The mechanics of three-dimensional cellular materialsthe mechanics of three-dimensional cellular materials

Gibson, L. J.<sup>1</sup>; Ashby, M. F.<sup>2</sup>

Affiliations

¹Arctec Canada Ltd, No. 16, 6325 11th Street S.E., Calgary, Alberta T2H 2L6, Canada

²Cambridge University Engineering Department, Trumpington Street Cambridge CB2 IPZ, U.K.

Abstract

The mechanical properties (the moduli and collapse strengths) of three-dimensional cellular solids or foams are related to the properties of the cell wall, and to the cell geometry. The results of the analyses give a good description of a large body of data for polymeric foams.

Links

DOI: 10.1098/rspa.1982.0088

WoS: A1982NX60200003

JSTOR: 2397268

History

Received: 1981-11-09

Cited Works (2)

Year	Entry
1970	Timoshenko SP, Goodier JN. Theory of Elasticity. 3rd ed. New York, NY: McGraw-Hill Book Co; 1970.
1981	Gibson LJ. The Elastic and Plastic Behaviour of Cellular Materials [PhD thesis]. Cambridge, UK: University of Cambridge; August 1981.

Cited By (38)

Year	Entry
1994	Linde F. Elastic and viscoelastic properties of trabecular bone by a compression testing approach. Dan Med Bull. April 1994;41(2):119-138.
1993	Wilson KH, Carr DJ. Head protection, the application of mathematical modelling. In: Proceedings of the 1993 International IRCOBI Conference on the Biomechanics of Impact. September 8-10, 1993; Eindhoven, The Netherlands.325-336.
2020	Janc K, Tarasiuk J, Lipinski P, Bonnet A-S, Wronski S. Assessment of mechanical properties of bone trabeculae as an inverse problem of heterogeneous material modeling. Arch Mech. 2020;72(5):385-414.
1999	Sugita H, Oka M, Toguchida J, Nakamura T, Ueo T, Hayami T. Anisotropy of osteoporotic cancellous bone. Bone. May 1999;24(5):513-516.
1992	Hollister SJ, Kikuchi N. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comput Mech. March 1992;10(2):73-95.
1986	Currey JD. Power law models for the mechanical properties of cancellous bone. Eng Med. July 1986;15(3):153-154.
2001	Munro RG. Effective medium theory of the porosity dependence of bulk moduli. J Am Ceram Soc. May 2001;84(5):1190-1192.
1985	Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.
1987	Ashman RB, Corin JD, Turner CH. Elastic properties of cancellous bone: measurement by an ultrasonic technique. J Biomech. 1987;20(10):979-986.
1988	Currey JD. The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone. J Biomech. 1988;21(2):131-139.
1988	Rice JC, Cowin SC, Bowman JA. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech. 1988;21(2):155-168.
1989	Ashman RB, Rho JY, Turner CH. Anatomical variation of orthotropic elastic moduli of the proximal human tibia. J Biomech. 1989;22(8-9):895-900.
1991	Martin RB. Determinants of the mechanical properties of bones. J Biomech. 1991;24(suppl 1):79-88.
1991	Linde F, Nørgaard P, Hvid I, Odgaard A, Søballe K. Mechanical properties of trabecular bone: dependency on strain rate. J Biomech. 1991;24(9):803-809.
1991	Hollister SJ, Fyhrie DP, Jepsen KJ, Goldstein SA. Application of homogenization theory to the study of trabecular bone mechanics. J Biomech. 1991;24(9):825-839.
1992	Turner CH. On Wolff's law of trabecular architecture. J Biomech. January 1992;25(1):1-9.
1994	Keaveny TM, Guo XE, Wachtel EF, McMahon TA, Hayes WC. Trabecular bone exhibits fully linear elastic behavior and yields at low strains. J Biomech. 1994;27(9):1127-1136.
2002	Kim HS, Al-Hassan STS. A morphological model of vertebral trabecular bone. J Biomech. August 2002;35(8):1101-1114.
2005	Gibson LJ. Biomechanics of cellular solids. J Biomech. 2005;38(3):377-399.
1989	Turner CH. Yield behavior of bovine cancellous bone [published correction appears in J Biomech Eng. 1989;111(4):335]. J Biomech Eng. August 1989;111(3):256-260.
2000	Vajjhala S, Kraynik AM, Gibson LJ. A cellular solid model for modulus reduction due to resorption of trabeculae in bone. J Biomech Eng. October 2000;122(5):511-515.
2002	Niebur GL, Feldstein MJ, Keaveny TM. Biaxial failure behavior of bovine tibial trabecular bone. J Biomech Eng. December 2002;124(6):699-705.
1987	Turner CH, Cowin SC. Dependence of elastic constants of an anisotropic porous material upon porosity and fabric. J Mater Sci. September 1987;22(9):3178-3184.
1990	Keller TS, Mao Z, Spengler DM. Young's modulus, bending strength, and tissue physical properties of human compact bone. J Orthop Res. 1990;8(4):592-603.
1991	Ciarelli MJ, Goldstein SA, Kuhn JL, Cody DD, Brown MB. Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography. J Orthop Res. May 1991;9(5):674-682.
1995	Rho JY, Hobatho MC, Ashman RB. Relations of mechanical properties to density and CT numbers in human bone. Med Eng Phys. July 1995;17(5):347-355.
1983	Ashby MF. The mechanical properties of cellular solids. Metall Trans. September 1983;A14:1755-1769.
2019	Middendorf JM. Establishing New Standards for Cartilage Repair: The Structure-Function Relationship of Human Tissue Engineered Cartilage [PhD thesis]. Ithaca, NY: Cornell University; June 2019.
2005	Stauber M. Volumetric Spatial Decomposition of Porous Microstructures: A Framework for Element Based Analysis of Trabecular Bone [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2005.
2012	Hamed E. Multiscale Modeling of Elastic Moduli and Strength of Bone [PhD thesis]. University of Illinois at Urbana-Champaign; 2012.
2002	Follet H. Caractérisation Biomécanique Et Modélisation 3D Par Imagerie X Et IRM Haute Résolution De L’os Spongieux Humain: Evaluation Du Risque Fracturaire [PhD thesis]. Institut national des sciences appliquées de Lyon (INSA Lyon); 2002.
1988	Lotz JC. Hip Fracture Risk Predictions by X-Ray Computed Tomography [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; August 1988.
2012	Kelly N. An Experimental and Computational Investigation of the Inelastic Behaviour of Trabecular Bone [PhD thesis]. Galway, Ireland: National University of Ireland Galway; September 2012.
2008	Crookshank MCM. Optimizing Fracture Management: Correlating the Physical and Mechanical Properties of Bone to Computed Tomography to Generate an Estimate of Bone Quality [Master's thesis]. Queen's University; January 2008.
1987	Turner CH. On the Relationship Between the Elastic Properties of Cancellous Bone and Its Structure [PhD thesis]. New Orleans, LA: Tulane University; 1987.
2013	Sanyal A. Bone Strength Multi-Axial Behavior: Volume Fraction, Anisotropy and Microarchitecture [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2013.
1991	Hollister SJ. Homogenization Analysis of Trabecular Bone and Prediction Ofbone Ingrowth Using Topology Optimization [PhD thesis]. University of Michigan; 1991.
2020	Belda González R. Mechanical and Morphometric Characterization of Cancellous Bone [PhD thesis]. Universität Politècnica de València; March 2020.