On the mechanical characterization of compact bone structure using the homogenization theory, Journal of Biomechanics, vol.29, issue.12, pp.1539-1547, 1996. ,
DOI : 10.1016/S0021-9290(96)80005-4
Relevance of 2d radiographic texture analysis for the assessment of 3d bone micro-architecture, Med Phys, vol.33, issue.9, pp.3546-3556, 2006. ,
Stochastic Differential Equations : Theory and Applications, 1973. ,
The use of micro-CT to evaluate cortical bone geometry and strength in nude rats: Correlation with mechanical testing, pQCT and DXA, Bone, vol.38, issue.1, pp.136-144, 2006. ,
DOI : 10.1016/j.bone.2005.07.028
Stochastic multi-scale prediction on the apparent elastic moduli of trabecular bone considering uncertainties of biological apatite (BAp) crystallite orientation and image-based modelling, Computer Methods in Biomechanics and Biomedical Engineering, vol.6, issue.5, pp.162-174, 2015. ,
DOI : 10.1142/S0219519412500923
High-Resolution Bone Imaging for Osteoporosis Diagnostics and Therapy Monitoring Using Clinical MDCT and MRI, Current Medicinal Chemistry, vol.20, issue.38, pp.204844-4852, 2013. ,
DOI : 10.2174/09298673113206660279
Regional differences in cortical porosity in the fractured femoral neck, Bone, vol.24, issue.1, pp.57-64, 1999. ,
DOI : 10.1016/S8756-3282(98)00143-4
Transmission scanning acoustic imaging of human cortical bone and relation with the microstructure, Clinical Biomechanics, vol.19, issue.6, pp.639-647, 2004. ,
DOI : 10.1016/j.clinbiomech.2004.02.009
Spatial distribution of acoustic and elastic properties of human femoral cortical bone, Journal of Biomechanics, vol.37, issue.4, pp.503-510, 2004. ,
DOI : 10.1016/j.jbiomech.2003.09.013
URL : https://hal.archives-ouvertes.fr/hal-00023425
Intravoxel bone micromechanics for microCT-based finite element simulations, Journal of Biomechanics, vol.46, issue.15, pp.2710-2721, 2013. ,
DOI : 10.1016/j.jbiomech.2013.06.036
URL : http://doi.org/10.1016/j.jbiomech.2013.06.036
The Degree of Mineralization of Bone Tissue Measured by Computerized Quantitative Contact Microradiography, Calcified Tissue International, vol.70, issue.6, pp.503-511, 2002. ,
DOI : 10.1007/s00223-001-2048-0
Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation, Journal of Biomechanics, vol.37, issue.5, pp.613-621, 2004. ,
DOI : 10.1016/j.jbiomech.2003.10.002
Distribution of Intracortical Porosity in Human Midfemoral Cortex by Age and Gender, Journal of Bone and Mineral Research, vol.26, issue.7, pp.1308-1317, 2001. ,
DOI : 10.1148/radiology.217.1.r00se11179
Cortical Bone in the Human Femoral Neck: Three-Dimensional Appearance and Porosity Using Synchrotron Radiation, Journal of Bone and Mineral Research, vol.24, issue.5, pp.794-801, 2004. ,
DOI : 10.2106/00004623-195840020-00015
Bone quality: where do we go from here?, Osteoporosis International, vol.14, issue.0, pp.118-127, 2003. ,
DOI : 10.1007/s00198-003-1489-x
Guidelines for assessment of bone microstructure in rodents using micro-computed tomography, Journal of Bone and Mineral Research, vol.22, issue.7, pp.251468-1486, 2010. ,
DOI : 10.1002/jbm.a.31142
Material and compositional properties of selectively demineralized cortical bone, Journal of Biomechanics, vol.28, issue.11, pp.1357-1368, 1995. ,
DOI : 10.1016/0021-9290(94)00184-6
High-resolution Computed Tomography for Clinical Imaging of Bone Microarchitecture, Clinical Orthopaedics and Related Research??, vol.375, issue.Suppl, pp.2179-2193, 2011. ,
DOI : 10.1016/S0140-6736(10)60320-0
Bone quality: understanding what matters, J. Musculoskelet. Neuronal Interact, vol.4, issue.2, pp.184-186, 2004. ,
