title: A symmetry invariant formulation of the relationship between the elasticity tensor and the fabric tensor.
abstract: 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 well-behavedness 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.
authors: Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, PB 2450, 3001 Leuven, Belgium ; Prometheus, Division of Skeletal Tissue Engineering, Katholieke Universiteit Leuven, O&N 1, Herestraat 49, PB 813, 3000 Leuven, Belgium.
authors: Maarten
authors: M
authors: Moesen
authors: Luis
authors: L
authors: Cardoso
authors: Stephen C
authors: SC
authors: Cowin
keywords: Anisotropy; Cancellous bone; Elastic constants; Fabric tensor; Orthogonal basis; Parameters