Abstract
The dynamic stress-strain characteristics of beef-femur bone as a function of elapsed post-mortem time have been determined directly using the split-Hopkinson-bar technique. Specimens were fabricated from dense cortical material of the posterior part of the femoral midshaft and and subjected to dynamic compressive loading (1∼6) × 108 psi/sec covering a wide range of strain rates (10∼450 sec−1). Eighty-two test runs were conducted using 43 bone specimens for a range of post-mortem ages (1∼240 days). A linear-viscoelastic model describing the mechanical behavior of bone was obtained, including an estimate of the parameters immediately after death.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A, A s :
-
cross-sectional area of rod and specimen, respectively
- C :
-
(E/ρ)1/2, elastic one-dimensional wave velocity
- D :
-
specimen diameter
- E :
-
Young's modulus of elasticity
- \(\bar E\) :
-
compressive modulus for viscoelastic material
- F :
-
force
- L :
-
specimen length
- P, Q :
-
polynomials in the operator (d/dt)
- t :
-
time
- U :
-
particle displacement
- V :
-
particle velocity
- ∈ S,∈ S :
-
specimen strain and strain rate, respectively
- ∈ I,∈ O,∈ R :
-
incident, transmitted and reflected strains, respectively
- η:
-
viscoelastic damping coefficient
- ρ:
-
density
- σ S :
-
specimen stress
- τ:
-
time
References
Sedlin, E. D., “A Rheological Model for Cortical Bone,”Acta Ortho. Scan., Sup. 83,36 (1965).
Piekarski, K., “Studies on the Mechanical Properties of Bone,” PhD Thesis, Cambridge University (1968).
Evans, F. G., “Stress and Strain in Bones,”C. C. Thomas, Springfield, Ill. (1957).
Kraus, H., “On the Mechanical Properties and Behavior of Human Compact Bone,” Advances in Biomedical Engineering and Medical Physics, S. N. Levine, ed., Wiley-Interscience,2 (1968).
Swanson, S. A. V., “Mechanical Properties of Bone,” Advances in Biomedical Engineering, R. M. Kenedi, ed., Pergamon,1 (1971).
McElhaney, J., Fogle, J., Byars, E. and Weaver, G., “Effect of Embalming on the Mechanical Properties of Beef Bone,”J. Appl. Physiol,19 (6) (1964).
Bird, F., Becker, H., Healer, J. and Messer, M., “Experimental Determination of the Mechanical properties of Bone,” J. Aerospace Med. (Jan. 1968).
Lang, S. B., “Elastic Coefficients of Animal Bone,” Science,165 (July 1969).
McElhaney, J. and Roberts, V., “Mechanical Properties of Cancellous Bone,” AIAA 9th Aerospace Sciences Meeting, Paper No. 71-111 (Jan. 1971).
Dempster, W. T. andLiddicoat, R. T., “Compact Bone as a Non-isotropic Material,”Am. J. Anat.,91,331 (1952).
Dempster, W. T. andColeman, R. F., “Tensile Strength of Bone Along and Across the Grain,”J. Appl. Physiol.,16,355 (1961).
Lugassy, A. A. andKorostoff, E., “Viscoelastic Behavior of Bovine Femoral Cortical Bone and Sperm Whale Dentin,”Research in Dental and Medical Materials, E. Korostoff, ed., Plenum Press, New York (1969).
Renton, D. and Piekarski, K., “Motion of Low Viscosity Liquids in Cortical Bone Subjected to Cyclic Loading,” Proc. 3rd Can. Med. and Biol. Eng. Conf., (Sept. 1970).
Smith, R. W. and Keiper, D. A., “Dynamic Measurement of Viscoelastic Properties of Bone,” Amer. J. of Med. Elect., (4) (1965).
McElhaney, J., “Dynamic Response of Bone and Muscle Tissue,”J. Appl. Physiol,21 (4) (1966).
Tennyson, R. C. and Ewert, R., “Application of the Split Hopkinson Bar to Determine the Dynamic Response of Bone,” Proc. 3rd Can. Med. and Biol. Eng. Conf., (Sept. 1970).
Kolsky, H., “An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading,”, Proc. Phys. Soc., Sec. B.,62 (1949).
Davies, E. D. H. and Hunter, S. C., “The Dynamic Compression Testing of Solids by the Method of the Split Hopkinson Pressure Bar,” J. Mech. and Phys. of Solids,11 (1963).
Lindholm, U. S., “Some Experiments With the Split Hopkinson Pressure Bar,” J. Mech. and Phys. of Solids,12 (1964).
Hauser, F. E., “Techniques for Measuring Stress-Strain Relations at High Strain Rates,”Experimental Mechanics,6 (8),395–402 (1966).
Bell, J. F., “An Experimental Diffraction Grating Study of the Quasi-Static Hypothesis of the Split Hopkinson Bar Experiment,” J. Mech. and Phys. of Solids,14 (1966).
Maiden, C. J. and Green, J., “Compressive Strain-Rate Tests on Six Selected Materials at Strain Rates from 10 −3 to 10 4 In/In/Sec,” Trans of the ASME, J. Applied Mech. (Sept. 1966).
Tulk, J. D., “Application of the Split Hopkinson Bar to the Dynamic Testing of Materials,” MASc Thesis, University of Toronto Institute for Aerospace Studies (April 1969).
Ascenzi, A., Bonucci, E. andCheccucci, A., “The Tensile Properties of Single Osteons Studied Using a Microwave Extensimeter,”Studies on the Anatomy and Function of Bone and Joints, F. G. Evans, ed.,Springer-Verlag, New York (1966).
Ascenzi, A. andBonucci, E., “The Ultimate Tensile Strength of Single Osteons,”Acta Anat.,58,160–183 (1964).
Ascenzi, A. andBonucci, E., “The Compressive Properties of Single Osteons,”Anat. Rec.,161,377–392 (1968).
Nevill, G. E., Lloyd, J. M. and Fuehrer, H. R., “Dynamic Properties of Metal Powder-Epoxy Resin Composites,” J. Composite Materials,3 (Jan. 1969).
Sierakowski, R. L., Nevill, G. E., Ross, C. A. and Jones, E. R., “Dynamic Compressive Strength and Failure of Steel Reinforced Epoxy Composites,” J. Composite Materials,5 (July 1971).
Zisman, W. A., “Comparison of the Statically and Seismologically Determined Elastic Constants of Rocks,”Proc. Nat. Acad. Sc.,19 (7),680–686 (July 1933).
Bland, D. R., “The Theory of Linear Viscoelasticity,”Pergamon Press, New York (1960).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tennyson, R.C., Ewert, R. & Niranjan, V. Dynamic viscoelastic response of bone. Experimental Mechanics 12, 502–507 (1972). https://doi.org/10.1007/BF02320746
Issue Date:
DOI: https://doi.org/10.1007/BF02320746