Investigation of crack growth in functionally graded materials using digital image correlation, Engineering Fracture Mechanics, vol.69, issue.14-16, pp.1695-1711, 2002. ,
DOI : 10.1016/S0013-7944(02)00058-9
Phase-eld modeling of crack propagation in piezoelectric and ferroelectric materials with dierent electromechanical crack conditions, Journal of the Mechanics and Physics of Solids, vol.60, pp.21002126-2012 ,
Image processing with imagej, Biophotonics international, vol.11, issue.7, p.3642, 2004. ,
Vibration Testing as a Nondestructive Test Tool for Composite Materials, Composite Reliability, ASTM STP, vol.580, p.159175, 1975. ,
DOI : 10.1520/STP32306S
Ultrasonic wave dispersion and attenuation in fresh mortar, NDT & E International, vol.37, issue.8, p.617631, 2004. ,
Mesoscopic mechanical analysis of lled elastomers, Rubber Chemistry and Technology, vol.81, issue.2, p.182189, 2008. ,
Experimental characterization of the local strain eld in a heterogeneous elastoplastic material, Acta Metallurgica et materialia, vol.42, issue.125, pp.38653880-118, 1994. ,
Approximation of functional depending on jumps by elliptic functional via t-convergence, Communications on Pure and Applied Mathematics, vol.17, issue.8, p.9991036, 1990. ,
DOI : 10.1002/cpa.3160430805
Approximation of functional depending on jumps by elliptic functional via t-convergence, Communications on Pure and Applied Mathematics, vol.17, issue.8, p.9991036, 1990. ,
DOI : 10.1002/cpa.3160430805
On the approximation of free discontinuity problems ,
Assessment of Digital Image Correlation Measurement Accuracy in the Ultimate Error Regime: Main Results of a Collaborative Benchmark, Strain, vol.45, issue.6, pp.483496-2013 ,
DOI : 10.1111/str.12054
URL : https://hal.archives-ouvertes.fr/hal-01069741
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.12091229-12091264, 2009. ,
DOI : 10.1016/j.jmps.2009.04.011
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.12091229-12091265, 2009. ,
DOI : 10.1016/j.jmps.2009.04.011
Damage initiation in model metallic materials: X-ray tomography and modelling, Acta Materialia, vol.52, issue.8, p.24752487, 2004. ,
DOI : 10.1016/j.actamat.2004.02.001
URL : https://hal.archives-ouvertes.fr/hal-00474482
Eect of polystyrene aggregate size on strength and moisture migration characteristics of lightweight concrete. Cement and Concrete Composites, p.520527, 2006. ,
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.622636, 1959. ,
DOI : 10.1016/0021-8928(59)90157-1
Digital volume correlation: Three-dimensional strain mapping using X-ray tomography, Experimental Mechanics, vol.27, issue.10???12, pp.217-226, 1999. ,
DOI : 10.1007/BF02323555
Wave propagation in a strain-softening bar: exact solution, Journal of Engineering Mechanics, vol.111, issue.3, p.381389, 1985. ,
Nonlocal Continuum Damage, Localization Instability and Convergence, Journal of Applied Mechanics, vol.55, issue.2, p.287293, 1988. ,
DOI : 10.1115/1.3173674
An element-failure algorithm for dynamic crack propagation in general directions, Engineering Fracture Mechanics, vol.61, issue.3-4, p.407425, 1998. ,
DOI : 10.1016/S0013-7944(98)00072-1
Arbitrary discontinuities in nite elements, International Journal for Numerical Methods in Engineering, vol.50, issue.4, p.9931013, 2001. ,
Bifurcation and stability issues in gradient theories with softening. Modelling and Simulation in, Materials Science and Engineering, vol.15, pp.283-295, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00551073
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.1127-61, 2012. ,
DOI : 10.1016/j.cma.2012.02.020
URL : https://hal.archives-ouvertes.fr/hal-01433786
How to study drying shrinkage microcracking in cementbased materials using optical and scanning electron microscopy? Cement and Concrete Research, p.279287, 2002. ,
Experimental determination of fully-coupled kinematical and thermal elds at the scale of grains under cyclic loading ,
Isogeometric analysis of phase-eld models for dynamic brittle and ductile fracture, 2012. ,
A higher-order phaseeld model for brittle fracture: Formulation and analysis within the isogeometric analysis framework, Computer Methods in Applied Mechanics and Engineering, vol.273, pp.100118-2014 ,
A phaseeld description of dynamic brittle fracture, Computer Methods in Applied Mechanics and Engineering, vol.217, pp.7795-2012 ,
Assessment of Digital Image Correlation Measurement Errors: Methodology and Results, Experimental Mechanics, vol.43, issue.4, pp.353370-120, 2009. ,
DOI : 10.1007/s11340-008-9204-7
URL : https://hal.archives-ouvertes.fr/hal-00881043
