Multi-Scale Finite Element Modelling of Human Cortical Bone: An Analysis of the Mechanical Properties and Microdamage Onset of Cortical Bone

Year	Entry
2010	Donnelly E, Chen DX, Boskey AL, Baker SP, van der Meulen MCH. Contribution of mineral to bone structural behavior and tissue mechanical properties. Calcif Tiss Int. November 2010;87(5):450-460.
2010	Reisinger AG, Pahr DH, Zysset PK. Sensitivity analysis and parametric study of elastic properties of an unidirectional mineralized bone fibril-array using mean field methods. Biomech Model Mechanobiol. October 2010;9(5):499-510.
1999	Zysset PK, Guo XE, Hoffler CE, Moore KE, Goldstein SA. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J Biomech. October 1999;32(10):1005-1012.
2008	MacNeil JA, Boyd SK. Bone strength at the distal radius can be estimated from high-resolution peripheral quantitative computed tomography and the finite element method. Bone. June 2008;42(6):1203-1213.
2020	Razi H, Predan J, Fischer FD, Kolednik O, Fratzl P. Damage tolerance of lamellar bone. Bone. January 2020;130:115102.
2009	Ritchie R, Buehler M, Hansma P. Plasticity and toughness in bone. Phys Today. June 2009;62(6):41-47.
1959	Currey JD. Differences in the tensile strength of bone of different histological types. J Anat. January 1959;93(1):87-95.
1995	Landis WJ. The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix. Bone. May 1995;16(5):533-544.
2004	Currey JD. Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content. J Biomech. April 2004;37(4):549-556.
1997	Braidotti P, Branca FP, Stagni L. Scanning electron microscopy of human cortical bone failure surfaces. J Biomech. February 1997;30(2):155-162.
1964	Hashin Z, Rosen BW. The elastic moduli of fiber-reinforced materials. J Appl Mech. June 1964;31(2):223-232.
1963	Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids. March–April 1963;11(2):127-140.
1997	Jepsen KJ, Davy DT. Comparison of damage accumulation measures in human cortical bone. J Biomech. September 1997;30(9):891-894.
2010	Nikander R, Sievänen H, Heinonen A, Daly RM, Uusi-Rasi K, Kannus P. Targeted exercise against osteoporosis: a systematic review and meta-analysis for optimising bone strength throughout life. BMC Med. 2010;8:47.
1975	Townsend PR, Rose RM, Radin EL. Buckling studies of single human trabeculae. J Biomech. July 1975;8(3-4):199-200.
2009	Espinosa HD, Rim JE, Barthelat F, Buehler MJ. Merger of structure and material in nacre and bone: perspectives on de novo biomimetic materials. Prog Mater Sci. November 2009;54(8):1059-1100.
1964	Gong JK, Arnold JS, Cohn SH. Composition of trabecular and cortical bone. Anat Rec. 1964;149(3):325-331.
2003	Rubin MA, Jasiuk I, Taylor J, Rubin J, Ganey T, Apkarian RP. TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone. Bone. March 2003;32(3):270-282.
1994	Crofts RD, Boyce TM, Bloebaum RD. Aging changes in osteon mineralization in the human femoral neck. Bone. March–April 1994;15(2):147-152.
1984	Ashman RB, Cowin SC, Van Buskirk WC, Rice JC. A continuous wave technique for the measurement of the elastic properties of cortical bone. J Biomech. 1984;17(5):349-361.
2005	Wilson EE, Awonusi A, Morris MD, Kohn DH, Tecklenburg MM, Beck LW. Highly ordered interstitial water observed in bone by nuclear magnetic resonance. J Bone Miner Res. 2005;20(4):625-634.
2014	Reznikov N, Shahar R, Weiner S. Bone hierarchical structure in three dimensions. Acta Biomater. September 2014;10(8):3815-3826.
1996	Prendergast PJ, Huiskes R. Microdamage and osteocyte-lacuna strain in bone: a microstructural finite element analysis. J Biomech Eng. May 1996;118(2):240-246.
1998	Fratzl P, Misof K, Zizak I, Rapp G, Amenitsch H, Bernstorff S. Fibrillar structure and mechanical properties of collagen. J Struct Biol. 1998;122(1-2):119-122.
2013	Feerick EM, Liu X, McGarry P. Anisotropic mode-dependent damage of cortical bone using the extended finite element method (XFEM). J Mech Behav Biomed Mater. April 2013;20:77-89.
