Using a radial point interpolation meshless method and the finite element method for application of a bio-inspired remodelling algorithm in the design of optimized bone scaffold

Abstract

The design of bone scaffold involves the analysis of stress shielding, which can occur when the Young’s modulus of the implant is higher than the Young’s modulus of the bone it is replacing, leading to bone decay in the surrounding tissue. It is therefore very important that the material is adequately designed to match the properties of the surrounding tissue, allowing an appropriate load transfer. While some approaches exist in the literature exploring functional gradients of material density, there are much less solutions based on biological laws. A homogenized model of gyroid infill obtained with PLA (E = 3145 MPa) was obtained through mechanical tests of 3D printed specimens, namely tensile and compression, and the obtained model was implemented in a bone remodelling algorithm. The homogenized law was compared to the results obtained with a bone tissue law to assess the equivalence of density distribution and mechanical properties. Through a radial point interpolation method, it was found that similar density fields were obtained for the gyroid infill and for bone tissue when subject to the same boundary conditions. The finite element method was also used for comparison and validation. With the density field results, the gyroid mechanical behaviour was extrapolated to other materials, and similar stiffness values were obtained for bone tissue and titanium alloy (E = 110 GPa) scaffold, which justify this proposal of gyroid scaffolds for mimicking bone properties.