Combining radial point interpolation meshless method with a new homogenization technique for trabecular bone multiscale structural analyses.

Purpose: Bone tissue is a dynamic tissue, possessing different functional requirements at different scales. This layered organization indicates the existence of a hierarchical structure, which can be characterized to distinguish macro-scale from micro-scale levels. Structurally, both scales can be linked by the use of classic multiscale homogenization techniques. Since in bone tissue each micro-scale domain is distinct form its neighbour, applying a classic multiscale homogenization technique to a complete bone structure could represent an inadmissible computational cost. Thus, this work proposes a homogenization methodology that is computationally efficient, presenting a reduced computational cost, and is capable to define the homogenized microscale mechanical properties of the trabecular bone highly heterogeneous medium.
Methods: The methodology uses the fabric tensor concept in order to define the material principal directions. Then, using an anisotropic phenomenological law for bone tissue correlating the local apparent density with directional elasticity moduli, the anisotropic homogenized material properties of the micro-scale patch are fully defined. To validate the developed methodology, several numerical tests were performed, measuring the sensitivity of the technique to changes in the micro-patch size and preferential orientation.
Results: The results show that the developed technique is robust and capable to provide a consistent material homogenization. Additionally, the technique was combined with two discrete numerical techniques: the finite element method and radial point interpolation meshless method.
Conclusions: Structural analyses were performed using real trabecular patches, showing that the proposed methodology is capable to accurately predict the micro-scale patch mechanical behavior in a fraction of the time required by classic homogenization techniques.