Chapter 10 - Determination of the Anisotropic Mechanical Properties of Bone Tissue Using a Homogenization Technique Combined With Meshless Methods

Abstract

Bone has different functional requirements at different scales, from the macroscale to the microscale. Bone remodeling has as a consequence the change of the bone morphology at its microscale, leading to the change of bone's mechanical properties. The literature shows that it is possible to obtain the fourth-rank elasticity tensor from the fabric tensor. Furthermore, previous studies have demonstrated that the fabric tensor can be directly correlated with a material image using a fabric tensor morphologic-based methodology—the mean intercept length tensor. In this work, the same methodology is applied in order to obtain the homogenized material elasticity tensor. Thus, the main objective of this work was to combine a new developed homogenization technique, applying the fabric tensor concept to medical CT/micro-CT images, with a previously developed bone tissue material law, allowing us to expeditiously define the homogenized mechanical properties of trabecular bone at its microscale and to reduce the analysis computational cost.