1995	Schaffler MB, Choi K, Milgrom C. Aging and matrix microdamage accumulation in human compact bone. Bone. December 1995;17(6):521-525.
2000	Sevostianov I, Kachanov M. Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone. J Biomech. July 2000;33(7):881-888.
2005	Qiu S, Rao DS, Fyhrie DP, Palnitkar S, Parfitt AM. The morphological association between microcracks and osteocyte lacunae in human cortical bone. Bone. July 2005;37(1):10-15.
2004	Fratzl P, Gupta HS, Paschalis EP, Roschger P. Structure and mechanical quality of the collagen–mineral nano-composite in bone. J Mater Chem. 2004;14(14):2115-2123.
2007	Fratzl P, Weinkamer R. Nature’s hierarchical materials. Prog Mater Sci. November 2007;52(8):1263-1334.
2006	Augat P, Schorlemmer S. The role of cortical bone and its microstructure in bone strength. Age Ageing. September 2006;35(suppl 2):ii27-ii31.
2011	Shen ZL, Kahn H, Ballarini R, Eppell SJ. Viscoelastic properties of isolated collagen fibrils. Biophys J. June 22, 2011;100(12):3008-3015.
1989	Mente PL, Lewis JL. Experimental method for the measurement of the elastic modulus of trabecular bone tissue. J Orthop Res. 1989;7(3):456-461.
1993	Sasaki N, Nakayama Y, Yoshikawa M, Enyo A. Stress relaxation function of bone and bone collagen. J Biomech. December 1993;26(12):1369-1376.
2013	Reznikov N, Almany-Magal R, Shahar R, Weiner S. Three-dimensional imaging of collagen fibril organization in rat circumferential lamellar bone using a dual beam electron microscope reveals ordered and disordered sub-lamellar structures. Bone. February 2013;52(2):676-683.
1999	Fondrk MT, Bahniuk EH, Davy DT. A damage model for nonlinear tensile behavior of cortical bone. J Biomech Eng. October 1999;121(5):533-541.
1976	Yoon HS, Katz JL. Ultrasonic wave propagation in human cortical bone, II: measurements of elastic properties and microhardness. J Biomech. 1976;9(7):459-464.
1971	Wood JL. Dynamic response of human cranial bone. J Biomech. January 1971;4(1):1-12.
1996	Courtney AC, Hayes WC, Gibson LJ. Age-related differences in post-yield damage in human cortical bone: experiment and model. J Biomech. November 1996;29(11):1463-1471.
1998	Zioupos P, Currey JD. Changes in the stiffness, strength, and toughness of human cortical bone with age. Bone. January 1998;22(1):57-66.
1976	Burstein AH, Reilly DT, Martens M. Aging of bone tissue: mechanical properties. J Bone Joint Surg. 1976;58A(1):82-86.
2001	Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001.
1990	Ascenzi A, Baschieri P, Benvenuti A. The bending properties of single osteons. J Biomech. 1990;23(8):763-771.
2005	Akkus O. Elastic deformation of mineralized collagen fibrils: an equivalent inclusion based composite model. J Biomech Eng. June 2005;127(3):383-390.
2002	Fan Z, Swadener JG, Rho JY, Roy ME, Pharr GM. Anisotropic properties of human tibial cortical bone as measured by nanoindentation. J Orthop Res. July 2002;20(4):806-810.
1969	Currey JD. The relationship between the stiffness and the mineral content of bone. J Biomech. October 1969;2(4):477-480.
1993	Mori S, Burr DB. Increased intracortical remodeling following fatigue damage. Bone. March–April 1993;14(2):103-109.
2008	Budyn E, Hoc T, Jonvaux J. Fracture strength assessment and aging signs detection in human cortical bone using an X-FEM multiple scale approach. Comput Mech. September 2008;42(4):579-591.
1997	Rho J-Y, Tsui TY, Pharr GM. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials. 1997;18(20):1325-1330.
2001	Rho JY, Currey JD, Zioupos P, Pharr GM. The anisotropic Young's modulus of equine secondary osteones and interstitial bone determined by nanoindentation. J Exp Biol. May 2001;204(10):1775-1781.