Comparison of synchrotron radiation and conventional x-ray microcomputed tomography for assessing trabecular bone microarchitecture of human femoral heads, Medical Physics, vol.46, issue.9, pp.3568-3577, 2006. ,
DOI : 10.1109/TMI.2002.1000259
URL : https://hal.archives-ouvertes.fr/hal-00443183
Intracapsular Hip Fracture and the Region-Specific Loss of Cortical Bone: Analysis by Peripheral Quantitative Computed Tomography, Journal of Bone and Mineral Research, vol.27, issue.Suppl 1, pp.1318-1328, 2001. ,
DOI : 10.1007/BF02508641
The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone, Journal of Biomechanics, vol.21, issue.2, pp.131-139, 1988. ,
DOI : 10.1016/0021-9290(88)90006-1
Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone, Journal of Biomechanics, vol.42, issue.13, pp.422061-2067, 2009. ,
DOI : 10.1016/j.jbiomech.2009.06.002
Non Uniform Random Variate Generation, 1986. ,
DOI : 10.1007/978-1-4613-8643-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.8896
Prediction of Cortical Bone Elastic Constants by a Two-Level Micromechanical Model Using a Generalized Self-Consistent Method, Journal of Biomechanical Engineering, vol.128, issue.3, pp.309-316, 2006. ,
DOI : 10.1115/1.2187039
Assessment of bone fragility with clinical imaging modalities, Hard Tissue, vol.2, issue.1, p.7, 2013. ,
DOI : 10.13172/2050-2303-2-1-351
Methods for Assessing Bone Quality: A Review, Clinical Orthopaedics and Related Research??, vol.20, issue.Suppl 1, pp.2128-2138, 2011. ,
DOI : 10.1007/s00198-009-0854-9
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3126959
To what extent can cortical bone millimeter-scale elasticity be predicted by a two-phase composite model with variable porosity?, Acta Biomaterialia, vol.12, pp.207-215, 2015. ,
DOI : 10.1016/j.actbio.2014.10.011
URL : https://hal.archives-ouvertes.fr/hal-01126647
A determination of the minimum sizes of representative volume elements for the prediction of cortical bone elastic properties, Biomechanics and Modeling in Mechanobiology, vol.23, issue.2???3, pp.925-937, 2011. ,
DOI : 10.1007/978-3-540-32360-0
A two-parameter model of the effective elastic tensor for cortical bone, Journal of Biomechanics, vol.44, issue.8, pp.1621-1625, 2011. ,
DOI : 10.1016/j.jbiomech.2011.03.006
Modeling of Femoral Neck Cortical Bone for the Numerical Simulation of Ultrasound Propagation, Ultrasound in Medicine & Biology, vol.40, issue.5, pp.1015-1026, 2014. ,
DOI : 10.1016/j.ultrasmedbio.2013.11.010
Integrated Imaging Approach to Osteoporosis: State-of-the-Art Review and Update, RadioGraphics, vol.31, issue.5, pp.311343-1364, 2011. ,
DOI : 10.1148/rg.315105712
Probabilistic modeling of apparent tensors in elastostatics: A MaxEnt approach under material symmetry and stochastic boundedness constraints, Probabilistic Engineering Mechanics, vol.28, pp.118-124, 2012. ,
DOI : 10.1016/j.probengmech.2011.07.004
URL : https://hal.archives-ouvertes.fr/hal-00686132
On the Statistical Dependence for the Components of Random Elasticity Tensors Exhibiting Material Symmetry Properties, Journal of Elasticity, vol.21, issue.5, pp.109-130, 2013. ,
DOI : 10.1016/S0065-2156(08)70332-6
URL : https://hal.archives-ouvertes.fr/hal-00724048
Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media, Multiscale Modeling & Simulation, vol.11, issue.3, pp.840-870, 2013. ,
DOI : 10.1137/120898346
URL : https://hal.archives-ouvertes.fr/hal-00854121
A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.17-20, pp.17-201637, 2011. ,
DOI : 10.1016/j.cma.2011.01.016
URL : https://hal.archives-ouvertes.fr/hal-00684305
Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: Application to axial transmission, The Journal of the Acoustical Society of America, vol.125, issue.6, pp.4043-4052, 2009. ,
