Dependence of elastic constants of an anisotropic porous material upon porosity and fabric
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These relations were further developed to uncouple volume fraction from fabric and to ensure positive definiteness of the elasticity tensor a priori.
“These relations were further developed to uncouple volume fraction from fabric (128) and to ensure positive definiteness of the elasticity tensor a priori (129).”
From Bone Mechanical Properties in Healthy and Diseased States (2018) · cites this paper as [128]
Cites
The compressive behavior of bone as a two-phase porous structure
Carter, D., & Hayes, W. (1977) · The Journal of Bone & Joint Surgery · doi:10.2106/00004623-197759070-00021 · Cited by 2,001 · see citing works
The mechanics of three-dimensional cellular materials
Gibson, I. J., & Ashby, M. F. (1982) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1982.0088 · Cited by 1,895 · see citing works
Initial Fabrics and their Relations to Mechanical Properties of Granular Material
Oda, M. (1972) · SOILS AND FOUNDATIONS · doi:10.3208/sandf1960.12.17 · Cited by 866 · see citing works
Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor
Harrigan, T. P., & Mann, R. W. (1984) · Journal of Materials Science · doi:10.1007/bf00540446 · Cited by 610 · see citing works
Spriggs, R. M. (1961) · Journal of the American Ceramic Society · doi:10.1111/j.1151-2916.1961.tb11671.x · Cited by 603 · see citing works
The quantitative morphology of anisotropic trabecular bone
Whitehouse, W. J. (1974) · Journal of Microscopy · doi:10.1111/j.1365-2818.1974.tb03878.x · Cited by 579 · see citing works
The relationship between the elasticity tensor and the fabric tensor
Cowin, S. C. (1985) · Mechanics of Materials · doi:10.1016/0167-6636(85)90012-2 · Cited by 570 · see citing works
Self-citationProperties and an Anisotropic Model of Cancellous Bone From the Proximal Tibial Epiphysis
Williams, J. L., & Lewis, J. L. (1982) · Journal of Biomechanical Engineering · doi:10.1115/1.3138303 · Cited by 418 · see citing works
Young's modulus of porous materials
Wang, J. C. (1984) · Journal of Materials Science · doi:10.1007/bf00540451 · Cited by 277 · see citing works
The deformation of foamed elastic materials
Gent, A. N., & Thomas, A. G. (1959) · Journal of Applied Polymer Science · doi:10.1002/app.1959.070010117 · Cited by 243 · see citing works
Some experimentally based fundamental results on the mechanical behaviour of granular materials
Oda, M., 小西, 純., & Nemat-Nasser, S. (1980) · Géotechnique · doi:10.1680/geot.1980.30.4.479 · Cited by 153 · see citing works
Elastic Compliance for Rock-Like Materials with Random Cracks
Oda, M., Suzuki, K., & Maeshibu, T. (1984) · SOILS AND FOUNDATIONS · doi:10.3208/sandf1972.24.3_27 · Cited by 108 · see citing works
Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials
Cowin, S. C., Satake, M., & Kenyon, D. E. (1979) · Journal of Applied Mechanics · doi:10.1115/1.3424704 · Cited by 93 · see citing works
Self-citationOda, M. (1983) · Mechanics of Materials · doi:10.1016/0167-6636(83)90035-2 · Cited by 83 · see citing works
Mechanical Properties of Plastic Foams
Chan, R. K. S., & Nakamura, M. (1969) · Journal of Cellular Plastics · doi:10.1177/0021955x6900500207 · Cited by 78 · see citing works
A digital computer technique for orientation analysis of micrographs of soil fabric
Tovey, N. K. (1980) · Journal of Microscopy · doi:10.1111/j.1365-2818.1980.tb04150.x · Cited by 62 · see citing works
The Deformational Behaviour of Foamed Thermoplastics
Moore, D. R., Couzens, K. H., & Iremonger, M. (1974) · Journal of Cellular Plastics · doi:10.1177/0021955x7401000307 · Cited by 39 · see citing works
The mechanical properties of high‐density rigid polyurethane foams in compression: I. Modulus
Phillips, P. J., & Waterman, N. R. (1974) · Polymer Engineering and Science · doi:10.1002/pen.760140111 · Cited by 27 · see citing works
Flagged first, then by citations
1 of the 19 references couldn’t be matched to a known paper.
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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 · see citing works
“These relations were further developed to uncouple volume fraction from fabric (128) and to ensure positive definiteness of the elasticity tensor a priori (129).”
