[1] A.L. Mescher, Junqueiras basic histology: text and atlas, Mcgraw-hill, 2013.
[2] A. Miller, Collagen: the organic matrix of bone, Philosophical Transactions of the Royal Society B: Biological Sciences, 304 (1984) 455-477.
[3] P. Fratzl, H. .Gupta, E. Paschalis, P.Roschger, Structure and mechanical quality of the collagen–mineral nano-composite in bone, Journal of materials chemistry, 14(14) (2004) 2115-2123.
[4] S. Eppell, W. .Tong, J. Katz, L. Kuhn, M. .Glimcher, Shape and size of isolated bone mineralites measured using atomic force microscopy, Journal of orthopaedic research, 19(6) (2001) 1027-1034.
[5] R.B.Martin, D.B. Burr, N.A. Sharkey, Skeletal Tissue Mechanics, New York, Springer Verlag, 1998.
[6] J.Y.Rho, L.Kuhn-Spearing, P.Zioupos, Mechanical properties and the hierarchical structure of bone, Medical engineering & physics, 20(2) (1998) 92-102.
[7] W. Voigt, Uber die beziehung zwischen den beiden elasticitats constantan isotroper korper, Annals of Physics, 38 (1889) 185-192.
[8] A. Reuss, Berechnung der fliebgrenze von mischkristallen auf grund der plasticitatsbedingung fur einkristalle, ZAAM, 9 (1929) 49-58.
[9] Z. Hashin, S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials, Journal of the Mechanics and Physics of Solids, 11(2) (1963) 127-140.
[10] K.Piekarski, Analysis of bone as a composite material, International Journal of Engineering Science, 11(6) (1973) 557-565.
[11] I.Jager, P. Fratzl, Mineralized collagen fibrils: A mechanical model with a staggered arrangement of mineral particles, Biophysical Journal, 79(4) (2000) 1737-1746.
[12] H. Gao, B. Ji, I. Jäger, E. Arzt, P. .Fratzl, Materials become insensitive to flaws at nanoscale: lessons from nature, Proceedings of the national Academy of Sciences, 100(10) (2003) 557-600.
[13] S.P. Kotha, N. Guzelsu, The effects of interphase and bonding on the elastic modulus of bone: changes with age-related osteoporosis, Medical Engineering & Physics, 22(8) (2000) 575-585.
[14] T. Mori, K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, 21(5) (1973) 571-574.
[15] A. G.Reisinger, D. H.Pahr, P.K. Zysset, Sensitivity analysis and parametric study of elastic properties of an unidirectional mineralized bone fibril-array using mean field methods, Biomechanics and modeling in mechanobiology, 9(5) (2010) 499-510.
[16] C. Hellmich, J.F. Barthélémy, L. Dormieux, Mineral–collagen interactions in elasticity of bone ultrastructure–a continuum micromechanics approach, European Journal of Mechanics-A/Solids, 23(5) (2004) 783-810.
[17] A. Fritsch, C. Hellmich, Universal microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity, Journal of Theoretical Biology, 244(4) (2007) 597-620.
[18] S. Nikolov, D. Raabe, Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization, Biophysical journal, 94(11) (2008) 4220-4232.
[19] E. Hamed, Y. Lee, I. Jasiuk, Multi-scale modeling of elastic properties of cortical bone, Acta Mechanica, 213(1-2) (2010) 131-154.
[20] B.H. Ji, H.J. Gao, Mechanical properties of nanostructure of biological materials, Journal of the Mechanics and Physics of Solids, 52 (2004) 1963-1990.
[21] T. Siegmund, M.R. Allen, D.B. Burr, Failure of mineralized collagen fibrils: Modeling the role of collagen cross-linking, Journal of Biomechanics, 41(7) (2008) 1427-1435.
[22] J. Ghanbari, R. Naghdabadi, Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure, Journal of Biomechanics, 42(10) (2009) 1560-1565.
[23] F. Yuan, S. Stock, D. Haeffner, J. Almer, D. Dunand, L. Brinson, a new model to simulate the elastic properties of mineralized collagen fibril, Biomechanics and modeling in mechanobiology, 10(2) (2011) 147-160.
[24] J.F. Mammone, S.M. Hudson, Micromechanics of bone strength and fracture, Journal of Biomechanics, 26(4-5) (1993) 439-446.
