pp.1075-1098, 2013.

Y. H. Gedik, H. Nakamura, Y. Yamamoto, and M. Kunieda, Evaluation of three-dimensional effects in short deep beams using a rigid-body-spring-model, Cem Concr Compos, vol.33, pp.978-991, 2011.

Y. Yamamoto, H. Nakamura, I. Kuroda, and N. Furuya, Crack propagation analysis of reinforced concrete wall under cyclic loading using RBSM, Eur J Environ Civ Eng, vol.18, pp.780-792, 2014.

P. A. Cundall and O. Strack, A discrete numerical model for granular assemblies, Géotechnique, vol.29, pp.47-65, 1979.

M. Obermayr, K. Dressler, C. Vrettos, and P. Eberhard, A bonded-particle model for cemented sand, Comput Geotech, vol.49, pp.299-313, 2013.

F. Camborde, C. Mariotti, and F. V. Donzé, Numerical study of rock and concrete behaviour by discrete element modelling, Comput Geotech, vol.27, pp.225-247, 2000.

C. Ergenzinger, R. Seifried, and P. Eberhard, A discrete element model to describe failure of strong rock in uniaxial compression, Granul Matter, vol.13, pp.1-24, 2010.

S. Utili and R. Nova, Dem analysis of bonded granular geomaterials, Int J Numer Anal Methods Geomech, vol.32, pp.1997-2031, 2008.

M. Obermayr, K. Dressler, C. Vrettos, and P. Eberhard, Prediction of draft forces in cohesionless soil with the discrete element method, J Terramechanics, vol.48, pp.347-358, 2011.

D. Addetta, G. A. Kun, F. Ramm, E. Herrmann, and H. J. , From solids to granulates-Discrete element simulations of fracture and fragmentation processes in geomaterials, Continuous and discontinuous modelling of cohesive frictional materials, pp.231-258, 2001.

D. Addetta, G. A. Kun, F. Ramm, and E. , On the application of a discrete model to the fracture process of cohesive granular materials, Granul Matter, vol.4, pp.77-90, 2002.

A. Ibrahimbegovic and A. Delaplace, Microscale and mesoscale discrete models for dynamic fracture of structures built of brittle material, Comput Struct, vol.81, pp.1255-1265, 2003.

A. Delaplace and A. Ibrahimbegovic, Performance of timestepping schemes for discrete models in fracture dynamic analysis, Int J Numer Meth Engng, vol.65, pp.1527-1544, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00018984

J. G. Rots and S. Invernizzi, Regularized sequentially linear saw-tooth softening model, Int J Numer Anal Meth Geomech, vol.28, pp.821-856, 2004.

J. C. Simo, J. Oliver, and F. Armero, An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Comput Mech, vol.12, pp.277-296, 1993.

M. Ortiz, Y. Leroy, and A. Needleman, A finite element method for localized failure analysis, Comput Methods Appl Mech Eng, vol.61, pp.189-214, 1987.

J. Simo and M. Rifai, A class of mixed assumed strain methods and the method of incompatible modes, Int J Numer Methods Eng, vol.29, pp.1595-1638, 1990.

A. Ibrahimbegovic and E. Wilson, A modified method of incompatible modes, Commun Appl Numer Methods, vol.7, pp.187-194, 1991.

A. Ibrahimbegovic and S. Melnyk, Embedded discontinuity finite element method for modeling of localized failure in heterogeneous materials with structured mesh: an alternative to extended finite element method, Comput Mech, vol.40, pp.149-155, 2007.

B. M. Pham, D. Brancherie, L. Davenne, and A. Ibrahimegovic, Stress resultant models for ultimate load design of reinforced concrete frames and multi-scale parameter estimates, Comput Mech, vol.51, pp.347-360, 2013.
DOI : 10.1007/s00466-012-0734-6

URL : https://hal.archives-ouvertes.fr/hal-02002878

N. N. Bui, M. Ngo, M. Nikolic, D. Brancherie, and A. Ibrahimbegovic, Enriched Timoshenko beam finite element for modeling bending and shear failure of reinforced concrete frames, Comput Struct, vol.143, pp.9-18, 2014.
DOI : 10.1016/j.compstruc.2014.06.004

URL : https://hal.archives-ouvertes.fr/hal-02002879

N. Stambuk-cvitanovic, M. Nikolic, and A. Ibrahimbegovic, Influence of specimen shape deviations on uniaxial compressive strength of limestone and similar rocks, Int J Rock Mech Min Sci, vol.80, pp.357-372, 2015.

J. Bolander and S. Berton, Simulation of shrinkage induced cracking in cement composite overlays, Cem Concr Compos, vol.26, pp.861-871, 2004.
DOI : 10.1016/j.cemconcomp.2003.04.001

H. Nakamura, W. Srisoros, R. Yashiro, and M. Kunieda, Timedependent structural analysis considering mass transfer to evaluate deterioration process of RC structures, J Adv Concr Technol, vol.4, pp.147-158, 2006.
DOI : 10.3151/jact.4.147

URL : https://www.jstage.jst.go.jp/article/jact/4/1/4_1_147/_pdf

L. Wang, M. Soda, and T. Ueda, Simulation of chloride diffusivity for cracked concrete based on RBSM and truss network model, J Adv Concr Technol, vol.6, pp.143-155, 2008.
DOI : 10.3151/jact.6.143

URL : https://www.jstage.jst.go.jp/article/jact/6/1/6_1_143/_pdf

L. Wang and T. Ueda, Mesoscale modelling of the chloride diffusion in cracks and cracked concrete, J Adv Concr Technol, vol.9, pp.241-249, 2011.

B. Savija, J. Pacheco, and E. Schlangen, Lattice modeling of chloride diffusion in sound and cracked concrete, Cem Concr Compos, vol.42, pp.30-40, 2013.

D. Asahina, J. E. Houseworth, J. T. Birkholzer, J. Rutqvist, and J. Bolander, Hydro-mechanical model for wetting/drying and fracture development in geomaterials, Comput Geosci, vol.65, pp.13-23, 2014.
DOI : 10.1016/j.cageo.2013.12.009

URL : https://cloudfront.escholarship.org/dist/prd/content/qt40c1m4qm/qt40c1m4qm.pdf

B. Damjanac, C. Detournay, and P. A. Cundall, Application of particle and lattice codes to simulation of hydraulic fracturing, Comput Part Mech, vol.3, pp.249-261, 2016.

M. A. Biot, Mechanics of incremental deformations, 1965.
URL : https://hal.archives-ouvertes.fr/hal-01352219

K. Terzaghi, Theoretical soil mechanics, 1943.
DOI : 10.1002/9780470172766

URL : https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780470172766.fmatter

R. W. Lewis and B. A. Schrefler, The finite element method in the static and dynamic deformation and consolidation of porous media, 1998.