Bone remodelling. I: Theory of adaptive elasticity. (English) Zbl 0335.73028


74L15 Biomechanical solid mechanics
74B99 Elastic materials
Full Text: DOI


[1] Herrman G. and Liebowitz H., ”Mechanics of Bone Fracture”, inFracture: An Advanced Treatise, Vol. 7, ed., Liebowitz H., Academic Press, New York, (1972) 771–840
[2] Coleman B. D. and Noll W., ”The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity”,Arch. Rat. Mech. Anal., 13 (1963) 167–178 · Zbl 0113.17802
[3] Coleman B. D. and Mizel V., ”Existence of Caloric Equations of State in Thermodynamics”,J. Chem. Phys. 40 (1964) 116–125
[4] Hegedus D. H. and Cowin S. C., Bone Remodeling II; Small Strain Adaptive Elasticity,Journal of Elasticity 6 (1976) 337–351 · Zbl 0342.73069
[5] McLean F. C. and Urist M. R.,Bone, 3rd ed., Univ. Chicago, Chicago, 1968
[6] Kummer B. K., ”Biomechanics of Bone”, inBiomechanics, ed. Fung Y. C., et al., Prentice Hall, Englewood Cliffs, N. J., (1972) 237–271
[7] Koch J. C., ”Laws of Bone Architecture”,Am. J. Anat., 21 (1917) 177–293
[8] Singh M. et al., ”Changes in Trabecular Pattern of the Upper End of the Femur as an Index of Osteoporosis”,J. Bone and Joint Surgery, 52-A (1970) 457–467
[9] Wolff J.,Das Gesetz der Transformation der Knochen, A. Hirschwald, Berlin, 1892
[10] Glucksmann A., ”Studies on Bone Mechanics in Vitro”,Anatomical Record, 72 (1938) 97–115
[11] Basset C. A. L. and Becker R. O., ”Generation of Electric Potentials in Bone in Response to Stress”,Science, 137 (1962) 1063–1064
[12] Shamos M. H. and Lavine L. S., ”Piezoelectric Effect in Bone”,Nature, 197 (1963) 81
[13] Justus R. and Luft J. H., ”A Mechanochemical Hypothesis for Bone Remodeling Induced by Mechanical Stress”,Calcified Tissue Research, 5 (1970) 222–235
[14] Frost H. M., ”Dynamics of Bone Remodeling”, inBone Biodynamics, ed. Frost H. M., Little and Brown, Boston, (1964) 316
[15] Gjelsvik A., ”Bone Remodeling and Piezoelectricity-I”,J. Biomechanics, 6 (1973) 69–77
[16] Gjelsvik A., ”Bone Remodeling and Piezoelectricity-II”.J. Biomechanics, 6 (1973) 187–193
[17] Martin R. B., ”The Effects of Geometric Feedback in the Development of Osteoporosis”,J. Biomechanics, 5 (1972) 447–455
[18] Frost H. M., ”Tetracycline-based Histological Analysis of Bone Remodeling”,Calcified Tissue Research, 3 (1969) 211–237
[19] Neuman W. F. and Neuman M. W., ”The Chemical Dynamics of Bone Mineral”, Univ. Chicago Press, Chicago, 1958
[20] Fukada E. and Yasuda I., ”On the Piezoelectric Effect of Bone”,J. Physical Soc. Japan, 12 (1957) 1158–1162
[21] Becker R. O. and Murray D. G., ”The Electrical Control System Regulating Fracture Healing in Amphibians”,Clinical Orthopedics, 73 (1970) 169–198
[22] Basset C. A. L. and Pawluk R. J., ”Effect of Electric Currents of Bone in Vivo”,Nature, 204 (1964) 652–653
[23] Truesdell C. and Toupin R., ”The Classical Field Theories”,Handbook of Physics, III/1, Springer, New York, 1960
[24] Truesdell C. and Noll W., ”Non-Linear Field Theories”,Handbook of Physics, III/3, Springer, New York, 1965 · Zbl 0779.73004
[25] Goodman M. A. and Cowin S. C., ”A Continuum Theory for Granular Materials”,Arch. Rat. Mech. Anal., 44 (1972) 249–266 · Zbl 0243.76005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.