1973	Piekarski K. Analysis of bone as a composite material. Int J Eng Sci. June 1973;11(6):557-565.
1989	Caler WE, Carter DR. Bone creep-fatigue damage accumulation. J Biomech. 1989;22(6-7):625-635.
2007	Kazanci M, Wagner HD, Manjubala NI, Gupta HS, Paschalis E, Roschger P, Fratzl P. Raman imaging of two orthogonal planes within cortical bone. Bone. September 2007;41(3):456-461.
2006	Buehler MJ. Atomistic and continuum modeling of mechanical properties of collagen: elasticity, fracture, and self-assembly. J Mater Res. August 2006;21(8):1947-1961.
2009	Ebacher V, Wang R. A unique microcracking process associated with the inelastic deformation of Haversian bone. Adv Funct Mater. January 9, 2009;19(1):57-66.
1999	Rho JY, Zioupos P, Currey JD, Pharr GM. Variations in the individual thick lamellar properties within osteons by nanoindentation. Bone. September 1999;25(3):295-300.
1999	Rho J-Y, Pharr GM. Effects of drying on the mechanical properties of bovine femur measured by nanoindentation. J Mater Sci Mater Med. 1999;10(8):485-488.
2012	Sroga GE, Vashishth D. Effects of bone matrix proteins on fracture and fragility in osteoporosis. Curr Osteoporos Rep. June 2012;10(2):141-150.
2002	Wachter NJ, Krischak GD, Mentzel M, Sarkar MR, Ebinger T, Kinz L, Claes L, Augat P. Correlation of bone mineral density with strength and microstructural parameters of cortical bone in vitro. Bone. July 2002;31(1):90-95.
2000	Hoffler CE, Moore KE, Kozloff K, Zysset PK, Goldstein SA. Age, gender, and bone lamellae elastic moduli. J Orthop Res. May 2000;18(3):432-437.
1997	Vashishth D, Behiri JC, Bonfield W. Crack growth resistance in cortical bone: concept of microcrack toughening. J Biomech. August 1997;30(8):763-769.
2006	Diab T, Condo KW, Burr DB, Vashishth D. Age-related change in the damage morphology of human cortical bone and its role in bone fragility. Bone. March 2006;38(3):427-431.
2005	Diab T, Vashishth D. Effects of damage morphology on cortical bone fragility. Bone. July 2005;37(1):96-102.
1988	Giraud-Guille MM. Twisted plywood architecture of collagen fibrils in human compact bone osteons. Calcif Tiss Int. May 1988;42(3):167-180.
1981	Carter DR, Caler WE, Spengler DM, Frankel VH. Fatigue behavior of adult cortical bone: the influence of mean strain and strain range. Acta Orthop Scand. 1981;52(5):481-490.
1984	Currey JD. Effects of differences in mineralization on the mechanical properties of bone. Philos Trans R Soc Lond B Biol Sci. February 13, 1984;304(1121):509-518.
2008	Yoon YJ, Cowin SC. The estimated elastic constants for a single bone osteonal lamella. Biomech Model Mechanobiol. February 2008;7(1):1-11.
1996	Cristofolini L, Viceconti M, Cappello A, Toni A. Mechanical validation of whole bone composite femur models. J Biomech. April 1996;29(4):525-535.
2011	Luo Q, Nakade R, Dong X, Rong Q, Wang X. Effect of mineral–collagen interfacial behavior on the microdamage progression in bone using a probabilistic cohesive finite element model. J Mech Behav Biomed Mater. October 2011;4(7):943-952.
1999	Rho J-Y, Roy ME II, Tsui TY, Pharr GM. Elastic properties of microstructural components of human bone tissue as measured by nanoindentation. J Biomed Mater Res. 1999;A45(1):48-54.
1977	Frasca P, Harper RA, Katz JL. Collagen fiber orientations in human secondary osteons. Acta Anat. 1977;98(1):1-13.
1970	Yamada H. Strength of Biological Materials. Evans FG, ed. Baltimore, MD: Williams & Wilkins Company; 1970.
1974	Crowninshield RD, Pope MH. The response of compact bone in tension at various strain rates. Ann Biomed Eng. 1974;2(2):217-225.
1876	Rauber AA. Elasticität Und Festigkeit Der Knochen: Anatomisch-Physiologische Studie. Leipzig, Germany: Verlag Von Wilhelm Engelmann; 1876.
1992	Hogan HA. Micromechanics modeling of Haversian cortical bone properties. J Biomech. May 1992;25(5):549-556.
2012	McNally EA, Schwarcz HP, Botton GA, Arsenault AL. A model for the ultrastructure of bone based on electron microscopy of ion-milled sections. PLoS One. January 17, 2012;7(1):e29258.