DOI : 10.1121/1.3117445
URL : https://hal.archives-ouvertes.fr/hal-00711923
Equivalent contributing depth investigated by a lateral wave with axial transmission in viscoelastic cortical bone, The Journal of the Acoustical Society of America, vol.129, issue.4, pp.114-120, 2011. ,
DOI : 10.1121/1.3554719
URL : https://hal.archives-ouvertes.fr/hal-00692844
Measure Theory, 1976. ,
DOI : 10.1007/978-1-4684-9440-2
Measurement of Forearm Bone Mineral Density: Comparison of Precision of Five Different Instruments, Calcified Tissue International, vol.62, issue.5, pp.383-387, 1998. ,
DOI : 10.1007/s002239900449
Cortical and trabecular bone in the femoral neck both contribute to proximal femur failure load prediction, Osteoporosis International, vol.22, issue.3, pp.445-453, 2009. ,
DOI : 10.4135/9781412985604
Radial Anatomic Variation of Ultrasonic Velocity in Human Cortical Bone, Ultrasound in Medicine & Biology, vol.39, issue.11, pp.392185-2193, 2013. ,
DOI : 10.1016/j.ultrasmedbio.2013.06.005
Relation between age, femoral neck cortical stability, and hip fracture risk, The Lancet, vol.366, issue.9480, pp.129-135, 2005. ,
DOI : 10.1016/S0140-6736(05)66870-5
Influence of viscoelastic and viscous absorption on ultrasonic wave propagation in cortical bone: Application to axial transmission, The Journal of the Acoustical Society of America, vol.127, issue.4, pp.2622-2634, 2010. ,
DOI : 10.1121/1.3353091
URL : https://hal.archives-ouvertes.fr/hal-00684320
Micromechanis: overall properties of heterogeneous materials Applied Mathematics and Mechanics, 1999. ,
In vivo assessment of trabecular and cortical bone microstructure, Clin Calcium, vol.21, issue.7, pp.1011-1019, 2011. ,
Quantification of the degree of mineralization of bone in three dimensions using synchrotron radiation microtomography, Medical Physics, vol.48, issue.11, pp.2672-2681, 2002. ,
DOI : 10.1109/23.940176
Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone, Biomechanics and Modeling in Mechanobiology, vol.32, issue.12, pp.883-901, 2012. ,
DOI : 10.1016/S0021-9290(99)00111-6
URL : https://hal.archives-ouvertes.fr/hal-00844608
Micro-CT examination of human bone: from biopsies towards the entire organ, Ann. Ist. Super. Sanita, vol.48, issue.1, pp.75-82, 2012. ,
Human cortical bone: the SiNuPrOs model, Computer Methods in Biomechanics and Biomedical Engineering, vol.14, issue.2, pp.169-187, 2008. ,
DOI : 10.1016/0021-9290(92)90286-A
URL : https://hal.archives-ouvertes.fr/hal-00485237
Elastic anisotropy of bone lamellae as a function of fibril orientation pattern, Biomechanics and Modeling in Mechanobiology, vol.32, issue.10, pp.67-77, 2011. ,
DOI : 10.1016/S0021-9290(99)00111-6
Mechanical properties and the hierarchical structure of bone, Medical Engineering & Physics, vol.20, issue.2, pp.92-102, 1998. ,
DOI : 10.1016/S1350-4533(98)00007-1
Instrumental diagnosis of osteoporosis, Aging Clinical and Experimental Research, vol.36, issue.Suppl.1, pp.240-248, 1998. ,
DOI : 10.1093/rheumatology/36.1.43
Simulation and the Monte Carlo Method, 1981. ,
Rate form of the Eshelby and Hill tensors, International Journal of Solids and Structures, vol.39, issue.21-22, pp.5659-5678, 2002. ,
DOI : 10.1016/S0020-7683(02)00369-4
Nanobiomechanics of Repair Bone Regenerated by Genetically Modified Mesenchymal Stem Cells, Tissue Engineering Part A, vol.14, issue.10, pp.141709-1720, 2008. ,
DOI : 10.1089/ten.tea.2007.0241
Age-related hypermineralization in the female proximal human femur, The Anatomical Record, vol.241, issue.2, pp.202-211, 1999. ,
DOI : 10.1179/his.1997.20.3.209