[25] Q. .Luo, R. .Nakade, X. .Dong, Q. .Rong, X. .Wang, Effect of mineral–collagen interfacial behavior on the microdamage progression in bone using a probabilistic cohesive finite element model, Journal of the mechanical behavior of biomedical materials, 4(7) (2011) 943-952.
[26] E.Hamed, I. Jasiuk, Multiscale damage and strength of lamellar bone modeled by cohesive finite elements, journal of the mechanical behavior of biomedical materials, 28 (2013) 94-110.
[27] A.Vercher-Martínez, E.Giner, C.Arango, F.J. Fuenmayor, Influence of the mineral staggering on the elastic properties of the mineralized collagen fibril in lamellar bone, Journal of the mechanical behavior of biomedical materials, 42 (2015) 243-256.
[28] Y. Wang, A. Ural, Mineralized collagen fibril network spatial arrangement influences cortical bone fracture behaviour, Journal of biomechanics, 66 (2018) 70-77.
[29] L. Lin, J. Samuel, X.Zeng, X. Wang, Contribution of extrafibrillar matrix to the mechanical behavior of bone using a novel cohesive finite element model, Journal of the mechanical behavior of biomedical materials, 65 (2017) 224-235.
[30] P.D. Falco, E. Barbieri, N.Pugno, H.S. Gupta, Staggered fibrils and damageable interfaces lead concurrently and independently to hysteretic energy absorption and inhomogeneous strain fields in cyclically loaded antler bone, ACS Biomaterials Science & Engineering, 3(11) (2017) 2779-2787.
[31] M.Maghsoudi-Ganjeh, L.Lin, X.Wang, X.Zeng, Computational investigation of ultrastructural behavior of bone using a cohesive finite element approach, Biomechanics and modeling in mechanobiology, 18(2) (2019) 463-478.
[32] A. K.Nair, A.Gautieri, S. W.Chang, M.J. Buehler, Molecular mechanics of mineralized collagen fibrils in bone, Nature communications, 4 (2013) 1711-1724.
[33] M.J. Buehler, Atomistic and continuum modeling of mechanical properties of collagen: elasticity, fracture, and self-assembly, Journal of Materials Research, 21(8) (2006) 1947-1961.
[34] M.J.Buehler, Nanomechanics of collagen fibrils under varying cross-link densities: atomistic and continuum studies, Journal of the mechanical behavior of biomedical materials, 1(1) (2008) 59-67.
[35] M.J.Buehler, Molecular nanomechanics of nascent bone: fibrillar toughening by mineralization, Nanotechnology, 18(29) (2007) 295102.
[36] D.K.Dubey, V.Tomar, Microstructure dependent dynamic fracture analyses of trabecular bone based on nascent bone atomistic simulations, Mechanics Research Communications, 35(1-2) (2008) 24-31.
[37] M. Sadat-Shojai, Calcium Phosphate–Reinforced Polyester Nanocomposites for Bone Regeneration Applications, In Biodegradable Polymeric Nanocomposites (2015) 12-45.
[38] M. Rubin, I. .Jasiuk, J. Taylor, J. Rubin, T. Ganey, R. Apkarian, TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone, Bone, 33(3) (2003) 270-282.
[39] K. Hibbitt, ABAQUS: User's Manual, 2013.
[40] Z.L.Shen, M.R.Dodge, H.Kahn, R.Ballarini, S.J.Eppell, In vitro fracture testing of submicron diameter collagen fibril specimens, Biophysical journal, 99(6) (2010) 1986-1995.
[41] M.Minary-Jolandan, M.F.Yu, Nanomechanical heterogeneity in the gap and overlap regions of type I collagen fibrils with implications for bone heterogeneity, Biomacromolecules, 10(9) (2009) 2565-2570.
[42] L.Yang, K.O.V.d. Werf, C.F.Fitié, M.L.Bennink, P.J.Dijkstra, J.Feijen, Mechanical properties of native and cross-linked type I collagen fibrils, Biophysical journal, 94(6) (2008) 2204-2211.
[43] C.A.Grant, D.J.Brockwell, S.E.Radford, N.H.Thomson, Effects of hydration on the mechanical response of individual collagen fibrils, Applied Physics Letters, 92(23) (2008) 233-902.
[44] M.J.Olszta, X.Cheng, S.S..Jee, R.Kumar, Y.Y.Kim, M.J.Kaufman, E.P.Douglas, L.B.Gower, Bone structure and formation: A new perspective, Materials Science and Engineering: R: Reports, 58(3-5) (2007) 77-116.
