In this study, the mechanical properties (elastic modulus, yield stress, and Poisson's ratio) of rhombic dodecahedron (RD) unit cell has been studied analytically and numerically. For the analytical study, two well-known beam theories, namely Euler Bernoulli and Timoshenko, have been implemented. For validating the analytical relationships, finite element model of unit cell with repetitive boundary condition has been created. Moreover, the experimental results of recent studies have been used for validation. The results showed that the presented analytical relationships for RD lattice structure have good agreement with numerical and experimental results in all the relative densities particularly in lower relative densities. Besides, the analytical relationships based on Timoshenko theory showed closer results with numerical/experimental data. The derived analytical relationships for RD as well as the data extracted from CT scan images of a femur bone, were combined and used to create a porous femur implant model. The stress and strain distributions of the porous femur model under typical static compressive load due to human weight as well as axial rigidity of the model in the same loading conditions have been obtained and compared with the experimental results from other studies. The stress and strain distributions of the porous femur implant model based on RD unit cells, as well as its axial rigidity, showed good agreement with the results obtained for human femur.

Original languageEnglish
Pages (from-to)801-823
Number of pages23
JournalApplied Mathematical Modelling
Publication statusPublished - 1 Jul 2020

    Research areas

  • Additive manufacturing, CT scan, Femur bone, Porous biomaterials, Rhombic dodecahedron

ID: 72216610