Are Subject-Specific Musculoskeletal Models Robust to the Uncertainties in Parameter Identification?, PLoS ONE, vol.33, issue.11, pp.9-112625, 2014. ,
DOI : 10.1371/journal.pone.0112625.s001
Investigation of the three-dimensional orientation of mineralized collagen fibrils in human lamellar bone using synchrotron X-ray phase nano-tomography, Acta Biomaterialia, vol.9, issue.9, pp.8118-8127, 2013. ,
DOI : 10.1016/j.actbio.2013.05.015
Nanoindentation Measurements of Biomechanical Properties in Mature and Newly Formed Bone Tissue Surrounding an Implant, Journal of Biomechanical Engineering, vol.134, issue.2, p.21007, 2012. ,
DOI : 10.1115/1.4005981
URL : https://hal.archives-ouvertes.fr/hal-00743684
Evolution of bone biomechanical properties at the micrometer scale around titanium implant as a function of healing time, Physics in Medicine and Biology, vol.59, issue.6, pp.1389-1406, 2014. ,
DOI : 10.1088/0031-9155/59/6/1389
URL : https://hal.archives-ouvertes.fr/hal-01082371
Deriving tissue density and elastic modulus from microCT bone scans, Bone, vol.49, issue.5, pp.931-938, 2011. ,
DOI : 10.1016/j.bone.2011.07.021
Distribution of longitudinal wave properties in bovine cortical bone in vitro, Ultrasonics, vol.44, pp.233-237, 2006. ,
DOI : 10.1016/j.ultras.2006.06.055
Size-dependent heterogeneity benefits the mechanical performance of bone, Journal of the Mechanics and Physics of Solids, vol.59, issue.1, pp.64-74, 2011. ,
DOI : 10.1016/j.jmps.2010.09.012
The estimated elastic constants for a single bone osteonal lamella, Biomechanics and Modeling in Mechanobiology, vol.32, issue.1, pp.1-11, 2008. ,
DOI : 10.1007/BF00369213
An estimate of anisotropic poroelastic constants of an osteon, Biomechanics and Modeling in Mechanobiology, vol.120, issue.1, pp.13-26, 2008. ,
DOI : 10.1007/978-1-4757-2968-9
Intracortical remodelling and porosity in the distal radius and post-mortem femurs of women: a cross-sectional study, The Lancet, vol.375, issue.9727, pp.3751729-1736, 2010. ,
DOI : 10.1016/S0140-6736(10)60320-0
Information Theory and Statistical Mechanics, Physical Review, vol.101, issue.4, pp.171-190, 1957. ,
DOI : 10.1103/PhysRev.101.1227
The effects of interphase and bonding on the elastic modulus of bone: changes with age-related osteoporosis, Medical Engineering & Physics, vol.22, issue.8, pp.575-585, 2000. ,
DOI : 10.1016/S1350-4533(00)00075-8
Developing CT based computational models of pediatric femurs, Journal of Biomechanics, vol.48, issue.10, pp.2034-2040, 2015. ,
DOI : 10.1016/j.jbiomech.2015.03.027
Quantification of the degree of mineralization of bone in three dimensions using synchrotron radiation microtomography, Medical Physics, vol.48, issue.11, pp.2672-2681, 2002. ,
DOI : 10.1109/23.940176
Finite Element-Based Mechanical Assessment of Bone Quality on the Basis of In Vivo Images, First Online), pp.1-12, 2016. ,
DOI : 10.1016/j.jbiomech.2013.11.004
Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone, Biomechanics and Modeling in Mechanobiology, vol.32, issue.12, pp.395659-5678, 2011. ,
DOI : 10.1016/S0021-9290(99)00111-6
URL : https://hal.archives-ouvertes.fr/hal-00844608
A Primer in Elasticity, 2000. ,
Prediction of Hip Failure Load: In Vitro Study of 80 Femurs Using Three Imaging Methods and Finite Element Models???The European Fracture Study (EFFECT), Radiology, vol.280, issue.3, 2016. ,
DOI : 10.1148/radiol.2016142796
URL : https://hal.archives-ouvertes.fr/hal-01366158
Human cortical bone: the SiNuPrOs model, Computer Methods in Biomechanics and Biomedical Engineering, vol.14, issue.2, pp.169-187, 2008. ,
DOI : 10.1016/0021-9290(92)90286-A
URL : https://hal.archives-ouvertes.fr/hal-00485237
