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Adaptive elasticity*

Published online by Cambridge University Press:  17 April 2009

Stephen C. Cowin
Affiliation:
Department of Biomedical Engineering, School of Engineering, Tulane University, New Orleans, Louisiana 70118, USA.
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Abstract

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Type
Australian Mathematical Society Applied Mathematics Conference
Copyright
Copyright © Australian Mathematical Society 1982

References

[1] Anonymous, “The shaken trees”, Time 42 (1971).Google Scholar
[2]Bassett, C. Andrew L., Becker, Robert O., “Generation of electric potentials in bone in response to mechanical stress”, Science 137 (1962), 10631064.CrossRefGoogle ScholarPubMed
[3]Burger, H. Robert, “Pressure-solution: How important a role?“, Geol. Soc. Amer. Abstr. Programs 6 (1974), 10261027.Google Scholar
[4]Cowin, S.C. and Firoozbakhsh, K., “Bone remodeling of diaphyseal surfaces under constant load: theoretical predictions”, J. Biomeah, 14 (1981),471484.CrossRefGoogle ScholarPubMed
[5]Cowin, S.C. and Hegedus, D.H., “Bone remodeling. I. Theory of adaptive elasticity”, J. Elasticity 6 (1976), 313326.CrossRefGoogle Scholar
[6]Cowin, S.C. and Nachlinger, R. Ray, “Bone remodeling. III. Uniqueness and stability in adaptive elasticity theory”, J. Elasticity 8 (1978), 285295.CrossRefGoogle Scholar
[7]Cowin, S.C. and Buskirk, W.C. Van, “Internal bone remodeling induced by a medullary pin”, J. Biomech. 11 (1978), 269275.CrossRefGoogle ScholarPubMed
[8]Cowin, S.C. and Van Buskirk, W.C., “Surface bone remodeling induced by a medullary pin”, J. Biomech. 12 (1979), 269276.CrossRefGoogle ScholarPubMed
[9]Currey, J.D., “Differences in the blood supply of bone of different histological types”, Quart. J. Microscopical Sci. 101 (1960), 351370.Google Scholar
[10]Durney, D.W., “Pressure-solution and crystallization deformation”, Phil. Trans. Roy. Soc. London Ser. A 283 (1976), 229240.Google Scholar
[11]Firoozbakhsh, K. and Cowin, S.C., “Devolution of inhomogeneities in bone structure – predictions of adaptive elasticity theory”, J. Biomech. Engr. 102 (1980), 287293.CrossRefGoogle ScholarPubMed
[12]Frost, H.M., “Dynamics of bone remodeling”, Bone biodynamics, (Little and Brown, Boston, 1964).Google Scholar
[13]Groshong, R.H. Jr, “Strain fractures and pressure solution in natural single layer folds”, Geol. Soc. Amer. Bull. 86 (1975), 13631376.2.0.CO;2>CrossRefGoogle Scholar
[14]Guzelsu, Nejat and Demiray, Hilmi, “Electromechanical properties and related models of bone tissues”, Internat. J. Engrg. Sci. 17 (1979), 813851.CrossRefGoogle Scholar
[15]Hegedus, D.H. and Cowin, S.C., “Bone modeling. II. Small strain adaptive elasticity”, J. Elasticity 6 (1976), 337352.CrossRefGoogle Scholar
[16]Jaworski, Z.F.G., Liskova-Kiar, M. and Uhthoff, H.K., “Effect of long-term immobilisation on the pattern of bone loss in older dogs”, J. Bone Joint Surg. 62B (1980), 104110.CrossRefGoogle Scholar
[17]Justus, R. and Luft, J.H., “A mechanochemical hypothesis for bone remodeling induced by mechanical stress”, Calcif. Tissue Res. 5 (1970), 222235.CrossRefGoogle ScholarPubMed