Mesure tridimensionnelle de champs cinématiques par imagerie volumique pour l'analyse des matériaux et des structures, pp.4-7, 2004. ,
Multiscale full-eld strain measurements for micromechanical investigations of the hydromechanical behaviour of clayey rocks, Strain, vol.46, issue.117, pp.3346-3357, 2010. ,
Fundamental issues in nite element analyses of localization of deformation. Engineering computations, p.99121, 1993. ,
Numerical implementation of the variational formulation for quasi-static brittle fracture, Interfaces and Free Boundaries, vol.9, p.411430, 2007. ,
DOI : 10.4171/IFB/171
Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, vol.48, issue.4, p.797826, 2000. ,
DOI : 10.1016/S0022-5096(99)00028-9
The Variational Approach to Fracture ,
URL : https://hal.archives-ouvertes.fr/hal-00551079
A time-discrete model for dynamic fracture based on crack regularization, International Journal of Fracture, vol.14, issue.1, p.133143, 2011. ,
DOI : 10.1007/s10704-010-9562-x
Approximation of Free Discontinuity Problems, 1998. ,
?-Convergence for Beginners, 2002. ,
DOI : 10.1093/acprof:oso/9780198507840.001.0001
Gradient enhanced damage for quasi-brittle materials, 1996. ,
A method for multiple crack growth in brittle materials without remeshing, International Journal for Numerical Methods in Engineering, vol.41, issue.4, p.6117411770, 2004. ,
DOI : 10.1002/nme.1130
URL : https://hal.archives-ouvertes.fr/hal-01004845
Three-dimensional visualisation of fatigue cracks in metals using high resolution synchrotron x-ray micro-tomography, Materials science and technology, vol.22, issue.9, p.10191024, 2006. ,
In situ experiments with x ray tomography: an attractive tool for experimental mechanics, Experimental mechanics, vol.50, issue.3, p.289305, 2010. ,
Characterization of internal damage in a mmc p using x-ray synchrotron phase contrast microtomography ,
Energy minimizing brittle crack propagation, Journal of Elasticity, vol.52, issue.3, pp.201-238, 1999. ,
DOI : 10.1023/A:1007545213010
A phaseeld model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.70, pp.27652778-66, 2010. ,
Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, vol.33, issue.20-22, p.28992938, 1996. ,
DOI : 10.1016/0020-7683(95)00255-3
The inuence of the interphase and associated interfaces on the deection of matrix cracks in ceramic matrix composites, Composites Part A: Applied Science and Manufacturing, issue.11, p.3111791190, 2000. ,
The location of defects in structures from measurements of natural frequencies, The Journal of Strain Analysis for Engineering Design, vol.1, issue.2, p.4957, 1979. ,
DOI : 10.1243/03093247V142049
Comparison of a phase-eld model and of a thick level set model for brittle and quasi-brittle fracture, International Journal for Numerical Methods in Engineering, p.61, 2015. ,
Some issues in the application of cohesive zone models for metalceramic interfaces, International Journal of Solids and Structures, vol.39, issue.10, p.28272855, 2002. ,
Analyse expérimentale et modélisation micromécaniques du comportement élastique et de l'endommagement de composites SiC/SiC unidirectionnels, Ecole Polytechnique X, 2011. ,
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, pp.101013-2014 ,
DOI : 10.1115/1.4028106
A non-local model with tension and compression damage mechanisms, European Journal of Mechanics - A/Solids, vol.20, issue.1, p.122, 2001. ,
DOI : 10.1016/S0997-7538(00)01111-6
Comparison of two forms of strain decomposition in an elastic -plastic damaging model for concrete. Modelling and Simulation in, Materials Science and Engineering, vol.15, issue.4, p.405, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00913304
An ecient way to perform the assembly of nite element matrices in matlab and octave, INRIA Research Report, 2013. ,
Automated crack identication for cement paste, Cement and concrete research, vol.25, issue.3, pp.605616-252, 1995. ,
Crack propagation and strain localization in metallic particulate-reinforced cementitious mortars, Materials & Design, vol.79, pp.1525-2015 ,
DOI : 10.1016/j.matdes.2015.04.038
Localized deformation induced by heterogeneities in porous carbonate analysed by multi-scale digital image correlation, Tectonophysics, vol.503, issue.1-2, pp.100116-100127, 2011. ,
DOI : 10.1016/j.tecto.2010.09.025
URL : https://hal.archives-ouvertes.fr/hal-00641788
Arbitrary branched and intersecting cracks with the extended nite element method, International Journal for Numerical Methods in Engineering, vol.48, p.17411760, 2000. ,
