Finite element analysis of the effect of boron nitride nanotubes in beta tricalcium phosphate and hydroxyapatite elastic modulus using the RVE model

A numerical study was carried out to determine the effect of the boron nitride nanotubes (BNNTs) as a reinforcement element for two different implant materials. Random distribution of the BNNTs was reconstructed using the random sequential adsorption algorithm in the beta tricalcium phosphate (β-TCP) and hydroxyapatite (HA) matrixes. A representative volume element (RVE) with 4% wt. of the BNNTs in β-TCP and HA matrixes was prepared. The predicted elastic moduli of the β-TCP-BNNTs and HA-BNNTs composites showed 24.1% and 26.3% enhancement, respectively, compared with the pure β-TCP and HA. To validate our finite element method (FEM) analysis results, we used a modified Halpin-Tsai (H-T) approach to calculate the elastic modulus of the models. The results showed that the FEM and H-T were in good agreement, with 1.5% and 2.7% deviations for the β-TCP-BNNTs and HA-BNNTs composites, respectively. In contrast, a major gap was found between our theoretical approaches and experimental results for the HA-BNNTs composite that is available in the literature. This deviation was probably a consequence of the manufacturing method of the composite, which was not considered in the RVE model.