[18]Kazarian, L.E., Gierke, H. Von, “Bone loss as a result of immobilization and chelation”, Clin. Orthop. 65 (1969), 6775.CrossRefGoogle ScholarPubMed
[19]Knets, I.V. and Malmeisters, A., “The deformability and strength of human compact bone tissue”, Mechanics of biological solids, – (Proc. Euromech Colloquium 68. Varna, Bulgaria, 1977).Google Scholar
[20]Lišková, M., Heřt, J., “Reaction of bone to mechanical stimuli. 2. Periosteal and endosteal reaction of tibial diaphysis in rabbit to intermittent loading”, Folia Morphol. 19 (1971), 301317.Google ScholarPubMed
[21]Logan, B.W. and Semeniuk, V., Dynamic metamorphism; processes and products in Devonian carbonate rocks, Canning Basin, Western Australia (Special Publication 6. Geological Society of Australia, Sydney, 1976).Google Scholar
[22]Meade, J.B., Cowin, S.C., Klawitter, J.J., Buskirk, W.C. Van, Skinner, H.B. and Weinstein, A.M., “Short term remodeling due to hyper-physiological stress”, J. Bone Joint Surg. (to appear).Google Scholar
[23]Neel, P.L. and Harris, R.W., “Motion-induced inhibition of elongation and induction of dormancy in liquidambar”, Science 173 (1971), 5859.CrossRefGoogle ScholarPubMed
[24]Russell, George A., “Crystal growth and solution under local stress”, Amer. Mineral. 20 (1935), 733737.Google Scholar
[25]Shamos, Morris H., Lavine, Leroy S., Shamos, Michael I., “Piezoelectric effect in bone”, Nature 197 (1963), 81.CrossRefGoogle ScholarPubMed
[26]Shumskii, V.V., Merten, A.A. and Dzenis, V.V., “Effect of the type of physical stress on the state of the tibial bones of highly trained athletes as measured by ultrasound techniques”, Mekhanika Polimerov 5 (1978), 884888.Google Scholar
[27]Somjen, Dalia, Binderman, Itzhak, Berger, Esther and Harell, Arie, “Bone remodelling induced by physical stress in prostaglandin E2 mediated”, Biochimica et Biophysica Acta 627 (1980), 91100.CrossRefGoogle ScholarPubMed
[28]Sprunt, Eve S., Nur, Amos, “Reduction of porosity by pressure solution: Experimental verification”, Geology 4 (1976), 463466.2.0.CO;2>CrossRefGoogle Scholar
[29]Sprunt, Eve S. and Nur, Amos, “Destruction of porosity through pressure solution”, Geophysics 42 (1977), 726741.CrossRefGoogle Scholar
[30]Sprunt, Eve S. and Nur, Amos, “Experimental study of the effects of stress on solution rate”, J. Geophy. Res. 82 (1977), 30133022.CrossRefGoogle Scholar
[31]Uhthoff, H.K. and Jaworski, Z.F., “Bone loss in response to long-term immobilisation”, J. Bone Joint Surg. [Br] 60B, (1978), 420429.CrossRefGoogle Scholar
[32]Wolff, J., Das Gesetz der Transformation der Knoahen (Hirschwald, Berlin, 1892).Google Scholar
[33]Woo, S.L.Y., Kuei, S.C., Dillon, W.A., Amiet, D., White, F.C. and Akeson, W.H., “The effect of prolonged physical training on the properties of long bone – a study of Wolff's law”, J. Bone Joint Surg. (to appear).Google Scholar
[34]Wright, T.M., Hayes, W.C., “Tensile testing of bone over a wide range of strain rates; effects of strain rate, microstructure and density”, Med. & Biol. Eng. (GB) 14 (1976), 671680.CrossRefGoogle Scholar
[35]Zimmermann, M.H., The formation of wood in forest trees (Academic Press, New York, London, 1964).Google Scholar
[36]Zimmermann, M.H. and Brown, C.L., Trees, structure and function (Springer-Verlag, Berlin, Heidelberg, New York, 1970).Google Scholar