The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
The Anisotropic Hooke's Law for Cancellous Bone and Wood
Abstract
A method of data analysis for a set of elastic constant measurements is applied to data bases for wood and cancellous bone. For these materials the identification of the type of elastic symmetry is complicated by the variable composition of the material. The data analysis method permits the identification of the type of elastic symmetry to be accomplished independent of the examination of the variable composition. This method of analysis may be applied to any set of elastic constant measurements, but is illustrated here by application to hardwoods and softwoods, and to an extraordinary data base of cancellous bone elastic constants. The solid volume fraction or bulk density is the compositional variable for the elastic constants of these natural materials. The final results are the solid volume fraction dependent orthotropic Hooke's law for cancellous bone and a bulk density dependent one for hardwoods and softwoods.
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Trabecular bone often exhibits orthotropic symmetry.
“Trabecular bone often exhibits orthotropic symmetry (94, 95), although in some cases, such as in the vertebrae, transverse isotropy has been reported (93).”
From Bone Mechanical Properties in Healthy and Diseased States (2018) · cites this paper as [94]
Citations
Cites
Voigt, W. (1966) · Vieweg+Teubner eBooks · doi:10.1007/978-3-663-15884-4 · Cited by 3,759
On the dependence of the elasticity and strength of cancellous bone on apparent density
Rice, J. C., Cowin, S. C., & Bowman, J. A. (1988) · Journal of Biomechanics · doi:10.1016/0021-9290(88)90008-5 · Cited by 726
EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS
Mehrabadi, M. M., & COWIN, S. C. (1990) · The Quarterly Journal of Mechanics and Applied Mathematics · doi:10.1093/qjmam/43.1.15 · Cited by 390
Systematic and random errors in compression testing of trabecular bone
Keaveny, T. M., Pinilla, T. P., Crawford, R. P., Kopperdahl, D. L., & Lou, A. (1997) · Journal of Orthopaedic Research® · doi:10.1002/jor.1100150115 · Cited by 377
Fabric and elastic principal directions of cancellous bone are closely related
Odgaard, A., Kabel, J., van Rietbergen, B., Dalstra, M., & Huiskes, R. (1997) · Journal of Biomechanics · doi:10.1016/s0021-9290(96)00177-7 · Cited by 338
Self-citationRychlewski, J. (1984) · Journal of Applied Mathematics and Mechanics · doi:10.1016/0021-8928(84)90137-0 · Cited by 298
Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture
van Rietbergen, B., Odgaard, A., Kabel, J., & Huiskes, R. (1996) · Journal of Biomechanics · doi:10.1016/s0021-9290(96)80021-2 · Cited by 263
Self-citationKabel, J., van Rietbergen, B., Odgaard, A., & Huiskes, R. (1999) · Bone · doi:10.1016/s8756-3282(99)00190-8 · Cited by 206
Self-citationThe role of an effective isotropic tissue modulus in the elastic properties of cancellous bone
Kabel, J., van Rietbergen, B., Dalstra, M., Odgaard, A., & Huiskes, R. (1999) · Journal of Biomechanics · doi:10.1016/s0021-9290(99)00045-7 · Cited by 191
Self-citationvan Rietbergen, B., Odgaard, A., Kabel, J., & Huiskes, R. (1998) · Journal of Orthopaedic Research® · doi:10.1002/jor.1100160105 · Cited by 184
Self-citationON THE IDENTIFICATION OF MATERIAL SYMMETRY FOR ANISOTROPIC ELASTIC MATERIALS
Cowin, S. C., & Mehrabadi, M. M. (1987) · The Quarterly Journal of Mechanics and Applied Mathematics · doi:10.1093/qjmam/40.4.451 · Cited by 181