Evolving Discontinuities and Cohesive Fracture, Procedia IUTAM, vol.10, pp.125137-2014 ,
DOI : 10.1016/j.piutam.2014.01.014
An In-Situ X-Ray Microtomography Study of Split Cylinder Fracture in Cement-Based Materials, Experimental Mechanics, vol.33, issue.9, pp.1227-1235 ,
DOI : 10.1007/s11340-014-9875-1
An improved description of the exponential Xu and Needleman cohesive zone law for mixed-mode decohesion, Engineering Fracture Mechanics, vol.73, issue.9, p.12201234, 2006. ,
DOI : 10.1016/j.engfracmech.2005.12.006
Micro-CT characterization of variability in 3D textile architecture, Composites Science and Technology, vol.65, issue.13, p.19201930, 2005. ,
DOI : 10.1016/j.compscitech.2005.04.008
The arlequin method as a exible engineering design tool, International journal for numerical methods in engineering, vol.62, issue.11, p.14421462, 2005. ,
Micromechanical Applications of Digital Image Correlation Techniques, Interferometry in Speckle Light, p.6774, 2000. ,
DOI : 10.1007/978-3-642-57323-1_9
URL : https://hal.archives-ouvertes.fr/hal-00116114
Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, issue.2, p.100104, 1960. ,
DOI : 10.1016/0022-5096(60)90013-2
Thers-method for material failure simulations, International Journal for Numerical Methods in Engineering, vol.14, issue.11, p.1607, 2008. ,
DOI : 10.1002/nme.2134
3-dimensional X-ray microtomography, Science, vol.487, p.14391444, 1987. ,
Acoustic emission and velocities associated with the formation of compaction bands in sandstone, Journal of Geophysical Research, vol.95, issue.B11, p.111, 2006. ,
DOI : 10.1029/2005JB003854
Acoustic emissions monitoring during inelastic deformation of porous sandstone: comparison of three modes of deformation, Rock Physics and Natural Hazards, p.823841, 2009. ,
Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, vol.46, issue.8, p.13191342, 1998. ,
DOI : 10.1016/S0022-5096(98)00034-9
Damage, gradient of damage and principle of virtual power, International Journal of Solids and Structures, vol.33, issue.8 ,
DOI : 10.1016/0020-7683(95)00074-7
Dynamic Fracture Mechanics, 1990. ,
A Method for Crack Detection on a Concrete Structure, 18th International Conference on Pattern Recognition (ICPR'06), p.901904, 2006. ,
DOI : 10.1109/ICPR.2006.98
Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, vol.46, p.13191342, 1998. ,
Bond eects in high-strength silica fume concretes, ACI Materials Journal, vol.86, issue.5, 1989. ,
Fluorescent liquid replacement technique. a means of crack detection and water: binder ratio determination in high strength concretes, Cement and concrete research, vol.25, issue.5, p.10631074, 1995. ,
Non-planar 3D crack growth by the extended nite element and level sets-partii: level set update, International Journal for Numerical Methods in Engineering, vol.53, issue.11, p.256986, 2002. ,
The phenomena of rupture and ow in solids, Phil. Trans. Royal Soc. Lond. A, vol.221, p.163198, 1921. ,
On the energy release rate in quasistatic elastic crack propagation, J. Elasticity, vol.9, issue.2, p.187195, 1979. ,
Thermodynamics and the Grith's criterion for brittle fracture, International Journal of Solids and Structures, vol.15, p.553560, 1979. ,
Ultrasonic measurement of weld penetration, Welding Journal, vol.63, issue.9, pp.273-281, 1984. ,
Crack Detection Method for Drain by Using Directional Smoothing, IEEJ Transactions on Electronics, Information and Systems, vol.127, issue.2, p.241246, 2007. ,
DOI : 10.1541/ieejeiss.127.241
Coupling between experimental measurements and polycrystal nite element calculations for micromechanical study of metallic materials, International Journal of Plasticity, vol.23, issue.9, p.15121539, 2007. ,
Three-dimensional analysis of a tensile test on a propellant with digital volume correlation, Archives of Mechanics, vol.63, pp.5-6120, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00634714
Evaluating damage with digital image correlation: A. introductory remarks and detection of physical damage, Handbook of Damage Mechanics, pp.12551275-2014 ,
On the use of 3d images and 3d displacement measurements for the analysis of damage mechanisms in concrete-like materials, VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures, pp.112-2013 ,
URL : https://hal.archives-ouvertes.fr/hal-01385670
A phase eld model of dynamic fracture: Robust eld updates for the analysis of complex crack patterns, International Journal for Numerical Methods in Engineering, vol.93, pp.276301-2013 ,
3D multiscale crack propagation using the XFEM applied to a gas turbine blade, Computational Mechanics, vol.48, issue.11, pp.173188-2014 ,
