Finite element analysis of the impact of bone nanostructure on its piezoelectric response

The piezoelectric response of bone at the submicron scale is analyzed under mechanical loadings using the finite element (FE) method. A new algorithm is presented to virtually reconstruct realistic bone nanostructures, consisting of collagen fibrils embedded in a hydroxyapatite mineral network. This algorithm takes into account potential misalignments between fibrils, as well the porous structure of the mineral phase. A parallel non-iterative mesh generation algorithm is utilized to create high-fidelity FE models for several representative volume elements (RVEs) of the bone with various fibrils volume fractions and misalignments. The piezoelectric response of each RVE is simulated under three types of loading: the longitudinal compression, lateral compression, and shear. The resulting homogenized stress and electric field in RVEs with aligned fibrils showed a linear variation with the fibrils volume fraction under all loading conditions. For RVEs with misaligned fibrils, although more oscillations were observed in homogenized results, their difference with the results of RVEs with aligned fibrils subject to lateral compression and shear loadings were negligible. However, under longitudinal compression, the electric field associated with RVEs with misaligned fibrils was notably higher than that of RVEs with aligned fibrils for the same volume fraction.