A bio-inspired remodelling algorithm combined with a natural neighbour meshless method to obtain optimized functionally graded materials

Abstract

Recent developments suggest the use of triply periodic minimal surfaces (such as the gyroid) as a possibility for bone tissue scaffold. Moreover, through functional gradients of cellular structures, the mechanical properties can be edited and enhanced to achieve the most efficient results. One of the main concerns when designing bone scaffold is avoiding stress shielding, which occurs when the Young’s modulus of the implant is higher than the Young’s modulus of the bone it is replacing. If so, bone decay occurs in the surrounding tissue. While the literature possesses some approaches exploring functional gradients of material density, there are no solutions based on bone tissue phenomenological laws. Thus, the gyroid infill obtained with PLA (E=3145 MPa) was characterized with mechanical tests, namely tensile and compression, and the obtained model was implemented in a bone remodelling algorithm. Using the natural neighbour radial point interpolation method (NNRPIM) it was found that similar bone density distributions were obtained for the gyroid infill and for bone tissue when subject to the same boundary conditions. Finally, the gyroid mechanical behaviour was extrapolated to other materials and it was concluded that similar properties can be obtained for bone tissue and titanium alloy (E=110GPa) scaffold.