Coupled multi-scale cohesive modeling of failure in heterogeneous adhesives, International Journal for Numerical Methods in Engineering, vol.84, issue.8, pp.916-946, 2010. ,
Homogenization-based multiscale crack modelling: from micro-diffusive damage to macro-cracks, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.9, pp.1220-1236, 2011. ,
A multiscale projection method for macro/microcrack simulations, International Journal for Numerical Methods in Engineering, vol.71, issue.12, pp.1466-1482, 2007. ,
Multiscale simulation of major crack/minor cracks interplay with the corrected XFEM. Archives of Civil and Mechanical Engineering, vol.17, pp.410-418, 2017. ,
A multi-scale approach to bridge microscale damage and macroscale failure: a nested computational homogenization-localization framework, International journal of fracture, vol.178, issue.1-2, pp.157-178, 2012. ,
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
Domain decomposition method for crack problems with nonpenetration condition, ESAIM Mathematical Modelling and Numerical Analysis, vol.50, pp.995-1009, 2016. ,
Phase field modeling of fracture in anisotropic brittle solids, Int. J. Nonlinear Mech, vol.97, pp.1-21, 2017. ,
An adaptive domain decomposition preconditioner for crack propagation problems modeled by XFEM, Journal for Multiscale Computational Engineering, vol.11, issue.6, pp.633-654, 2013. ,
Effective toughness of heterogeneous media, Journal of the Mechanics and Physics of Solids, vol.71, pp.15-32, 2014. ,
Identification of fracture models based on phase field for crack propagation in heterogeneous lattices in a context of non-separated scales, Computational Mechanics, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-02265335
Fracture and Size Effect in Concrete and Other Quasibrittle Materials, 1998. ,
,
, Probabilistic Nonlocal Theory for Quasibrittle Fracture Initiation and Size Effect. I: Theory, Journal of Engineering Mechanics, vol.126, issue.2, pp.166-174, 2000.
Experimental investigation of size effect in concrete and sandstone under uniaxial tension, Engineering Fracture Mechanics, vol.65, issue.2, pp.165-188, 2000. ,
Scaling strength distributions in quasi-brittle materials from micro-to macro-scales: A computational approach to modeling Nature-inspired structural ceramics, Journal of the Mechanics and Physics of Solids, vol.68, pp.93-106, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01196360
Modeling the effect of mesoscale randomness on concrete fracture, Probabilistic Engineering Mechanics, vol.21, issue.3, pp.217-225, 2006. ,
Predicting variability in the dynamic failure strength of brittle materials considering pre-existing flaws, Journal of the Mechanics and Physics of Solids, vol.59, issue.2, pp.297-319, 2011. ,
Stochastic multiscale fracture analysis of three-dimensional functionally graded composites, Engineering Fracture Mechanics, vol.78, issue.1, pp.27-46, 2011. ,
Voronoi tessellation based statistical volume element characterization for use in fracture modeling, Computer Methods in Applied Mechanics and Engineering, vol.336, pp.135-155, 2018. ,
Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, vol.46, issue.8, pp.1319-1342, 1998. ,
Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, vol.48, issue.4, pp.797-826, 2000. ,
The variational approach to fracture, Journal of elasticity, vol.91, issue.1-3, pp.5-148, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00551079
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, vol.199, pp.2765-2778, 2010. ,
Optimal approximations by piecewise smooth functions and associated variational problems. Communications on pure and applied mathematics, vol.42, pp.577-685, 1989. ,
Approximation of functional depending on jumps by elliptic functional via t-convergence, Communications on Pure and Applied Mathematics, vol.43, issue.8, pp.999-1036, 1990. ,
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, 2014. ,
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. ,
The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models, Journal of the Mechanics and Physics of Solids, vol.59, issue.6, pp.1163-1190, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00578995
On the choice of parameters in the phase field method for simulating crack initiation with experimental validation, International Journal of Fracture, vol.197, issue.2, pp.213-226, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01258035
On degradation functions in phase field fracture models, Computational Materials Science, vol.108, pp.374-384, 2015. ,
Comment on "packing hyperspheres in high-dimensional Euclidean spaces, Physical Review E -Statistical, Nonlinear, and Soft Matter Physics, vol.75, issue.4, 2007. ,
,
, Microstructural Randomness and Scaling in Mechanics of Materials, 2008.
A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales, International Journal of Solids and Structures, vol.51, issue.1, pp.196-209, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00880393
Macroscopically consistent non-local modeling of heterogeneous media, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.218-238, 2014. ,
Stochastic modeling of mesoscopic elasticity random field, Mechanics of Materials, vol.93, pp.1-12, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01226337
Random field models of heterogeneous materials, International Journal of Solids and Structures, vol.35, pp.2429-2455, 1998. ,
Application of variational concepts to size effects in elastic heterogeneous bodies, Journal of the Mechanics and Physics of Solids, vol.38, issue.6, pp.813-841, 1990. ,
Order relationships for boundary condition effect in heterogeneous bodies smaller than the representative volume, Journal of the Mechanics and Physics of Solids, vol.42, issue.12, pp.1995-2011, 1994. ,
Non-Gaussian simulation of local material properties based on a moving-window technique, Probabilistic Engineering Mechanics, vol.18, issue.3, pp.223-234, 2003. ,
Stochastic modeling of anisotropy in multiscale analysis of heterogeneous materials: A comprehensive overview on random matrix approaches, Mechanics of Materials, vol.44, pp.35-46, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00684288
Stochastic model and generator for random fields with symmetry properties: Application to the mesoscopic modeling of elastic random media, SIAM Multiscale Modeling & Simulation, vol.11, pp.840-870, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00854121
On the statistical dependence for the components of random elasticity tensors exhibiting material symmetry properties, Journal of Elasticity, vol.111, pp.109-130, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00724048
Stochastic modeling and generation of random fields of elasticity tensors: A unified information-theoretic approach, Comptes Rendus Mécanique, vol.345, issue.6, pp.399-416, 2017. ,
Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial derivative operators, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.26-64, 2006. ,
, Non-Gaussian Random Fields in Multiscale Mechanics of Heterogeneous Materials:1-9, 2017.
A random field formulation of Hooke's law in all elasticity classes, Journal of Elasticity, vol.127, issue.2, pp.269-302, 2017. ,
Statistical inference with bivariate gamma distributions, BiometrikaTrust, vol.56, pp.627-634, 1969. ,
An overview of nonintrusive characterization, propagation, and sensitivity analysis of uncertainties in computational mechanics, International Journal for Uncertainty Quantification, vol.4, issue.5, 2014. ,
A probabilistic multiscale framework for crack propagation in random heterogeneous medium, IJMNE, year, vol.00, pp.1-6, 2016. ,