1985	Cezayirlioglu H, Bahniuk E, Davy DT, Heiple KG. Anisotropic yield behavior of bone under combined axial force and torque. J Biomech. 1985;18(1):61-69.
2006	Yang QD, Cox BN, Nalla RK, Ritchie RO. Fracture length scales in human cortical bone: the necessity of nonlinear fracture models. Biomaterials. March 2006;27(9):2095-2113.
2015	Seref-Ferlengez Z, Kennedy OD, Schaffler MB. Bone microdamage, remodeling and bone fragility: how much damage is too much damage? BoneKEy Rep. March 2015;4:644.
1999	Weiner S, Traub W, Wagner HD. Lamellar bone: structure–function relations. J Struct Biol. June 1999;126(3):241-255.
1998	Weiner S, Wagner HD. The material bone: structure-mechanical function relations. Ann Rev Mater Sci. August 1998;28:271-298.
1992	Weiner S, Traub W. Bone structure: from ȧngstroms to microns. FASEB J. February 1992;6(3):879-885.
1997	Weiner S, Arad T, Sabanay I, Traub. W. Rotated plywood structure of primary lamellar bone in the rat: orientations of the collagen fibril arrays. Bone. June 1997;20(6):509-514.
2005	O'Brien FJ, Taylor D, Lee TC. The effect of bone microstructure on the initiation and growth of microcracks. J Orthop Res. March 2005;23(2):475-480.
1984	Currey JD. Mechanical Adaptations of Bone. Princeton, NJ: Princeton University Press; 1984.
2019	Burr DB. Stress concentrations and bone microdamage: John Currey's contributions to understanding the initiation and arrest of cracks in bone. Bone. October 2019;127:517-525.
2008	Nikolov S, Raabe D. Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization. Biophys J. June 2008;94(11):4220-4232.
1999	Jepsen KJ, Davy DT, Krzypow DJ. The role of the lamellar interface during torsional yielding of human cortical bone. J Biomech. March 1999;32(3):303-310.
2013	Ural A, Mischinski S. Multiscale modeling of bone fracture using cohesive finite elements. Eng Fract Mech. May 2013;103:141-152.
1999	Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM. The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech. April 1999;32(4):437-441.
2012	Erdemir A, Guess TM, Halloran J, Tadepalli SC, Morrison TM. Considerations for reporting finite element analysis studies in biomechanics. J Biomech. February 23, 2012;45(4):625-633.
2003	O’Brien FJ, Taylor D, Lee TC. Microcrack accumulation at different intervals during fatigue testing of compact bone. J Biomech. July 2003;36(7):973-980.
1971	Katz JL, Ukraincik K. On the anisotropic elastic properties of hydroxyapatite. J Biomech. May 1971;4(3):221-227.
2011	Reisinger AG, Pahr DH, Zysset PK. Elastic anisotropy of bone lamellae as a function of fibril orientation pattern. Biomech Model Mechanobiol. February 2011;10(1):67-77.
1998	Wang XD, Masilamani NS, Mabrey JD, Alder ME, Agrawal CM. Changes in the fracture toughness of bone may not be reflected in its mineral density, porosity, and tensile properties. Bone. July 1998;23(1):67-72.
1996	Ziv V, Wagner HD, Weiner S. Microstructure-microhardness relations in parallel-fibered and lamellar bone. Bone. May 1996;18(5):417-428.
2010	Hamed E, Lee Y, Jasiuk I. Multiscale modeling of elastic properties of cortical bone. Acta Mech. August 2010;213(1):131-154.
2008	Burgers TA. Press-Fit Fixation and Viscoelastic Response of a Bone-Implant Interface in the Distal Femur [PhD thesis]. University of Wisconsin – Madison; 2008.
2008	Siegmund T, Allen MR, Burr DB. Failure of mineralized collagen fibrils: modeling the role of collagen cross-linking. J Biomech. 2008;41(7):1427-1435.
2007	Vashishth D. Hierarchy of bone microdamage at multiple length scales. Int J Fatigue. June 2007;29(6):1024-1033.
2010	Katti DR, Pradhan SM, Katti KS. Directional dependence of hydroxyapatite-collagen interactions on mechanics of collagen. J Biomech. June 18, 2010;43(9):1723-1730.