Three-dimensional methods for quantification of cancellous bone architecture
Odgaard, A. (1997) · Bone · doi:10.1016/s8756-3282(97)00007-0 · Cited by 781 · see citing works
The fabric dependence of the orthotropic elastic constants of cancellous bone
Turner, C. H., Cowin, S. C., Rho, J. Y., ASHMAN, R. B., & Rice, J. C. (1990) · Journal of Biomechanics · doi:10.1016/0021-9290(90)90048-8 · Cited by 347 · see citing works
Self-citationSilva, M. J., Hayes, W. C., & Gibson, L. J. (1995) · International Journal of Mechanical Sciences · doi:10.1016/0020-7403(94)00018-f · Cited by 336 · see citing works
A 20-Year Perspective on the Mechanical Properties of Trabecular Bone
Keaveny, T. M., & Hayes, W. C. (1993) · Journal of Biomechanical Engineering · doi:10.1115/1.2895536 · Cited by 318 · see citing works
Determinants of the mechanical properties of bones
Martin, R. B. (1991) · Journal of Biomechanics · doi:10.1016/0021-9290(91)90379-2 · Cited by 317 · see citing works
A review of morphology–elasticity relationships in human trabecular bone: theories and experiments
Zysset, P. K. (2003) · Journal of Biomechanics · doi:10.1016/s0021-9290(03)00128-3 · Cited by 223 · see citing works
On Wolff's law of trabecular architecture
Turner, C. H. (1992) · Journal of Biomechanics · doi:10.1016/0021-9290(92)90240-2 · Cited by 123 · see citing works
Self-citationComputational methods for ultrasonic bone assessment
Luo, G., Kaufman, J. J., Chiabrera, A., Bianco, B., Kinney, J. H., Haupt, D., Ryaby, J. T., & Siffert, R. S. (1999) · Ultrasound in Medicine & Biology · doi:10.1016/s0301-5629(99)00026-5 · Cited by 116 · see citing works
Siffert, R. S., Luo, G., Cowin, S. C., & Kaufman, J. J. (1996) · Bone · doi:10.1016/8756-3282(95)00446-7 · Cited by 78 · see citing works
Self-citationAnisotropic poroelasticity: fabric tensor formulation
Cowin, S. C. (2003) · Mechanics of Materials · doi:10.1016/j.mechmat.2003.05.001 · Cited by 77 · see citing works
Self-citationPark, S., Choi, S., & Jhang, K.-Y. (2021) · International Journal of Precision Engineering and Manufacturing-Green Technology · doi:10.1007/s40684-021-00319-6 · Cited by 65 · see citing works
Biaxial Failure Behavior of Bovine Tibial Trabecular Bone
Niebur, G. L., Feldstein, M. J., & Keaveny, T. M. (2002) · Journal of Biomechanical Engineering · doi:10.1115/1.1517566 · Cited by 57 · see citing works
Properties of growing trabecular ovine bone
Nafei, A., Danielsen, C. C., Linde, F., & Hvid, I. (2000) · Journal of Bone and Joint Surgery - British Volume · doi:10.1302/0301-620x.82b6.9836 · Cited by 94 · see citing works
Fabric dependence of wave propagation in anisotropic porous media
Cowin, S. C., & Cardoso, L. (2010) · Biomechanics and Modeling in Mechanobiology · doi:10.1007/s10237-010-0217-7 · Cited by 51 · see citing works
Self-citationMoesen, M., Cardoso, L., & Cowin, S. C. (2012) · Mechanics of Materials · doi:10.1016/j.mechmat.2012.07.004 · Cited by 49 · see citing works
Self-citationMicro-macro mechanics of damage and healing in rocks
Arson, C. F. (2020) · Open Geomechanics · doi:10.5802/ogeo.4 · Cited by 48 · see citing works
Levrero-Florencio, F., Margetts, L., Sales, E., Xie, S., Manda, K., & Pankaj, P. (2016) · Journal of the Mechanical Behavior of Biomedical Materials · doi:10.1016/j.jmbbm.2016.04.008 · Cited by 46 · see citing works
Properties of growing trabecular ovine bone
Nafei, A., Kabel, J., Odgaard, A., Linde, F., & Hvid, I. (2000) · Journal of Bone and Joint Surgery - British Volume · doi:10.1302/0301-620x.82b6.9837 · Cited by 50 · see citing works
Gauthier, O., Bouler, J., Weiss, P., Bosco, J., Daculsi, G., & Aguado, E. (1999) · Journal of Biomedical Materials Research · doi:10.1002/(sici)1097-4636(199910)47:1 · Cited by 148 · see citing works
Role of structural anisotropy of biological tissues in poroelastic wave propagation