XXI. Elements of a mathematical theory of elasticity
THOMSON, W. J. (1856) · Philosophical Transactions of the Royal Society of London · doi:10.1098/rstl.1856.0022 · Cited by 179
Anisotropic Symmetries of Linear Elasticity
Cowin, S. C., & Mehrabadi, M. M. (1995) · Applied Mechanics Reviews · doi:10.1115/1.3005102 · Cited by 164
Application of homogenization theory to the study of trabecular bone mechanics
Hollister, S. J., Fyhrie, D. P., Jepsen, K. J., et al. (1991) · Journal of Biomechanics · doi:10.1016/0021-9290(91)90308-a · Cited by 153
Hodgskinson, R., & Currey, J. D. (1990) · Proceedings of the Institution of Mechanical Engineers Part H Journal of Engineering in Medicine · doi:10.1243/pime_proc_1990_204_240_02 · Cited by 136
Effects of Structural Variation on Young's Modulus of Non-Human Cancellous Bone
Hodgskinson, R., & Currey, J. D. (1990) · Proceedings of the Institution of Mechanical Engineers Part H Journal of Engineering in Medicine · doi:10.1243/pime_proc_1990_204_227_02 · Cited by 90
Goda, I., & Ganghoffer, J.-F. (2015) · International Journal of Engineering Science · doi:10.1016/j.ijengsci.2014.10.007 · Cited by 51
Averaging Anisotropic Elastic Constant Data
Cowin, S. C., & Yang, G. (1997) · Journal of Elasticity · doi:10.1023/a:1007335407097 · Cited by 39
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Research works printed but not linked: 2
- S.C. Cowin, Bone Mechanics. CRC Press, Boca Raton, FL (1989).
- W.K. Thomson (Lord Kelvin), Elasticity, In: Encyclopaedia Britannica, Adam and Charles Black, Edinburgh (1878).
Cited by
Sorted by citations
Trabecular bone modulus–density relationships depend on anatomic site
Morgan, E. F., Bayraktar, H. H., & Keaveny, T. M. (2003) · Journal of Biomechanics · doi:10.1016/s0021-9290(03)00071-x · Cited by 1,209
Bone Mechanical Properties in Healthy and Diseased States
Morgan, E. F., Unnikrisnan, G. U., & Hussein, A. I. (2018) · Annual Review of Biomedical Engineering · doi:10.1146/annurev-bioeng-062117-121139 · Cited by 1,026
“Trabecular bone often exhibits orthotropic symmetry (94, 95), although in some cases, such as in the vertebrae, transverse isotropy has been reported (93).”
Metadata
- Authors
- Yang, G., Kabel, J., Van Rietbergen, B., Odgaard, A., Huiskes, R., & Cown, S. C.
- Affiliations
- City College of New York (US)
- Aarhus University Hospital (DK)
- Radboud University Nijmegen (NL)
- Venue
- Journal of Elasticity
- Published
- 1998-11
- Volume
- 53
- Issue
- 2
- Pages
- 125-146
- ISSN
- 0374-3535 (ISSN-L)
- 1573-2681
- OpenAlex
- W3101779966
- Cited by
- 140
- References
- 18
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 5 · 2023: 4 · 2022: 2 · 2021: 4 · 2020: 5 · 2019: 4 · 2018: 9 · 2017: 5 · 2016: 3 · 2015: 5 · 2014: 9 · 2013: 4 · 2012: 8
- FWCI
- 2.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Journal of Elasticity (publishedVersion)
- TU/e Research Portal (publishedVersion)
- Radboud Repository (Radboud University) (submittedVersion)
- Funders
- National Cancer Institute (CMS-9401518)
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Elasticity and Material Modeling
- Physical Sciences › Engineering › Mechanics of Materials › Composite Material Mechanics
- Physical Sciences › Engineering › Mechanics of Materials › Elasticity and Wave Propagation
- Keywords
- elastic anisotropy, Hooke's law, trabecular bone, wood, elastic constants, elastic symmetry, orthotropic materials, solid volume fraction, bulk density, hardwood, softwood, natural materials
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