DOI : 10.1007/s00466-013-0900-5
The extended finite element method for fracture in composite materials, International Journal for Numerical Methods in Engineering, vol.45, issue.5, pp.214-239, 2009. ,
DOI : 10.1002/nme.2259
Numerical modelling of discrete crack propagation in reinforced and plain concrete Fracture Mechanics of Concrete, p.171225, 1984. ,
Rock mechanics and engineering, pp.42-86, 1979. ,
Experimental study of the cracking behavior of specimens containing inclusions (under uniaxial compression), International Journal of Fracture, vol.20, issue.4, p.83102, 2010. ,
DOI : 10.1007/s10704-010-9457-x
Nonlocal models for damage and fracture: Comparison of approaches, International Journal of Solids and Structures, vol.35, issue.31-32, p.41334145, 1998. ,
DOI : 10.1016/S0020-7683(97)00306-5
Inelastic analysis of structures, 2002. ,
Eroding interface and improved tetrahedral element algorithms for high-velocity impact computations in three dimensions, International Journal of Impact Engineering, vol.5, issue.1-4, p.411421, 1987. ,
DOI : 10.1016/0734-743X(87)90057-1
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
Phase-Field Model of Mode III Dynamic Fracture, Physical Review Letters, vol.87, issue.4, p.45501, 2001. ,
DOI : 10.1103/PhysRevLett.87.045501
Detection and quantication of distributed damage in concrete using transient stress waves, ACI Materials Journal, vol.101, issue.4, 2004. ,
Fatigue crack growth simulation in heterogeneous material using s-version FEM, International Journal of Fatigue, vol.58, p.2014 ,
DOI : 10.1016/j.ijfatigue.2013.04.022
Fluorescent thin sections to observe the fracture zone in mortar, Cement and Concrete Research, vol.14, issue.3, p.339344, 1984. ,
DOI : 10.1016/0008-8846(84)90051-6
Finite-element simulation of the shear process using the element-kill method, Journal of Materials Processing Technology, vol.72, issue.1, p.129140, 1997. ,
DOI : 10.1016/S0924-0136(97)00144-1
Ultrasonic testing of materials, 1990. ,
A continuum phase eld model for fracture, Engineering Fracture Mechanics, vol.77, issue.18, p.36253634, 2010. ,
The Variational Approach to Fracture Mechanics. A??Practical Application to the French Panth??on in Paris, Journal of Elasticity, vol.36, issue.1-2, p.130, 2009. ,
DOI : 10.1007/s10659-009-9189-1
X-ray microtomography for fracture studies in cementbased materials, SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, pages 105113. International Society for Optics and Photonics, 1999. ,
Three-dimensional work of fracture for mortar in compression, Engineering Fracture Mechanics, vol.65, issue.2-3, p.223234, 2000. ,
DOI : 10.1016/S0013-7944(99)00124-1
Microstructure and fracture in three dimensions, Engineering Fracture Mechanics, vol.70, issue.7-8, p.911925, 2003. ,
DOI : 10.1016/S0013-7944(02)00157-1
Cracking, damage and fracture in four dimensions, Materials and Structures, vol.70, issue.7, p.357364, 2007. ,
DOI : 10.1617/s11527-006-9145-5
Characterization and modeling of void nucleation by interface decohesion in dual phase steels, Scripta Materialia, vol.63, issue.10, p.973976, 2010. ,
DOI : 10.1016/j.scriptamat.2010.07.021
URL : https://hal.archives-ouvertes.fr/hal-00523143
Validation of void growth models using X-ray microtomography characterization of damage in dual phase steels, Acta Materialia, vol.59, issue.20, p.75647573, 2011. ,
DOI : 10.1016/j.actamat.2011.08.046
Localization limiters in transient problems, International Journal of Solids and Structures, vol.24, issue.6, p.581597, 1988. ,
DOI : 10.1016/0020-7683(88)90059-5
Fracture mechanics parameters inuencing the mechanical properties of high-performance concrete, ACI Special Publication, vol.149, 1994. ,
Strength or toughness? A criterion for crack onset at a notch, European Journal of Mechanics - A/Solids, vol.21, issue.1, pp.6172-181, 2002. ,
DOI : 10.1016/S0997-7538(01)01184-6
Volumetric Digital Image Correlation Applied to X-ray Microtomography Images from Triaxial Compression Tests on Argillaceous Rock, Strain, vol.23, issue.3, p.133, 2007. ,
DOI : 10.1111/j.1475-1305.2007.00348.x
URL : https://hal.archives-ouvertes.fr/hal-00541503
Theoretical and computational numerical aspects of a thermodynamically consistent framework for geometrically linear gradient damage, Computer Methods in Applied Mechanics and Engineering, vol.190, p.65556576, 2001. ,
Crack closure and stress intensity factor measurements in nodular graphite cast iron using three-dimensional correlation of laboratory X-ray microtomography images, Acta Materialia, vol.57, issue.14, pp.4090-4101, 2009. ,