Mechanical properties and the hierarchical structure of bone, Medical Engineering & Physics, vol.20, issue.2, pp.92-102, 1998. ,
DOI : 10.1016/S1350-4533(98)00007-1
Determination of the heterogeneous anisotropic elastic properties of human femoral bone: From nanoscopic to organ scale, Journal of Biomechanics, vol.43, issue.10, pp.431857-1863, 2010. ,
DOI : 10.1016/j.jbiomech.2010.03.034
URL : https://hal.archives-ouvertes.fr/hal-00692863
Anatomical distribution of the degree of mineralization of bone tissue in human femoral neck: Impact on biomechanical properties, Bone, vol.50, issue.4, pp.876-884, 2012. ,
DOI : 10.1016/j.bone.2011.12.020
URL : https://hal.archives-ouvertes.fr/hal-00692613
A stochastic homogenization approach to estimate bone elastic properties, Comptes Rendus M??canique, vol.342, issue.5, pp.326-333, 2014. ,
DOI : 10.1016/j.crme.2013.12.007
URL : https://hal.archives-ouvertes.fr/hal-00845654
Stochastic multiscale modelling of cortical bone elasticity based on high-resolution imaging, Biomechanics and Modeling in Mechanobiology, vol.375, issue.9727, pp.111-131, 2016. ,
DOI : 10.1016/S0140-6736(10)60320-0
URL : https://hal.archives-ouvertes.fr/hal-01285137
A mathematical theory of communication, Tech. J. Bell Syst, vol.27, 1948. ,
Maximum entropy approach for modeling random uncertainties in transient elastodynamics, The Journal of the Acoustical Society of America, vol.109, issue.5, pp.1979-1996, 2001. ,
DOI : 10.1121/1.1360716
URL : https://hal.archives-ouvertes.fr/hal-00686287
Probabilités et Modélisation des incertitudes. Eléments de base et concepts fondamentaux Lecture notes, 2004. ,
Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure, SIAM Journal on Scientific Computing, vol.26, issue.2, pp.395-410, 2004. ,
DOI : 10.1137/S1064827503424505
URL : https://hal.archives-ouvertes.fr/hal-00686211
Rate form of the Eshelby and Hill tensors, International Journal of Solids and Structures, vol.39, issue.21-22, 2002. ,
DOI : 10.1016/S0020-7683(02)00369-4
A survey of micro-finite element analysis for clinical assessment of bone strength: The first decade, Journal of Biomechanics, vol.48, issue.5, pp.823-841, 2015. ,
DOI : 10.1016/j.jbiomech.2014.12.024
Patient-specific bone modeling and analysis: The role of integration and automation in clinical adoption, Journal of Biomechanics, vol.48, issue.5, pp.750-760, 2015. ,
DOI : 10.1016/j.jbiomech.2014.12.018
Finite element analysis for prediction of bone strength, BoneKEy Reports, vol.2, issue.386 ,
DOI : 10.1038/bonekey.2013.120
Relevance of 2d radiographic texture analysis for the assessment of 3d bone micro-architecture, Med Phys, vol.33, issue.9, pp.3546-3556, 2006. ,
Finite element 3D modeling of mechanical behavior of mineralized collagen microfibrils, Journal of Applied Biomaterials & Biomechanics, vol.9, issue.3, pp.199-205, 2011. ,
DOI : 10.5301/JABB.2011.8876
URL : https://hal.archives-ouvertes.fr/hal-01089530
Nanomechanical properties of mineralised collagen microfibrils based on finite elements method: biomechanical role of cross-links, Computer Methods in Biomechanics and Biomedical Engineering, vol.28, issue.5, pp.1590-1601, 2014. ,
DOI : 10.1007/s10237-010-0223-9
FFT-based methods for the mechanics of composites: A general variational framework, Computational Materials Science, vol.49, issue.3, 2010. ,
DOI : 10.1016/j.commatsci.2010.06.009
URL : https://hal.archives-ouvertes.fr/hal-00722339
Material and compositional properties of selectively demineralized cortical bone, Journal of Biomechanics, vol.28, issue.11, pp.1357-1368, 1995. ,
DOI : 10.1016/0021-9290(94)00184-6
