The relationship between the elasticity tensor and the fabric tensor

Cowin, Stephen C.

Year	Entry
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2019	Marques M, Belinha J, Oliveira AF, Manzanares-Céspedes MC, Jorge RN. Combining radial point interpolation meshless method with a new homogenization technique for trabecular bone multiscale structural analyses. Acta Bioeng Biomech. 2019;21(2):101-113.
2020	Marques M, Belinha J, Oliveira AF, Manzanares Cespedes MC, Natal Jorge RM. A 3D trabecular bone homogenization technique. Acta Bioeng Biomech. 2020;22(3):139-152.
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2009	Rincón-Kohli L, Zysset PK. Multi-axial mechanical properties of human trabecular bone. Biomech Model Mechanobiol. June 2009;8(3):195-208.
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1999	Kabel J, van Rietbergen B, Odgaard A, Huiskes R. Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture. Bone. October 1999;25(4):481-486.
2007	Tang SY, Vashishth D. A non-invasive in vitro technique for the three-dimensional quantification of microdamage in trabecular bone. Bone. May 2007;40(5):1259-1264.
2022	Simon M, Indermaur M, Schenk D, Hosseinitabatabaei S, Willie BM, Zysset P. Fabric-elasticity relationships of tibial trabecular bone are similar in osteogenesis imperfecta and healthy individuals. Bone. February 2022;155:116282.
2008	Nazarian A, von Stechow D, Zurakowski D, Müller R, Snyder BD. Bone volume fraction explains the variation in strength and stiffness of cancellous bone affected by metastatic cancer and osteoporosis. Calcif Tiss Int. December 2008;83(6):368-379.
1993	Hodgskinson R, Currey JD. Separate effects of osteoporosis and density on the strength and stiffness of human cancellous bone. Clin Biomech (Bristol, Avon). September 1993;8(5):262-268.
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2016	Schwiedrzik J, Gross T, Bina M, Pretterklieber M, Zysset P, Pahr D. Experimental validation of a nonlinear μFE model based on cohesive-frictional plasticity for trabecular bone. Int J Num Meth Biomed Eng. April 2016;32(4):e02739.
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1992	Turner CH. On Wolff's law of trabecular architecture. J Biomech. January 1992;25(1):1-9.
1992	Cowin SC, Turner CH. On the relationship between the orthotropic Young's moduli and fabric. J Biomech. December 1992;22(12):1493-1494.
1993	Dalstra M, Huiskes R, Odgaard A, van Erning L. Mechanical and textural properties of pelvic trabecular bone. J Biomech. April–May 1993;26(4-5):523-535.
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2008	Mittra E, Rubin C, Gruber B, Qin Y-X. Evaluation of trabecular mechanical and microstructural properties in human calcaneal bone of advanced age using mechanical testing, μCT, and DXA. J Biomech. 2008;41(2):368-375.
2008	Dendorfer S, Maier HJ, Taylor D, Hammer J. Anisotropy of the fatigue behaviour of cancellous bone. J Biomech. 2008;41(3):636-641.
2009	Pahr DH, Zysset PK. A comparison of enhanced continuum FE with micro FE models of human vertebral bodies. J Biomech. March 11, 2009;42(4):455-462.
2011	Cherkaev E, Bonifasi-Lista C. Characterization of structure and properties of bone by spectral measure method. J Biomech. January 11, 2011;44(2):345-351.
2012	Hazrati Marangalou J, Ito K, van Rietbergen B. A new approach to determine the accuracy of morphology–elasticity relationships in continuum FE analyses of human proximal femur. J Biomech. November 15, 2012;45(15):2884-2892.
2013	Hazrati Marangalou J, Ito K, Cataldi M, Taddei F, van Rietbergen B. A novel approach to estimate trabecular bone anisotropy using a database approach. J Biomech. September 27, 2013;46(14):2356-2362.
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1993	Huiskes R, Hollister SJ. From structure to process, from organ to cell: recent developments of FE-analysis in orthopaedic biomechanics. J Biomech Eng. November 1993;115(4B):520-527.
1993	Keaveny TM, Hayes WC. A 20-year perspective on the mechanical properties of trabecular bone. J Biomech Eng. November 1993;115(4B):534-542.
1998	Zysset PK, Goulet RW, Hollister SJ. A global relationship between trabecular bone morphology and homogenized elastic properties. J Biomech Eng. October 1998;120(5):640-646.
2001	Adachi T, Tsubota K-i, Tomita Y, Hollister SJ. Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models. J Biomech Eng. October 2001;123(5):403-409.
2002	Niebur GL, Feldstein MJ, Keaveny TM. Biaxial failure behavior of bovine tibial trabecular bone. J Biomech Eng. December 2002;124(6):699-705.
2011	Trabelsi N, Yosibash Z. Patient-specific finite-element analyses of the proximal femur with orthotropic material properties validated by experiments. J Biomech Eng. June 2011;133(6):061001.
2015	Oftadeh R, Perez-Viloria M, Villa-Camacho JC, Vaziri A, Nazarian A. Biomechanics and mechanobiology of trabecular bone: a review. J Biomech Eng. January 2015;137(1):010802.