DOI : 10.1016/j.actamat.2009.05.005
URL : https://hal.archives-ouvertes.fr/hal-00410325
Inuence of closure on the 3d propagation of fatigue cracks in a nodular cast iron investigated by x-ray tomography and 3d volume correlation, Acta Materialia, issue.8, p.5829572967, 2010. ,
Experimental study of the inuence of eps particle size on the mechanical properties of eps lightweight concrete, Construction and Building Materials, vol.68, pp.227232-2014 ,
Gradient constitutive relations: numerical aspects and application to gradient damage, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.50-52, p.51915220, 2005. ,
DOI : 10.1016/j.cma.2004.12.016
URL : https://hal.archives-ouvertes.fr/hal-00089126
X-ray microtomographic studies of pore structure and permeability in portland cement concrete, Materials and Structures, vol.39, issue.103, pp.611620-611633, 2006. ,
Characterisation of 3d woven composite internal architecture and eect of compaction, Composites Part A: Applied Science and Manufacturing, vol.41, issue.7, p.872880, 2010. ,
Double pulse infrared thermography, NDT & E International, vol.37, issue.7, p.559564, 2004. ,
DOI : 10.1016/j.ndteint.2004.03.003
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.5664
An Introduction to ?-Convergence, 1993. ,
Identication of interlaminar fracture properties of a composite laminate using local full-eld kinematic measurements and nite element simulations, Composites Part A: Applied Science and Manufacturing, vol.49, pp.203213-2013 ,
Hild, and volume=36 number=1 pages=146154 year=2012 publisher=Elsevier S. Roux, journal=International Journal of Fatigue. Identication of a crack propagation law by digital image correlation ,
A numerical assessment of phase-eld models for brittle and cohesive fracture: ?-convergence and stress oscillations, European Journal of Mechanics-A/Solids, vol.52, issue.234, pp.7284-7317, 2015. ,
Estimation of stress intensity factor by digital image correlation, Engineering Fracture Mechanics, vol.28, issue.1, p.101112, 1987. ,
DOI : 10.1016/0013-7944(87)90124-X
Mechanisms of crack propagation in dry plaster, Journal of the European Ceramic Society, vol.23, issue.16, p.31053112, 2003. ,
DOI : 10.1016/S0955-2219(03)00094-3
URL : https://hal.archives-ouvertes.fr/hal-00587077
The partition of unity finite element method: Basic theory and applications, Computer Methods in Applied Mechanics and Engineering, vol.139, issue.1-4, pp.289-314, 1996. ,
DOI : 10.1016/S0045-7825(96)01087-0
Recent advances in the use of infrared thermography. Measurement science and technology, p.27, 2004. ,
Phase eld modeling of fracture in multi-physics problems. part ii. coupled brittle-to-ductile failure criteria and crack propagation in thermo-elasticplastic solids, Computer Methods in Applied Mechanics and Engineering, p.2014 ,
A phase eld model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.26, pp.27762778-27762809, 2010. ,
Algorithms for computation of stresses and elasticity moduli in terms of Seth-Hill's family of generalized strain tensors, Communications in Numerical Methods in Engineering, vol.139, issue.5, pp.337353-337378, 2001. ,
DOI : 10.1002/cnm.404
Phase eld modeling of fracture in rubbery polymers. part i: Finite elasticity coupled with brittle failure, Journal of the Mechanics and Physics of Solids, vol.65, pp.93113-2014 ,
Phase eld modeling of fracture in multi-physics problems. part i. balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids, Computer Methods in Applied Mechanics and Engineering, p.2014 ,
A phase eld model of electromechanical fracture, Journal of the Mechanics and Physics of Solids, vol.58, p.17161740, 2010. ,
Thermodynamically consistent phase-eld models of fracture: Variational principles and multi-eld FE implementations ,
Compressive behavior of an idealized EPS lightweight concrete: size effects and failure mode, Mechanics of Materials, vol.36, issue.11, pp.1031-1046, 2004. ,
DOI : 10.1016/j.mechmat.2003.08.004
Particle size eect on eps lightweight concrete compressive strength: experimental investigation and modelling, Mechanics of Materials, vol.39, issue.3, p.222240, 2007. ,
Particle size eect on eps lightweight concrete compressive strength: Experimental investigation and modelling, Mechanics of Materials, vol.39, p.222240, 2007. ,
A preliminary SEM study of crack propagation in mortar, Cement and Concrete Research, vol.10, issue.4, p.509519, 1980. ,
DOI : 10.1016/0008-8846(80)90095-2
Computation and analysis of image motion: A synopsis of current problems and methods, International Journal of Computer Vision, vol.7, issue.4, p.2955, 1996. ,