[45] M.P.Wenger, L.Bozec, M.A.Horton, P.Mesquida, Mechanical properties of collagen fibrils, Biophysical journal, 93(4) (2007) 1255-1263.
[46] L.Yang, K.O.v.d. Werf, B.F.Koopman, V.Subramaniam, M.L.Bennink, P.J.Dijkstra, J.Feijen, Micromechanical bending of single collagen fibrils using atomic force microscopy, Journal of Biomedical Materials Research Part A, 82(1) (2007) 160-168.
[47] J.A.V.D. Rijt, K.O.V.D. Werf, M.L.Bennink, P.J.Dijkstra, J.Feijen, Micromechanical testing of individual collagen fibrils, Macromolecular bioscience, 6(9) (2006) 697-702.
[48] A.J.Heim, W.G.Matthews, T.J.Koob, Determination of the elastic modulus of native collagen fibrils via radial indentation, Applied physics letters, 89(18) (2006) 181-902.
[49] A.C.Lorenzo, E.R.Caffarena, Elastic properties, Young's modulus determination and structural stability of the tropocollagen molecule: a computational study by steered molecular dynamics, Journal of biomechanics, 38(7) (2005) 1527-1533.
[50] S.J.Eppell, B.N.Smith, H.Kahn, R.Ballarini, Nano measurements with micro-devices: mechanical properties of hydrated collagen fibrils, Journal of the Royal Society Interface, 3(6) (2005) 117-121.
[51] S.Vesentini, C.F.Fitié, F.M.Montevecchi, A.Redaelli, Molecular assessment of the elastic properties of collagen-like homotrimer sequences, Biomechanics and modeling in mechanobiology, 3(4) (2005) 224-234.
[52] N.Sasaki, S.Odajima, Stress-strain curve and Young's modulus of a collagen molecule as determined by the X-ray diffraction technique, Journal of biomechanics, 29(5) (1996) 655-658.
[53] H.Hofmann, T.Voss, K.Kühn, J.Engel, Localization of flexible sites in thread-like molecules from electron micrographs: Comparison of interstitial, basement membrane and intima collagens, Journal of molecular biology, 172(3) (1984) 325-343.
[54] S.Cusack, A.Miller, Determination of the elastic constants of collagen by Brillouin light scattering, Journal of molecular biology, 135(1) (1979) 39-51.
[55] R.Harley, D.James, A.Miller, J.W.White, Phonons and the elastic moduli of collagen and muscle, Nature, 267(5608) (1977) 285-298.
[56] M.Amaral, M.A.Lopes, R.F.Silva, J.D.Santos, Densification route and mechanical properties of Si3N4–bioglass biocomposites, Biomaterials, 23(3) (2002) 857-862.
[57] A.Ravaglioli, A.Krajewski, Bioceramics: Materials· Properties· Applications, Springer Science & Business Media, (1991).
[58] V.R.Sherman, A.n.W. Yang, M.A. Meyers, The materials science of collagen, journal of mechanical behaviour of biomedical materials, (2015).
[59] Q. Luo, R. Nakade, X. Dong, Q. Rong, X. Wang, Effect of mineral–collagen interfacial behavior on the microdamage progression in bone using a probabilistic cohesive finite element model, Journal of the mechanical behavior of biomedical materials, 4(7) (2011) 943-952.
[60] F.Hang, A.H. Barber, Nano-mechanical properties of individual mineralized collagen fibrils from bone tissue, Journal of The Royal Society Interface, (1555) 500-505.
[61] E. Wilson, A. Awonusi, M. Morris, D. Kohn, M. Tecklenburg, L. Beck, Highly ordered interstitial water observed in bone by nuclear magnetic resonance, Journal of bone and mineral research, 20(4) (2005) 625-634.
[62] A.Groetsch, A.Gourrier, J.Schwiedrzik, M.Sztucki, R.J.Beck, J.D.Shephard, J.Michler, P.K.Zysset, U.Wolfram, Compressive behaviour of uniaxially aligned individual mineralised collagen fibres at the micro-and nanoscale, Acta biomaterialia, 89 (2019) 313-329.
[63] W.Wu, J.Owino, A.Al-Ostaz, L.Cai, Applying periodic boundary conditions in finite element analysis, In SIMULIA Community Conference, Providence, (2014) 707-719.
[64] Y. Liu, R. Ballarini, S.J. Eppell, Tension tests on mammalian collagen fibrils, Interface focus, (2016).