2006	Hoc T, Henry L, Verdier M, Aubry D, Sedel L, Meunier A. Effect of microstructure on the mechanical properties of Haversian cortical bone. Bone. April 2006;38(4):466-474.
1982	Gilmore RS, Katz JL. Elastic properties of apatites. J Mater Sci. 1982;17:1131-1141.
2009	Franzoso G, Zysset PK. Elastic anisotropy of human cortical bone secondary osteons measured by nanoindentation. J Biomech Eng. February 2009;131(2):021001.
2000	Jäger I, Fratzl P. Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys J. October 2000;79(4):1737-1746.
2000	Vashishth D, Koontz J, Qiu SJ, Lundin-Cannon D, Yeni YN, Schaffler MB, Fyhrie DP. In vivo diffuse damage in human vertebral trabecular bone. Bone. February 2000;26(2):147-152.
2003	Vashishth D, Tanner KE, Bonfield W. Experimental validation of a microcracking-based toughening mechanism for cortical bone. J Biomech. January 2003;36(1):121-124.
1993	Rho JY, Ashman RB, Turner CH. Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech. February 1993;26(2):111-119.
1990	Burr DB, Stafford T. Validity of the bulk-staining technique to separate artifactual from in vivo bone microdamage. Clin Orthop Relat Res. November 1990;260:305-308.
2012	Vaughan TJ, McCarthy CT, McNamara LM. A three-scale finite element investigation into the effects of tissue mineralisation and lamellar organisation in human cortical and trabecular bone. J Mech Behav Biomed Mater. August 2012;12:50-62.
1998	Burr DB, Turner CH, Naick P, Forwood MR, Ambrosius W, Hasan MS, Pidaparti R. Does microdamage accumulation affect the mechanical properties of bone? J Biomech. April 1998;31(4):337-345.
1998	Rho J-Y, Kuhn-Spearing L, Zioupos P. Mechanical properties and the hierarchical structure of bone. Med Eng Phys. 1998;20(2):92-102.
1994	Schaffler MB, Pitchford WC, Choi K, Riddle JM. Examination of compact bone microdamage using back-scattered electron microscopy. Bone. September–October 1994;15(5):483-488.
2007	Buehler MJ. Molecular nanomechanics of nascent bone: fibrillar toughening by mineralization. Nanotechnology. July 25, 2007;18(9):295102.
1975	Runkle JC, Pugh J. The micro-mechanics of cancellous bone, II: determination of the elastic modulus of individual trabeculae by a buckling analysis. Bull Hosp Joint Dis. April 1975;36(1):2-10.
2006	Gupta HS, Wagermaier W, Zickler GA, Hartmann J, Funari SS, Roschger P, Wagner HD, Fratzl P. Fibrillar level fracture in bone beyond the yield point. Int J Fract. June 2006;139(3-4):425-436.
2008	Buehler MJ. Nanomechanics of collagen fibrils under varying cross-link densities: atomistic and continuum studies. J Mech Behav Biomed Mater. January 2008;1(1):59-67.
2012	Wolfram U, Gross T, Pahr DH, Schwiedrzik J, Wilke H-J, Zysset PK. Fabric-based Tsai-Wu yield criteria for vertebral trabecular bone in stress and strain space. J Mech Behav Biomed Mater. November 2012;15:218-228.
2004	Iyo T, Maki Y, Sasaki N, Nakata M. Anisotropic viscoelastic properties of cortical bone. J Biomech. September 2004;37(9):1433-1437.
2002	Martin RB. Is all cortical bone remodeling initiated by microdamage? Bone. January 2002;30(1):8-13.
2006	Dong XN, Guo XE. Prediction of cortical bone elastic constants by a two-level micromechanical model using a generalized self-consistent method. J Biomech Eng. June 2006;128(3):309-316.
1992	Huiskes R, Weinans H, Van Rietbergen B. The relationship between stress shielding and bone resorption around total hip stems and the effects of flexible materials. Clin Orthop Relat Res. January 1992;274:124-134.
1985	Burr DB, Martin RB, Schaffler MB, Radin EL. Bone remodeling in response to in vivo fatigue microdamage. J Biomech. 1985;18(3):189-200.
1998	Akiva U, Wagner HD, Weiner S. Modelling the three-dimensional elastic constants of parallel-fibred and lamellar bone. J Mater Sci. March 15, 1998;33(6):1497-1509.
1976	Evans FG. Mechanical properties and histology of cortical bone from younger and older men. Anat Rec. 1976;185(1):1-12.