DOI : 10.1007/BF00131147
A nite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131150-61, 1999. ,
Non-planar 3d crack growth by the extended nite element and level set part i: Mechanical model, International Journal for Numerical Methods in Engineering, vol.53, issue.11, p.25492568, 2002. ,
A level set based model for damage growth: The thick level set approach, International Journal for Numerical Methods in Engineering, vol.61, issue.1, p.358380, 2011. ,
DOI : 10.1002/nme.3069
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
A Continuum Model for Void Nucleation by Inclusion Debonding, Journal of Applied Mechanics, vol.54, issue.3, p.525531, 1987. ,
DOI : 10.1115/1.3173064
Fracture analysis of concrete using scanning electron microscopy, Scanning, vol.30, issue.4, p.426430, 1997. ,
DOI : 10.1002/sca.4950190605
Analysis of compressive stress-induced cracks in concrete, ACI Materials Journal, vol.95, issue.5, 1998. ,
A phase-eld method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography, Computer Methods in Applied Mechanics and Engineering, p.2015 ,
A phase eld method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure, Engineering Fracture Mechanics, vol.139, pp.1839-1859, 2015. ,
On the choice of parameters in the phase eld method for simulating crack initiation with experimental validation, International Journal of Fracture, vol.197, issue.181, pp.213226-213259, 2016. ,
Finite-deformation irreversible cohesive elements for threedimensional crack-propagation analysis, International Journal for Numerical Methods in Engineering, vol.44, issue.9, p.12671282, 1999. ,
Geometric level set methods in imaging, vision, and graphics, 2003. ,
An eigenerosion approach to brittle fracture, International Journal for Numerical Methods in Engineering, vol.92, issue.8, pp.694714-2012 ,
Anisotropic damage model for the multiaxial static and fatigue behaviour of plain concrete, Engineering Fracture Mechanics, vol.55, issue.2, p.163179, 1996. ,
DOI : 10.1016/0013-7944(96)00004-5
Using x-ray tomography to image cracks in cement pastes, Proc., Int. Conf. on High-Performance Fiber-Reinforced Concrete Composites (HPFRCC), page 8, 2007. ,
Localisation issues in local and nonlocal continuum approaches to fracture, European Journal of Mechanics - A/Solids, vol.21, issue.2, p.175189, 2002. ,
DOI : 10.1016/S0997-7538(02)01211-1
GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS, International Journal for Numerical Methods in Engineering, vol.23, issue.19, p.33913403, 1996. ,
DOI : 10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D
The variational approach to damage: I. the foundations, C. R. Mecanique, vol.338, 2010. ,
Finite element analysis of deformation of strain-softening materials, International Journal for Numerical Methods in Engineering, vol.105, issue.3, p.327334, 1981. ,
DOI : 10.1002/nme.1620170303
Nonlocal Damage Theory, Journal of Engineering Mechanics, vol.113, issue.10, p.15121533, 1987. ,
DOI : 10.1061/(ASCE)0733-9399(1987)113:10(1512)
A review of non local continuum damage: Modelling of failure? Networks and Heterogeneous Media, pp.575597-2014 ,
Identication algorithm for fracture parameters by combining dic and fem approaches, International journal of fracture, vol.170, issue.2, p.101114, 2011. ,
Advanced waveform-based acoustic emission detection of matrix cracking in composites, Materials evaluation, vol.53, issue.9, p.10521058, 1995. ,
Orthotropic behavior of concrete with directional aspects: modelling and experiments, Nuclear Engineering and Design, vol.133, issue.1, p.97111, 1992. ,
DOI : 10.1016/0029-5493(92)90094-C
Analysis of reinforced concrete pressure vessels, Nucl. Eng. Des, vol.7, p.334344, 1968. ,
Scanning Electron Microscopy: Physics of Image Formation and Microanalysis, Second Edition, Measurement Science and Technology, vol.11, issue.12, p.1826, 2000. ,
DOI : 10.1088/0957-0233/11/12/703
Two-dimensional x-ray ct image based mesoscale fracture modelling of concrete, Engineering Fracture Mechanics, vol.133, pp.2439-2015 ,
Estimation of mixed-mode stress intensity factors using digital image correlation and an interaction integral, International Journal of Fracture, vol.132, issue.1, p.6579, 2005. ,
Extended three-dimensional digital image correlation (x3d-dic) Comptes Rendus Mécanique, p.643649, 2008. ,
Measure of texture anisotropy for crack detection on textured surfaces, Electronics Letters, vol.32, issue.14, p.12741275, 1996. ,
DOI : 10.1049/el:19960872
