Design of Menger sponge fractal structural NiTi as bone implants

Finite element simulations were performed to investigate potential applications of Menger sponge fractal NiTi structures as bone implants. The tunable correlations between porosity and fractal parameters in Menger sponge fractal structures were explored to match the characteristics of the natural bones, including porosity, hierarchical porous structures, and fractal dimensions. The computational results demonstrate that the broad range of elastic modulus and yield stress in our designed fractal NiTi structures can satisfy the mechanical requirements of natural bones. In addition, the hierarchical-stepwise phase transformation in fractal NiTi structures exhibits a statistical power-law behavior, which is compatible with the multiscale failure process during deformation in natural bones. These results indicate that Menger sponge fractal NiTi structures may have great potentials for bone implants. The present design concept of fractal structures may open new avenues in biomechanical capabilities that conventional metal structures cannot achieve.