High-resolution Computed Tomography for Clinical Imaging of Bone Microarchitecture, Clinical Orthopaedics and Related Research??, vol.375, issue.Suppl, pp.2179-2193, 2011. ,
DOI : 10.1016/S0140-6736(10)60320-0
Bone Mechanics Handbook, 2001. ,
DOI : 10.1115/1.1579463
Compact bone: Numerical simulation of mechanical characteristics, Journal of Biomechanics, vol.26, issue.6, pp.677-687, 1993. ,
DOI : 10.1016/0021-9290(93)90031-9
Non Uniform Random Variate Generation, 1986. ,
DOI : 10.1007/978-1-4613-8643-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.8896
The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.241, issue.1226, pp.376-396, 1226. ,
DOI : 10.1098/rspa.1957.0133
Tissue mineral density measured at the sub-millimeter scale can provide reliable statistics of elastic properties of bone matrix, Biomechanics and Modeling in Mechanobiology, p.2016 ,
To what extent can cortical bone millimeter-scale elasticity be predicted by a two-phase composite model with variable porosity?, Acta Biomaterialia, vol.12, pp.207-215, 2015. ,
DOI : 10.1016/j.actbio.2014.10.011
URL : https://hal.archives-ouvertes.fr/hal-01126647
On the Statistical Dependence for the Components of Random Elasticity Tensors Exhibiting Material Symmetry Properties, Journal of Elasticity, vol.21, issue.5, pp.883-901, 2013. ,
DOI : 10.1016/S0065-2156(08)70332-6
URL : https://hal.archives-ouvertes.fr/hal-00724048
Mineral???collagen interactions in elasticity of bone ultrastructure ??? a continuum micromechanics approach, European Journal of Mechanics - A/Solids, vol.23, issue.5, pp.783-810, 2004. ,
DOI : 10.1016/j.euromechsol.2004.05.004
Probability Essentials, 2003. ,
Information Theory and Statistical Mechanics, Physical Review, vol.101, issue.4, pp.620-630, 1957. ,
DOI : 10.1103/PhysRev.101.1227
Information Theory and Statistical Mechanics, Physical Review, vol.101, issue.4, pp.171-190, 1957. ,
DOI : 10.1103/PhysRev.101.1227
X-Ray Phase Nanotomography Resolves the 3D Human Bone Ultrastructure, PLoS ONE, vol.7, issue.8, p.35691, 2012. ,
DOI : 10.1371/journal.pone.0035691.s005
URL : https://hal.archives-ouvertes.fr/hal-00827779
The determination of stress and strain concentrations at an ellipsoidal inclusion in an anisotropic material, Journal of Elasticity, vol.23, issue.1, pp.91-97, 1977. ,
DOI : 10.1007/BF00041133
A note on penny-shaped cracks in transversely isotropic materials, Mechanics of Materials, vol.4, issue.2, pp.209-212, 1985. ,
DOI : 10.1016/0167-6636(85)90017-1
EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS, The Quarterly Journal of Mechanics and Applied Mathematics, vol.43, issue.1, pp.15-41, 1990. ,
DOI : 10.1093/qjmam/43.1.15
Combining FFT methods and standard variational principles to compute bounds and estimates for the properties of elastic composites, Computer Methods in Applied Mechanics and Engineering, vol.283, pp.454-473, 2015. ,
DOI : 10.1016/j.cma.2014.10.005
URL : https://hal.archives-ouvertes.fr/hal-01165844
A polarization-based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast, International Journal for Numerical Methods in Engineering, vol.21, issue.3, pp.1419-1436, 2012. ,
DOI : 10.1016/S0065-2156(08)70332-6
URL : https://hal.archives-ouvertes.fr/hal-00687816
A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2, pp.69-94, 1998. ,
DOI : 10.1016/S0045-7825(97)00218-1
URL : https://hal.archives-ouvertes.fr/hal-01282728
Micromechanis: overall properties of heterogeneous materials Applied Mathematics and Mechanics, 1999. ,
Quantification of the degree of mineralization of bone in three dimensions using synchrotron radiation microtomography, Medical Physics, vol.48, issue.11, pp.2672-2681, 2002. ,
DOI : 10.1109/23.940176
Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone, Biomechanics and Modeling in Mechanobiology, vol.32, issue.12, pp.395659-5678, 2011. ,
DOI : 10.1016/S0021-9290(99)00111-6
URL : https://hal.archives-ouvertes.fr/hal-00844608
Primer in Elasticity, Applied Mechanics Reviews, vol.54, issue.5, 2000. ,
DOI : 10.1115/1.1399676
Nano and Macro Structure of Cortical Bone: Numerical Investigations, Mechanics of Advanced Materials and Structures, vol.29, issue.8, pp.655-663, 2007. ,
DOI : 10.1016/0021-9290(87)90024-8
URL : https://hal.archives-ouvertes.fr/hal-00484747
Multiscale modeling of a fluid saturated medium with double porosity: Relevance to the compact bone, Journal of the Mechanics and Physics of Solids, vol.60, issue.5, pp.857-881, 2012. ,
DOI : 10.1016/j.jmps.2012.01.013
The bone mineralization density distribution as a fingerprint of the mineralization process, Bone, vol.40, issue.5, pp.1308-1319, 2007. ,
DOI : 10.1016/j.bone.2007.01.012
Determination of the heterogeneous anisotropic elastic properties of human femoral bone: From nanoscopic to organ scale, Journal of Biomechanics, vol.43, issue.10, pp.431857-1863, 2010. ,
DOI : 10.1016/j.jbiomech.2010.03.034
URL : https://hal.archives-ouvertes.fr/hal-00692863
A stochastic homogenization approach to estimate bone elastic properties, Comptes Rendus M??canique, vol.342, issue.5, pp.326-333, 2014. ,
DOI : 10.1016/j.crme.2013.12.007
URL : https://hal.archives-ouvertes.fr/hal-00845654
Stochastic multiscale modelling of cortical bone elasticity based on high-resolution imaging, Biomechanics and Modeling in Mechanobiology, vol.375, issue.9727, pp.111-131, 2016. ,
DOI : 10.1016/S0140-6736(10)60320-0
URL : https://hal.archives-ouvertes.fr/hal-01285137
A mathematical theory of communication, Tech. J. Bell Syst, vol.27, 1948. ,
Rate form of the Eshelby and Hill tensors, International Journal of Solids and Structures, vol.39, issue.21-22, 2002. ,
DOI : 10.1016/S0020-7683(02)00369-4
Fourth-Rank Tensors of the Thirty-Two Crystal Classes: Multiplication Tables, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.391, issue.1800, pp.149-179, 1800. ,
DOI : 10.1098/rspa.1984.0008
Equazioni differenziali stocastiche e applicazioni, Pitagora, vol.28, 1984. ,
Tissue mineral density measured at the sub-millimeter scale can provide reliable statistics of elastic properties of bone matrix, Biomechanics and modeling in mechanobiology, p.2016 ,
Handbook of stochastic methods, 1985. ,
DOI : 10.1007/978-3-662-05389-8
Generalized stochastic approach for constitutive equation in linear elasticity: a random matrix model, International Journal for Numerical Methods in Engineering, vol.94, issue.108, pp.613-635, 2012. ,
DOI : 10.1007/s10659-008-9180-2
URL : https://hal.archives-ouvertes.fr/hal-00699345
Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media, Multiscale Modeling & Simulation, vol.11, issue.3, pp.840-870, 2013. ,
DOI : 10.1137/120898346
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.21, issue.5, pp.883-901, 2013. ,
DOI : 10.1016/S0065-2156(08)70332-6
URL : https://hal.archives-ouvertes.fr/hal-00724048
An Introduction to Continuum Mechanics, Journal of Applied Mechanics, vol.51, issue.4, 1982. ,
DOI : 10.1115/1.3167763
Information theory and statistical mechanics. I. Physical Review, pp.620-630, 1957. ,
DOI : 10.1103/physrev.106.620
Information Theory and Statistical Mechanics, Physical Review, vol.101, issue.4, pp.171-190, 1957. ,
DOI : 10.1103/PhysRev.101.1227
Optimal control theory: an introduction, 2004. ,
Mathematics of random phenomena: random vibrations of mechanical structures, 2012. ,
DOI : 10.1007/978-94-009-4770-2
Introduction to stochastic calculus applied to finance, 2007. ,