Rupture en compression des structures hétérogènes à base de matériaux quasifragiles, 2013. ,
Detection of crack onset in double cleavage drilled specimens of plaster under compression by digital image correlationtheoretical predictions based on a coupled criterion, European Journal of Mechanics - A/Solids, vol.51, issue.110, pp.172182-2015 ,
Computational modeling of concrete fracture ,
Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches, International Journal of Fracture, vol.40, issue.1, pp.141157-141169, 2006. ,
DOI : 10.1007/s10704-006-6631-2
URL : https://hal.archives-ouvertes.fr/hal-00013818
Three-dimensional image correlation from X-ray computed tomography of solid foam, Composites Part A: Applied Science and Manufacturing, vol.39, issue.8, p.12531265, 2008. ,
DOI : 10.1016/j.compositesa.2007.11.011
URL : https://hal.archives-ouvertes.fr/hal-01006730
Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks, Journal of Physics D: Applied Physics, vol.42, issue.21, pp.214004-214018, 2009. ,
DOI : 10.1088/0022-3727/42/21/214004
URL : https://hal.archives-ouvertes.fr/hal-00381646
Iterative methods for sparse linear systems. Siam, 2003. ,
Slow crack growth study of plaster using the double torsion method, Ceramics International, vol.26, issue.4, p.435439, 2000. ,
DOI : 10.1016/S0272-8842(99)00078-4
Applications of pulse heating thermography and lock-in thermography to quantitative nondestructive evaluations, Infrared Physics & Technology, vol.43, issue.3-5, p.211218, 2002. ,
DOI : 10.1016/S1350-4495(02)00141-X
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, p.273286, 2003. ,
DOI : 10.1016/S0168-583X(02)01689-0
URL : https://hal.archives-ouvertes.fr/hal-00475146
The failure of brittle porous solids under compressive stress states, Acta Metallurgica, vol.34, issue.3, p.51126, 1986. ,
DOI : 10.1016/0001-6160(86)90087-8
Predicting the permeability of trabecular bone by micro-computed tomography and nite element modeling, The Journal of Biochemistry, vol.47, pp.31293134-2014 ,
X-ray computed microtomography of internal damage in ber reinforced polymer matrix composites, Composites Science and Technology, issue.14, p.6520712078, 2005. ,
Phase eld approximation of dynamic brittle fracture, Computational Mechanics, vol.54, issue.5, pp.11411161-2014 ,
Eigenfracture: An Eigendeformation Approach to Variational Fracture, Multiscale Modeling & Simulation, vol.7, issue.3, p.12371266, 2009. ,
DOI : 10.1137/080712568
Systematic errors in digital image correlation due to undermatched subset shape functions, Experimental Mechanics, vol.41, issue.1, p.303310, 2002. ,
DOI : 10.1007/BF02410987
Digital volume correlation including rotational degrees of freedom during minimization, Experimental Mechanics, vol.48, issue.10, p.272278, 2002. ,
DOI : 10.1007/BF02410982
Specimen preparation and image processing and analysis techniques for automated quantication of concrete microcracks and voids, Cement and concrete Research, vol.33, issue.12, 2003. ,
X-ray tomography for evaluation of damage in concrete bond, 2006. ,
Initiation and propagation of compaction bands in dry and wet bentheim sandstone, Rock Physics and Natural Hazards, p.846868, 2009. ,
Computed tomography part III: Volumetric, High-Resolution X-Ray analysis of fatigue crack closure, JOM, vol.51, issue.1, p.1923, 1995. ,
DOI : 10.1007/BF03221124
Epoxy impregnation of hardened cement for microstructural characterization, Journal of Materials Science Letters, vol.114, issue.6, p.632634, 1989. ,
DOI : 10.1007/BF01730426
Fast in-situ X-ray micro tomography characterisation of microstructural evolution and strain-induced damage in alloys at various temperatures, International Journal of Materials Research, vol.101, issue.9, pp.1080-1088 ,
DOI : 10.3139/146.110386
Arbitrary branched and intersecting cracks with the extended nite element method, International Journal for Numerical Methods in Engineering, vol.48, p.17411760, 2000. ,
Extended nite element method for three-dimensional crack modelling, International Journal for Numerical Methods in Engineering, vol.48, p.15491570, 2000. ,
Measuring Microscopic Deformations with Digital Image Correlation, Optics and Lasers in Engineering, vol.27, issue.4, p.409428, 1997. ,
DOI : 10.1016/S0143-8166(96)00041-3
Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications, 2009. ,
Determination of displacements using an improved digital correlation method, Image and Vision Computing, vol.1, issue.3, p.133139, 1983. ,
DOI : 10.1016/0262-8856(83)90064-1
Elastic crack growth in nite elements with minimal remeshing. International Advances in Surgical OncologyJournal for Numerical Methods in Engineering, p.601620, 1999. ,
