Analysis of viscoelastic behaviour of bones on the basis of microstructure

Gottesman, Tamar; Hashin, Zvi

Affiliations

¹Department of Solid Mechanics, Materials and Structures, School of Engineering, Tel Aviv University, Ramat Aviv, Israel

Abstract

Viscoelastic properties of bone are obtained by means of a micromechanical mode, based on the structure of the bone as a composite material. Relaxation functions, creep functions, differential stress-strain relations and corresponding rheological models are calculated as a function of the properties of the osteons and an organic bonding material.

Links

DOI: 10.1016/0021-9290(80)90182-7

PubMed: 7364783

WoS: A1980JK74600003

History

Received: 1978-04-11

Revised: 1979-05-08

Cited Works (7)

Year	Entry
1976	Yoon HS, Katz JL. Ultrasonic wave propagation in human cortical bone, I: theoretical considerations for hexagonal symmetry. J Biomech. 1976;9(6):407-412.
1971	Katz JL, Ukraincik K. On the anisotropic elastic properties of hydroxyapatite. J Biomech. May 1971;4(3):221-227.
1971	Katz JL. Hard tissue as a composite material, I: bounds on the elastic behavior. J Biomech. October 1971;4(5):455-473.
1974	Lakes RS, Katz JL. Interrelationships among the viscoelastic functions for anisotropic solids: application to calcified tissues and related systems. J Biomech. May 1974;7(3):259-270.
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.
1972	Ascenzi A, Bonucci E. The shearing properties of single osteons. Anat Rec. March 1972;172B(3):499-510.

Cited By (21)

Year	Entry
1996	Egerer AK, Saha S, McMillan PJ, Rivera J. Morphology of the cement line in human bone and its relationship to bone strength. In: Proceedings of the 15th Southern Biomedical Engineering Conference. March 29-31, 1996; Dayton, OH.7-10.
1981	Piekarski K. Mechanically enhanced perfusion of bone. In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:185-191.
2001	Lucchinetti E. Composite models of bone properties. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:12-1–12-19.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
1987	Schaffler MB, Burr DB, Frederickson RG. Morphology of the osteonal cement line in human bone. Anat Rec. March 1987;217(3):223-228.
2005	Skedros JG, Holmes JL, Vajda EG, Bloebaum AD. Cement lines of secondary osteons in human bone are not mineral‐deficient: new data in a historical perspective. Anat Rec. September 2005;286A(1):781-803.
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.
2007	Budyn É, Hoc T. Multiple scale modeling for cortical bone fracture in tension using X-FEM. Eur J Comput Mech. 2007;16(2):213-236.
2009	Budyn É, Hoc T. Analysis of micro fracture in human Haversian cortical bone under transverse tension using extended physical imaging. Int J Num Meth Eng. 2009;82(8):940-965.
1984	Pollack SR, Petrov N, Salzstein R, Brankov G, Blagoeva R. An anatomical model for streaming potentials in osteons. J Biomech. 1984;17(8):627-636.
1986	Fischer RA, Arms SW, Pope MH, Seligson D. Analysis of the effect of using two different strain rates on the acoustic emission in bone. J Biomech. 1986;19(2):119-127.
1988	Burr DB, Schaffler MB, Frederickson RG. Composition of the cement line and its possible mechanical role as a local interface in human compact bone. J Biomech. 1988;21(11):939-945.
1996	Norman TL, Nivargikar SV, Burr DB. Resistance to crack growth in human cortical bone is greater in shear than in tension. J Biomech. August 1996;29(8):1023-1031.
1996	Aoubiza B, Crolet JM, Meunier A. On the mechanical characterization of compact bone structure using the homogenization theory. J Biomech. December 1996;29(12):1539-1547.
1983	Carter DR, Caler WE. Cycle-dependent and time-dependent bone fracture with repeated loading. J Biomech Eng. May 1983;105(2):166-170.
2004	İnceoğlu S. Failure of Pedicle Screw-Bone Interface: Biomechanics of Pedicle Screw Insertion and Pullout [PhD thesis]. Cleveland State University; December 2004.
1994	Zysset P. A Constitutive Law for Trabecular Bone [PhD thesis]. Lausanne, Switzerland: École Polytechnique Fédérale de Lausanne; 1994.
1997	Bowman SM. Creep of Trabecular Bone [PhD thesis]. Cambridge, MA: Harvard University; May 1997.
2002	Egerer AK. The Relationship Between the Osteonal Cement Line and Bone Strength [PhD thesis]. Loma Linda University; June 2002.
1994	Yetkinler DN. Viscoelastic Behavior of Acrylic Bone Cements [PhD thesis]. The Ohio State University; 1994.
2004	McNamara LM. Biomechanical Origins of Osteoporosis [PhD thesis]. Trinity College Dublin; March 2004.