Optimization by vector space methods, 1969. ,
EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS, The Quarterly Journal of Mechanics and Applied Mathematics, vol.43, issue.1, pp.15-41, 1990. ,
DOI : 10.1093/qjmam/43.1.15
Random matrices, 1991. ,
Probability, random variables, and random signal principles, 2001. ,
Primer in Elasticity, Applied Mechanics Reviews, vol.54, issue.5, 2000. ,
DOI : 10.1115/1.1399676
Determination of the heterogeneous anisotropic elastic properties of human femoral bone: From nanoscopic to organ scale, Journal of Biomechanics, vol.43, issue.10, pp.431857-1863, 2010. ,
DOI : 10.1016/j.jbiomech.2010.03.034
URL : https://hal.archives-ouvertes.fr/hal-00692863
A mathematical theory of communication, Tech. J. Bell Syst, vol.27, 1948. ,
Steady-state solution of Fokker-Planck equation in higher dimension, Probabilistic Engineering Mechanics, vol.3, issue.4, pp.196-206, 1988. ,
DOI : 10.1016/0266-8920(88)90012-4
URL : https://hal.archives-ouvertes.fr/hal-00770322
A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic engineering mechanics, pp.277-294, 2000. ,
DOI : 10.1016/S0266-8920(99)00028-4
URL : https://hal.archives-ouvertes.fr/hal-00686293
Random matrix theory formodeling uncertainties in computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.194, pp.12-161333, 2005. ,
DOI : 10.1016/j.cma.2004.06.038
URL : https://hal-upec-upem.archives-ouvertes.fr/hal-00686187/document
Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.1-3, pp.26-64, 2006. ,
DOI : 10.1016/j.cma.2004.12.014
URL : https://hal.archives-ouvertes.fr/hal-00686157
Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices, International Journal for Numerical Methods in Engineering, vol.195, issue.4, pp.761583-1611, 2008. ,
DOI : 10.1007/978-3-662-12616-5
URL : https://hal.archives-ouvertes.fr/hal-00684517
Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Physical Review, vol.30, issue.1, p.98, 1967. ,
DOI : 10.1016/0031-8914(64)90224-1
Fourth-Rank Tensors of the Thirty-Two Crystal Classes: Multiplication Tables, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.391, issue.1800, pp.391149-179, 1800. ,
DOI : 10.1098/rspa.1984.0008
Tissue mineral density measured at the sub-millimeter scale provides reliable statistical estimates of elastic properties of bone matrix, Biomechanics and Modeling in Mechanobiology, 2016. ,
Stochastic multiscale modelling of cortical bone elasticity based on high-resolution imaging, Biomechanics and Modeling in Mechanobiology, vol.375, issue.9727, pp.111-131, 2016. ,
DOI : 10.1016/S0140-6736(10)60320-0
URL : https://hal.archives-ouvertes.fr/hal-01285137
Prise en compte des incertitudes dans la modélisation multiéchelle de l'´ elasticité de l'osàosà partir de l'imagerie, 22 e Congrès Français de Mécanique, pp.24-28, 2015. ,
On the uncertainty propagation in multiscale modeling of cortical bone elasticity., Computer methods in biomechanics and biomedical engineering, pp.2054-2055, 2015. ,
Direct C/GMRES Control of The Air Path of a Diesel Engine, IFAC Proceedings Volumes, pp.47-3000, 2014. ,
DOI : 10.3182/20140824-6-ZA-1003.02481
On uncertain quantification in image-based micro-mechanical modelling of bone elasticity, 22 nd European Society of Biomechanics Congress 10-13, 2016. ,
Prise en compte des incertitudes dans la modélisation multiéchelle de l'´ elasticité de l'osàosà partir de l'imagerie, 22 e Congrès Français de Mécanique, pp.24-28, 2015. ,
Prise en compte des incertitudes dans la modélisation multiéchelle de l'´ elasticité de l'osàosà partir de l'imagerie, Rencontres franciliennes de mécanique Fédération de recherche F2M-msp, pp.11-12, 2015. ,