Cardoso, L., & Cowin, S. C. (2011) · Mechanics of Materials · doi:10.1016/j.mechmat.2011.08.007 · Cited by 39 · see citing works
Self-citationFabric dependence of quasi-waves in anisotropic porous media
Cardoso, L., & Cowin, S. C. (2011) · The Journal of the Acoustical Society of America · doi:10.1121/1.3557032 · Cited by 31 · see citing works
Self-citationWu, Z., LaNeve, A. J., & Niebur, G. L. (2013) · Bone · doi:10.1016/j.bone.2013.02.019 · Cited by 29 · see citing works
A Note on Fabric in Terms of Voids
小西, 純., & NARUSE, F. (1988) · Studies in applied mechanics · doi:10.1016/b978-0-444-70523-5.50012-6 · Cited by 29 · see citing works
Hosokawa, A. (2011) · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control · doi:10.1109/tuffc.2011.1958 · Cited by 28 · see citing works
A probabilistic constitutive model for closed-cell foams
Beckmann, C., & Hohe, J. (2016) · Mechanics of Materials · doi:10.1016/j.mechmat.2016.01.016 · Cited by 24 · see citing works
Bauer, J. K., & Böhlke, T. (2022) · Mechanics of Materials · doi:10.1016/j.mechmat.2022.104307 · Cited by 22 · see citing works
Martin, R. B., Burr, D. B., Sharkey, N. A., & Fyhrie, D. P. (2015) · Springer eBooks · doi:10.1007/978-1-4939-3002-9_7 · Cited by 22 · see citing works
An, K., & Luo, Z. (1998) · Journal of Mathematical Biology · doi:10.1007/s002850050114 · Cited by 20 · see citing works
Fabric tensors and effective properties of granular materials with application to snow
Shertzer, R. H. (2011) · Montana State University ScholarWorks (Montana State University) · Cited by 14 · see citing works
Micromechanical Modeling of the Anisotropy of Elastic Biological Composites
Rahmoun, J., Chaari, F., Markiewicz, É., & Drazétic, P. (2009) · Multiscale Modeling and Simulation · doi:10.1137/080745377 · Cited by 13 · see citing works
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Cowin, S. C. (1991) · Journal of Materials Science · doi:10.1007/bf01143206 · Cited by 12 · see citing works
Self-citationBahrami, M., Khonakdar, H., Moghaddam, A., Mahand, S. N., Bambizi, P. E., Kruppke, B., & Khonakdar, H. A. (2024) · Progress in Biophysics and Molecular Biology · doi:10.1016/j.pbiomolbio.2024.10.001 · Cited by 7 · see citing works
Thermal Effects in Anisotropic Porous Elastic Rods
Cicco, S. D., & Ieşan, D. (2013) · Journal of Thermal Stresses · doi:10.1080/01495739.2013.770696 · Cited by 7 · see citing works
A Note on the Microstructural Dependence of the Anisotropic Elastic Constants of Textured Materials
Cowin, S. C. (1992) · Studies in applied mechanics · doi:10.1016/b978-0-444-89213-3.50013-4 · Cited by 6 · see citing works
Self-citationA graph-based approach for computational model of bone microstructure
Kim, T., Ramanathan, M. K., & Zhang, A. (2010) · ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics (ACM-BCB) · doi:10.1145/1854776.1854883 · Cited by 6 · see citing works
Shore, S. W., Unnikrishnan, G. U., Hussein, A. I., & Morgan, E. F. (2012) · CRC Press eBooks · doi:10.1201/b13733-3 · Cited by 6 · see citing works
Lim, D., Seliktar, R., Wee, J., Tom, J. A., & Nunes, L. W. (2005) · Journal of Biomechanical Engineering · doi:10.1115/1.2165698 · Cited by 6 · see citing works
An orthotropic flow rule for superplastic Ti-6A1-4V
Mosher, D. A., & Dawson, P. R. (1994) · Mechanics of Materials · doi:10.1016/0167-6636(94)90037-x · Cited by 6 · see citing works
Noninvasive Measurement of Bone Integrity
Kaufman, J. J., & Siffert, R. S. (2001) · CRC Press eBooks · doi:10.1201/b14263-41 · Cited by 6 · see citing works
Strain and the quantitative characterization of anisotropic microstructures
Hartley, C. S. (2006) · Metallurgical and Materials Transactions A · doi:10.1007/s11661-006-1048-0 · Cited by 5 · see citing works
Cardoso, L., & Schaffler, M. B. (2014) · Journal of Biomechanical Engineering · doi:10.1115/1.4029179 · Cited by 5 · see citing works
