A symmetry invariant formulation of the relationship between the elasticity tensor and the fabric tensor

Moesen, Maarten; Cardoso, Luis; Cowin, Stephen C.

Affiliations

¹Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, PB 2450, 3001 Leuven, Belgium

²Prometheus, Division of Skeletal Tissue Engineering, Katholieke Universiteit Leuven, O&N 1, Herestraat 49, PB 813, 3000 Leuven, Belgium

³The New York Center for Biomedical Engineering, The Departments of Biomedical & Mechanical Engineering, The School of Engineering of The City College, and The Graduate School of The City University of New York, NY 10031, USA

Abstract and keywords

The fabric tensor is employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium. Earlier work showed that the fabric tensor can be used additionally to the porosity to describe the anisotropy in the elastic constants of the porous medium. This contribution presents a reformulation of the relationship between fabric tensor and anisotropic elastic constants that is approximation free and symmetry-invariant. From specific data on the elastic constants and the fabric, the parameters in the reformulated relationship can be evaluated individually and efficiently using a simplified method that works independent of the material symmetry. The wellbehavedness of the parameters and the accuracy of the method was analyzed using the Mori–Tanaka model for aligned ellipsoidal inclusions and using Buckminster Fuller’s octet-truss lattice. Application of the method to a cancellous bone data set revealed that employing the fabric tensor allowed explaining 75–90% of the total variance. An implementation of the proposed methods was made publicly available.

Keywords: Anisotropy; Elastic constants; Fabric tensor; Orthogonal basis; Parameters; Cancellous bone

Links

DOI: 10.1016/j.mechmat.2012.07.004

PubMed: 23467780

WoS: 000309029900006

History

Received: 2011-09-09

Online: 2012-07-16

Cited Works (22)

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Cited By (1)

Year	Entry
2013	Souzanchi MF. The Effect of Microarchitecture and Fabric Anisotropy of Trabecular Bone on Its Mechanical Behavior [PhD thesis]. New York, NY: The City University of New York; 2013.