Modeling of compression-induced splitting failure in heterogeneous brittle porous solids, Engineering Fracture Mechanics, vol.72, issue.4, pp.597615-597660, 2005. ,
DOI : 10.1016/j.engfracmech.2004.04.008
A gradient approach to localization of deformation. I. Hyperelastic materials, Journal of Elasticity, vol.5, issue.3, p.225237, 1986. ,
DOI : 10.1007/BF00040814
Micro-nite element modelling of oke blends using x-ray microtomography, Fuel, vol.87, pp.13-1429832987, 2008. ,
Computerized tomography and C-Scan for measuring delamination in the drilling of composite materials using various drills, International Journal of Machine Tools and Manufacture, vol.45, issue.11, p.12821287, 2005. ,
DOI : 10.1016/j.ijmachtools.2005.01.009
Model studies of bre breakage and debonding in a metal reinforced by short bres, Journal of the Mechanics and Physics of Solids, vol.41, issue.8, p.13091326, 1993. ,
The inuence of plasticity on mixed mode interface toughness, Journal of the Mechanics and Physics of Solids, vol.41, issue.6, p.11191135, 1993. ,
A digital image correlation method for fatigue test experiments, Optics and Lasers in Engineering, vol.47, issue.3-4, p.371378, 2009. ,
DOI : 10.1016/j.optlaseng.2008.03.016
Vector level-sets for description of propagating cracks in nite elements, International Journal for Numerical Methods in Engineering, vol.58, issue.10, p.157192, 2003. ,
A phase-eld model for cohesive fracture, International Journal for Numerical Methods in Engineering, vol.96, pp.4362-2013 ,
A phase-eld model for cohesive fracture, International Journal for numerical methods in Engineering, vol.96, issue.7, pp.4362-2013 ,
A three-dimensional digital image correlation technique for strain measurements in microstructures, Journal of Biomechanics, vol.37, issue.9, p.13131320, 2004. ,
DOI : 10.1016/j.jbiomech.2003.12.036
Phase-eld models for brittle and cohesive fracture, Meccanica, vol.49, issue.11, pp.25872601-2014 ,
In situ compressive damage of cement paste characterized by lab source X-ray computer tomography, Materials Characterization, vol.82, pp.3240-2013 ,
DOI : 10.1016/j.matchar.2013.05.004
micro-mechanical experimental investigation and modelling of strain and damage of argillaceous rocks under combined hydric and mechanical loads, 2012. ,
On the mechanical modeling of functionally graded interfacial zone with a grith crack: plane deformation, International journal of fracture, vol.125, issue.1, p.189205, 2004. ,
A new method for modelling cohesive cracks using nite elements, International Journal for Numerical Methods in Engineering, vol.50, issue.82, pp.26672682-83, 2001. ,
Listening to the sound of materials: Acoustic emission for the analysis of material behaviour, NDT & E International, vol.30, issue.2, p.99106, 1997. ,
DOI : 10.1016/S0963-8695(96)00051-5
Crack opening displacements during fatigue crack growth in tisic bre metal matrix composites by x-ray tomography, Materials science and technology, vol.22, issue.9, p.10521058, 2006. ,
Experimental and numerical study on splitting failure of brittle solids containing single pore under uniaxial compression, Mechanics of Materials, vol.38, issue.1-2, p.142159, 2006. ,
DOI : 10.1016/j.mechmat.2005.05.017
Ultra high resolution computed tomography of damage in notched carbon berepoxy composites, Journal of Composite Materials, vol.42, issue.19, 2008. ,
Numerical simulations of fast crack growth in brittle solids, Journal of the Mechanics and Physics of Solids, vol.42, issue.9, p.13971434, 1994. ,
DOI : 10.1016/0022-5096(94)90003-5
Optimized optical setup for DIC in rock mechanics, EPJ Web of Conferences, pp.22019-121, 2010. ,
DOI : 10.1051/epjconf/20100622019
URL : https://hal.archives-ouvertes.fr/hal-00545562
Damage assessment and reliability evaluation of existing structures, Engineering Structures, vol.1, issue.5, p.245251, 1979. ,
DOI : 10.1016/0141-0296(79)90005-1
A fast method for solving microstructural problems dened by digital images: a space lippmann-schwinger scheme, International Journal for Numerical Methods in Engineering, vol.92, issue.2, pp.178205-2012 ,
Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency, International Journal for Numerical Methods in Engineering, vol.59, issue.1, p.124, 2004. ,
DOI : 10.1002/nme.857
A method for growing multiple cracks without remeshing and its application to fatigue crack growth, Modelling and Simulation in Materials Science and Engineering, vol.12, issue.5, p.901, 2004. ,
DOI : 10.1088/0965-0393/12/5/009