Mesoscopic Mechanical Analysis of Filled Elastomer with 3D-Finite Element Analysis and Transmission Electron Microtomography, Rubber Chemistry and Technology, vol.81, issue.2, pp.182-189, 2008. ,
DOI : 10.5254/1.3548203
Approximation of functional depending on jumps by elliptic functional via t-convergence, Communications on Pure and Applied Mathematics, vol.17, issue.8, pp.43999-1036, 1990. ,
DOI : 10.1002/cpa.3160430805
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, Journal of the Mechanics and Physics of Solids, vol.57, issue.8, pp.1209-1229, 2009. ,
DOI : 10.1016/j.jmps.2009.04.011
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, pp.622-636, 1959. ,
DOI : 10.1016/0021-8928(59)90157-1
Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings, Computer Methods in Applied Mechanics and Engineering, vol.233, issue.236, pp.11-27, 2012. ,
DOI : 10.1016/j.cma.2012.02.020
URL : https://hal.archives-ouvertes.fr/hal-01433786
A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework, Computer Methods in Applied Mechanics and Engineering, vol.273, pp.100-118, 2012. ,
DOI : 10.1016/j.cma.2014.01.016
Approximation of Free Discontinuity Problems, 1998. ,
Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, vol.33, issue.20-22, pp.2899-2938, 1996. ,
DOI : 10.1016/0020-7683(95)00255-3
Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture, International Journal for Numerical Methods in Engineering, vol.339, issue.1, 2015. ,
DOI : 10.1002/nme.4886
Some issues in the application of cohesive zone models for metal???ceramic interfaces, International Journal of Solids and Structures, vol.39, issue.10, pp.392827-2855, 2002. ,
DOI : 10.1016/S0020-7683(02)00149-X
Large-Scale Finite Element Analysis of Human Cancellous Bone Tissue Micro Computer Tomography Data: A Convergence Study, Journal of Biomechanical Engineering, vol.136, issue.10, p.136101013, 2014. ,
DOI : 10.1115/1.4028106
Evolving Discontinuities and Cohesive Fracture, Procedia IUTAM, vol.10, pp.125-137, 2014. ,
DOI : 10.1016/j.piutam.2014.01.014
An improved description of the exponential Xu and Needleman cohesive zone law for mixed-mode decohesion, Engineering Fracture Mechanics, vol.73, issue.9, pp.1220-1234, 2006. ,
DOI : 10.1016/j.engfracmech.2005.12.006
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
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
Bond effects in high-strength silica fume concretes, ACI. Mater. J, vol.86, issue.5, 1989. ,
Rock mechanics and engineering, 1979. ,
Determination of the size of the representative volume element for random composites: statistical and numerical approach, International Journal of Solids and Structures, vol.40, issue.13-14, pp.13-143647, 2003. ,
DOI : 10.1016/S0020-7683(03)00143-4
Fracture mechanics parameters influencing the mechanical properties of high-performance concrete, ACI. Spe. P, p.149, 1994. ,
A phase field model for rateindependent crack propagation: Robust algorithmic implementation based on operator splits, Comput. Meth. Appl. Mech. Eng, vol.199, pp.2776-2778, 2010. ,
Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, International Journal for Numerical Methods in Engineering, vol.55, issue.10, pp.1273-1311, 2010. ,
DOI : 10.1002/nme.2861
A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131-150, 1999. ,
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A
Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989. ,
DOI : 10.1002/cpa.3160420503
The influence of the interphase and associated interfaces on the deflection of matrix cracks in ceramic matrix composites, Compos. Part A, vol.31, pp.1179-1190, 2000. ,
A Continuum Model for Void Nucleation by Inclusion Debonding, Journal of Applied Mechanics, vol.54, issue.3, pp.525-531, 1987. ,
DOI : 10.1115/1.3173064
On the choice of numerical parameters in the phase field method for simulating crack initiation with experimental validations ,
A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure, Engineering Fracture Mechanics, vol.139, pp.18-39, 2014. ,
DOI : 10.1016/j.engfracmech.2015.03.045
URL : https://hal.archives-ouvertes.fr/hal-01140963
Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, International Journal for Numerical Methods in Engineering, vol.142, issue.9, pp.1267-1282, 1999. ,
DOI : 10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7
Geometric level set methods in imaging, vision, and graphics, 2003. ,
Two-dimensional X-ray CT image based meso-scale fracture modelling of concrete, Engineering Fracture Mechanics, vol.133, pp.24-39, 2015. ,
DOI : 10.1016/j.engfracmech.2014.10.016
Detection of crack onset in double cleavage drilled specimens of plaster under compression by digital image correlation ??? Theoretical predictions based on a coupled criterion, European Journal of Mechanics - A/Solids, vol.51, pp.172-182, 2015. ,
DOI : 10.1016/j.euromechsol.2014.12.002
Computational modeling of concrete fracture, 1988. ,
X-ray micro-tomography an attractive characterisation technique in materials science, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol.200, pp.273-286, 2003. ,
DOI : 10.1016/S0168-583X(02)01689-0
URL : https://hal.archives-ouvertes.fr/hal-00475146
Predicting the permeability of trabecular bone by micro-computed tomography and finite element modeling, Journal of Biomechanics, vol.47, issue.12, pp.3129-3134, 2014. ,
DOI : 10.1016/j.jbiomech.2014.06.024
Extended finite element method for three-dimensional crack modelling, International Journal for Numerical Methods in Engineering, vol.15, issue.11, pp.1549-1570, 2000. ,
DOI : 10.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A
URL : https://hal.archives-ouvertes.fr/hal-01006859
Micro-finite element modelling of oke blends using x-ray microtomography, Fuel, vol.87, pp.13-142983, 2008. ,
Model studies of fibre breakage and debonding in a metal reinforced by short fibres, Journal of the Mechanics and Physics of Solids, vol.41, issue.8, pp.1309-1326, 1993. ,
DOI : 10.1016/0022-5096(93)90081-P
The influence of plasticity on mixed mode interface toughness, Journal of the Mechanics and Physics of Solids, vol.41, issue.6, pp.1119-1135, 1993. ,
DOI : 10.1016/0022-5096(93)90057-M
A phase-field model for cohesive fracture, International Journal for Numerical Methods in Engineering, vol.1, issue.220, pp.43-62, 2013. ,
DOI : 10.1002/nme.4553
On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: plane deformation, International Journal of Fracture, vol.125, issue.1, pp.189-205, 2004. ,
DOI : 10.1023/B:FRAC.0000021042.28804.f1
A new method for modelling cohesive cracks using finite elements, International Journal for Numerical Methods in Engineering, vol.3, issue.12, pp.502667-2682, 2001. ,
DOI : 10.1002/nme.143
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
A fast method for solving microstructural problems defined by digital images: a space Lippmann-Schwinger scheme, International Journal for Numerical Methods in Engineering, vol.40, issue.1, pp.178-205, 2012. ,
DOI : 10.1002/nme.4334
URL : https://hal.archives-ouvertes.fr/hal-00822037
Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency, International Journal for Numerical Methods in Engineering, vol.59, issue.1, pp.1-24, 2004. ,
DOI : 10.1002/nme.857