The Meshless Methods in the Bone Tissue Remodelling Analysis

Abstract

This work shows the advantages of using meshless methods to study the bone tissue remodelling phenomenon. The meshless method used in this work is the Natural Neighbour Radial Point Interpolation Method, a truly and organic meshless method. The inclusion of the NNRPIM in the process is an asset, since, when compared with other numerical approaches, it permits to produce smoother and more accurate variable fields, such as the displacement field and the stress/strain fields.Regarding the remodelling algorithm, in this work, it is considered a phenomenological bone tissue mathematical law capable to correlate the bone tissue mechanical properties (Young's modulus and ultimate compression stress) with the bone tissue apparent density. This anisotropic phenomenological law was constructed using experimental data found in the literature. Additionally, the remodelling algorithm used in this study seeks the minimization of the strain energy density. Thus, using an anisotropic material law for the mechanical behaviour of the bone tissue, the assumed biomechanical model is able to iteratively correct the local bone tissue apparent density for each integration point, using the obtained level of stress from the numerical analysis.