Dependence of elastic constants of an anisotropic porous material upon porosity and fabric

Turner, Charles H.; Cowin, Stephen C.

Affiliations

¹Department of Biomedical Engineering, Tulane University, New Orleans, USA

Abstract

The elastic properties of an anisotropic porous material can be represented as functions of the material's solid volume fraction (or porosity) and the principal diameters of the material's fabric ellipsoid. The fabric ellipsoid is a measure of the anisotropy of the microstructure of a material. The definitions and measurement techniques for fabric ellipsoids in granular materials, foams, cancellous bone, and rocks are discussed. The principal results presented in this work are algebraic expressions for the dependence of the orthotropic elastic constants upon both solid volume fraction and the fabric ellipsoid.

Links

DOI: 10.1007/BF01161180

WoS: A1987K274900014

History

Received: 1986-06-09

Accepted: 1986-08-18

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Cited By (19)

Year	Entry
2001	Kaufman JJ, Siffert RS. Noninvasive measurement of bone integrity. In: Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001:34-1–34-25.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
1997	Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone. 1997;20(4):315-328.
1990	Turner CH, Cowin SC, Rho JY, Ashman RB, Rice JC. The fabric dependence of the orthotropic elastic constants of cancellous bone. J Biomech. 1990;23(6):549-561.
1991	Martin RB. Determinants of the mechanical properties of bones. J Biomech. 1991;24(suppl 1):79-88.
1992	Turner CH. On Wolff's law of trabecular architecture. J Biomech. January 1992;25(1):1-9.
2003	Zysset PK. A review of morphology–elasticity relationships in human trabecular bone: theories and experiments. J Biomech. October 2003;36(10):1469-1485.
1993	Keaveny TM, Hayes WC. A 20-year perspective on the mechanical properties of trabecular bone. J Biomech Eng. November 1993;115(4B):534-542.
2002	Niebur GL, Feldstein MJ, Keaveny TM. Biaxial failure behavior of bovine tibial trabecular bone. J Biomech Eng. December 2002;124(6):699-705.
2000	Nafei A, Kabel J, Odgaard A, Linde F, Hvid I. Properties of growing trabecular ovine bone, II: architectural and mechanical properties. J Bone Joint Surg. August 2000;82B(6):921-927.
2012	Moesen M, Cardoso L, Cowin SC. A symmetry invariant formulation of the relationship between the elasticity tensor and the fabric tensor. Mech Mater. November 2012;54:70-83.
2005	Day JS. Bone Quality: The Mechanical Effects of Microarchitecture and Matrix Properties [PhD thesis]. Erasmus University Rotterdam; 2005.
1996	Silva MJ. Predicting the Failure Behavior of the Human Vertebral Body [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; February 1996.
2023	Branni MG. Constitutive Models of Bone: The Human Femur [PhD thesis]. Queensland University of Technology; 2023.
2011	Yao H. Microstructure-Based Characterization and Modeling of Trabecular Bone Deformation and Failure [PhD thesis]. Southern Methodist University; August 3, 2011.
1987	Turner CH. On the Relationship Between the Elastic Properties of Cancellous Bone and Its Structure [PhD thesis]. New Orleans, LA: Tulane University; 1987.
1994	Fritton SP. Computational Simulation of Trabecular Bone Adaptation [PhD thesis]. Tulane University; January 1994.
2000	Niebur GL. A Computational Investigation of Multiaxial Failure in Trabecular Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2000.
2010	Wald MJ. Mapping Trabecular Bone Fabric Tensor by in Vivo Magnetic Resonance Imaging [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2010.