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1995	Chung H, Wehrli FW, Williams JL, Wehrli SL. Three‐dimensional nuclear magnetic resonance microimaging of trabecular bone. J Bone Miner Res. October 1995;10(10):1452-1461.
2012	Souzanchi MF, Palacio-Mancheno P, Borisov YA, Cardoso L, Cowin SC. Microarchitecture and bone quality in the human calcaneus: local variations of fabric anisotropy. J Bone Miner Res. December 2012;27(12):2562-2572.
2015	Maquer G, Musy SN, Wandel J, Gross T, Zysset PK. Bone volume fraction and fabric anisotropy are better determinants of trabecular bone stiffness than other morphological variables. J Bone Miner Res. June 2015;30(6):1000-1008.
2003	van Ruijven LJ, Giesen EBW, Farella M, van Eijden TMGJ. Prediction of mechanical properties of the cancellous bone of the mandibular condyle. J Dent Res. October 2003;82(10):819-823.
1987	Turner CH, Cowin SC. Dependence of elastic constants of an anisotropic porous material upon porosity and fabric. J Mater Sci. September 1987;22(9):3178-3184.
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1986	Cowin SC. Fabric dependence of an anisotropic strength criterion. Mech Mater. September 1986;5(3):251-260.
1995	Zysset PK, Curnier A. An alternative model for anisotropic elasticity based on fabric tensors. Mech Mater. November 1995;21(4):243-250.
2012	Moesen M, Cardoso L, Cowin SC. A symmetry invariant formulation of the relationship between the elasticity tensor and the fabric tensor. Mech Mater. November 2012;54:70-83.
2010	Kadir MRA, Syahrom A, Öchsner A. Finite element analysis of idealised unit cell cancellous structure based on morphological indices of cancellous bone. Med Biol Eng Comput. May 2010;48(5):497-505.
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2012	Tabor Z. Equivalence of mean intercept length and gradient fabric tensors: 3d study. Med Eng Phys. June 2012;34(5):598-604.
2021	Bennison MBL, Pilkey AK, Lievers WB. Evaluating a theoretical and an empirical model of "side effects" in cancellous bone. Med Eng Phys. August 2021;94:8-15.
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1996	Silva MJ. Predicting the Failure Behavior of the Human Vertebral Body [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; February 1996.
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1996	Livesay GA. Development of Homogenization Theory for Soft Tissues Undergoing Finite Elastic Deformation [PhD thesis]. University of Pittsburgh; 1996.
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2007	Tang SY-C. Effects of Non-Enzymatic Glycation on the Biomechanical Behavior of Bone [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; 2007.
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1987	Turner CH. On the Relationship Between the Elastic Properties of Cancellous Bone and Its Structure [PhD thesis]. New Orleans, LA: Tulane University; 1987.
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2002	Bellezza AJ. Biomechanical Properties of the Normal and Early Glaucomatous Optic Nerve Head: An Experimental and Computational Study Using the Monkey Model [PhD thesis]. Tulane University; 2002.
2009	Varga P. Prediction of Distal Radius Fracture Load Using HR-PQCT-Based Finite Element Analysis [PhD thesis]. Vienna University of Technology; December 2009.
2014	Gross T. Development and Application of 3d CT Image-Based Micro and Macro Finite Element Models for Human Bones and Orthopedic Implant Systems [PhD thesis]. Vienna University of Technology; 2014.
2001	Boyd SK. Microstructural Bone Adaptation in an Experimental Model of Osteoarthritis [PhD thesis]. Calgary, AB: University of Calgary; January 2001.
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2010	Wald MJ. Mapping Trabecular Bone Fabric Tensor by in Vivo Magnetic Resonance Imaging [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2010.
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2018	Hosseini Kalajahi SM. Addressing Partial Volume Artifacts With Quantitative Computed Tomography-Based Finite Element Modeling of the Human Proximal Tibia [Master's thesis]. University of Saskatchewan; April 2018.
2020	Zaluski D. Validation of Subject Specific Computed Tomography-Based Finite Element Models of the Human Proximal Tibia Using Full-Field Experimental Displacement Measurements from Digital Volume Correlation [Master's thesis]. University of Saskatchewan; December 2020.
2022	Xiao P. Medical Image-Based AI Techniques in Prediction of Trabecular Bone Microarchitecture and Mechanical Properties [PhD thesis]. San Antionio, TX: University of Texas at San Antonio; December 2022.
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2022	Winsor C. Femoral Bone Quantitative CT Analyses With Internal Tissue-Based Phantomless Densitometric CT Calibration [PhD thesis]. University of Wisconsin – Madison; 2022.

Year	Entry
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