Investigation on the orientation dependence of elastic response in Gyroid cellular structures

Abstract

Materials used for hard tissue replacement should match the elastic properties of human bone tissue. Therefore, cellular structures are more favourable for the use of implants than solid materials for their custom-designed mechanical properties. The superimposed load from various directions in vivo makes uniaxial compression testing insufficient for describing the mechanical responses. In this paper, the rotational symmetry of Gyroid cellular structure (GCS) was discussed. An approach using structural simplification and analytical solution was presented to investigate the relationship between Young's modulus and volume fraction, as well as the orientation dependence of the mechanical responses for GCS loaded in various orientations. It is concluded that the analytical solution is reasonable for a low volume fraction, through the comparison between analytical results, finite element (FE) and experimental data. Gained polar diagrams illustrate the anisotropic property of GCS and also confirm the superiority for their stable mechanical responses of diverse loading directions.

Keywords: Analytical solution; Gyroid cellular structure; Triply periodic minimal surface; Young's modulus.