A discrete element approach to elastic properties of layered geomaterials
Buechler, S. R., Berger, J. R., & Mustoe, G. G. W. (2011) · International Journal for Numerical and Analytical Methods in Geomechanics · doi:10.1002/nag.1115 · Cited by 5 · see citing works
A Modified Mullins Model for Compressive Behavior of Goose Down Fiber Assemblies
Wilde, T. P., McDowell, D., Jacob, K. I., & Aneja, A. P. (2005) · Mechanics of Advanced Materials and Structures · doi:10.1080/15376490500343832 · Cited by 5 · see citing works
Fabric tensor based boundary element analysis of porous solids
Berger, J. R. (2010) · Engineering Analysis with Boundary Elements · doi:10.1016/j.enganabound.2010.09.008 · Cited by 4 · see citing works
Allen, M. R., & Wallace, J. M. (2025) · Springer eBooks · doi:10.1007/978-3-031-90609-1_5 · Cited by 4 · see citing works
Development of mechanical equivalent porous structures for 3D-printed artificial femoral heads
Liu, M., Wang, J., Li, Y., Cheng, K.-Y., Huan, Y., & Li, N. (2024) · Acta Mechanica Sinica · doi:10.1007/s10409-024-24089-x · Cited by 3 · see citing works
Mathematical network model for bone mineral density (BMD) and bone quality assessment
Kim, T., Ramanathan, M. K., Bone, L. B., & Zhang, A. (2011) · ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics (ACM-BCB) · doi:10.1145/2147805.2147813 · Cited by 3 · see citing works
Inversions related to the stress-strain-fabric relationship
Sadegh, A. M., Cowin, S. C., & Luo, G. (1991) · Mechanics of Materials · doi:10.1016/0167-6636(91)90030-4 · Cited by 3 · see citing works
Self-citationApparent stiffness tensors for porous solids using symmetric Galerkin boundary elements
Elmabrouk, B., Berger, J. R., Phan, A. ‐., & Gray, L. J. (2011) · Computational Mechanics · doi:10.1007/s00466-011-0650-1 · Cited by 3 · see citing works
Elmabrouk, B., & Berger, J. R. (2012) · Computational Mechanics · doi:10.1007/s00466-012-0753-3 · Cited by 2 · see citing works
Modeling the change in the stiffness parameters of bone tissue under the influence of external loads
Gerasimov, O. V., Yaikova, V. V., Baltina, T., Baltin, M. E., Fedianin, A., Zamaliev, R. R., & Александрович, С. О. (2019) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1158/2/022045 · Cited by 2 · see citing works
Fabric Tensor-based Poroelastic Materials: a "Direct" Approach
Pernice, M. C. (2008) · Università degli Studi di Napoli Federico II · doi:10.6092/unina/fedoa/3128 · Cited by 1 · see citing works
Lim, D., Kim, H., Kim, J.-S., Seliktar, R., & Lee, S. J. (2009) · Journal of Mechanical Science and Technology · doi:10.1007/s12206-008-1103-4 · Cited by 1 · see citing works
Cowin, S. C. (1990) · MRS Proceedings · doi:10.1557/proc-207-83
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- Authors
- Turner, C. H., & Cowin, S. C.
- Affiliations
- Tulane University (US)
- Venue
- Journal of Materials Science
- Published
- 1987-09
- Volume
- 22
- Issue
- 9
- Pages
- 3178-3184
- ISSN
- 0022-2461 (ISSN-L)
- 1573-4803
- OpenAlex
- W2005243630
- Cited by
- 60
- References
- 19
- Citations by year
- 2025: 1 · 2024: 2 · 2023: 1 · 2022: 1 · 2021: 1 · 2020: 1 · 2019: 1 · 2018: 1 · 2016: 3 · 2015: 2 · 2014: 1 · 2013: 2 · 2012: 4
- FWCI
- 2.15
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Journal of Materials Science (publishedVersion)
- Topics
- Physical Sciences › Engineering › Mechanics of Materials › Composite Material Mechanics
- Physical Sciences › Engineering › Mechanical Engineering › Cellular and Composite Structures
- Physical Sciences › Engineering › Computational Mechanics › Heat and Mass Transfer in Porous Media
- Keywords
- elastic constants, anisotropic porous media, porosity, microstructural anisotropy, solid volume fraction, orthotropic elasticity, granular materials, foams, trabecular bone, rocks
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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