2004	Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech. January 2004;37(1):27-35.
2005	Hoffler CE, Guo XE, Zysset PK, Goldstein SA. An application of nanoindentation technique to measure bone tissue lamellae properties. J Biomech Eng. January 2005;127(7):1046-1053.
1998	Boyce TM, Fyhrie DP, Glotkowski MC, Radin EL, Schaffler MB. Damage type and strain mode associations in human compact bone bending fatigue. J Orthop Res. May 1998;16(3):322-329.
1975	Reilly DT, Burstein AH. The elastic and ultimate properties of compact bone tissue. J Biomech. 1975;8(6):393-405.
1974	Black J, Mattson R, Korostoff E. Haversian osteons: size, distribution, internal structure, and orientation. J Biomed Mater Res. September 1974;8(5):299-319.
1966	McElhaney JH. Dynamic response of bone and muscle tissue. J Appl Physiol. 1966;21(4):1231-1236.
2004	Dong XN, Guo XE. The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. J Biomech. August 2004;37(8):1281-1287.
2002	Puxkandl R, Zizak I, Paris O, Keckes J, Tesch W, Bernstorff S, Purslow P, Fratzl P. Viscoelastic properties of collagen: synchrotron radiation investigations and structural model. Proc R Soc B. February 28, 2002;357(1418):191-197.
2003	Taylor D, Lee TC. Microdamage and mechanical behaviour: predicting failure and remodelling in compact bone. J Anat. August 2003;203(2):203-211.
1992	Wagner HD, Weiner S. On the relationship between the microstructure of bone and its mechanical stiffness. J Biomech. November 1992;25(11):1311-1320.
1998	Kopperdahl DL, Keaveny TM. Yield strain behavior of trabecular bone. J Biomech. July 1998;31(7):601-608.
1997	Norman TL, Wang Z. Microdamage of human cortical bone: incidence and morphology in long bones. Bone. April 1997;20(4):375-379.
2012	Abdel-Wahab AA, Maligno AR, Silberschmidt VV. Micro-scale modelling of bovine cortical bone fracture: analysis of crack propagation and microstructure using X-FEM. Comp Mater Sci. February 2012;52(1):128-135.
2007	Fritsch A, Hellmich C. "Universal" microstructural patterns in bone: micromechanics-based prediction of anisotropic material behavior. J Theo Biol. February 21, 2007;244(4):597-620.
1999	Cody DD, Gross GJ, Hou FJ, Spencer HJ, Goldstein SA, Fyhrie DP. Femoral strength is better predicted by finite element models than QCT and DXA. J Biomech. October 1999;32(10):1013-1020.
2006	Gupta HS, Seto J, Wagermaier W, Zaslansky P, Boesecke P, Fratzl P. Cooperative deformation of mineral and collagen in bone at the nanoscale. Proc Natl Acad Sci USA. November 21, 2006;103(47):17741-17746.
2006	Wagermaier W, Gupta HS, Gourrier A, Burghammer M, Roschger P, Fratzl P. Spiral twisting of fiber orientation inside bone lamellae. Biointerphases. March 2006;1(1):1-5.
2009	Fritsch A, Hellmich C, Dormieux L. Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: experimentally supported micromechanical explanation of bone strength. J Theo Biol. September 21, 2009;260(2):230-252.
1993	Marotti G. A new theory of bone lamellation. Calcif Tiss Int. February 1993;53(suppl 1):S47-S56.
2005	Fantner GE, Hassenkam T, Kindt JH, Weaver JC, Birkedal H, Pechenik L, Cutroni JA, Cidade GAG, Stucky GD, Morse DE, Hansma PK. Sacrificial bonds and hidden length dissipate energy as mineralized fibrils separate during bone fracture. Nat Mater. August 2005;4(8):612-616.
2006	Gao H. Application of fracture mechanics concepts to hierarchical biomechanics of bone and bone-like materials. Int J Fract. March–April 2006;138(1-4):101-137.
2013	Nair AK, Gautieri A, Chang S-W, Buehler MJ. Molecular mechanics of mineralized collagen fibrils in bone. Nat Commun. 2013;r:1724.
2003	Gao H, Ji B, Jäger IL, Arzt E, Fratzl P. Materials become insensitive to flaws at nanoscale: lessons from nature. Proc Natl Acad Sci USA. May 13, 2003;100(10):5597-5600.