Using Radius of Gyration in Order to Determine Surrogate Mechanical Properties of a Porous Structure

Abstract Advances in additive manufacturing have now made printing very fine design features possible, giving rise to the possibility of incorporating a porous structure within a component to act as a thermal barrier. The model of such a component may be simplified during finite element analysis by replacing the topographically complex porous structure with that of a homogeneous material having surrogate material properties equivalent to those of the porous structure. Determining changes in length within a porous structure for the purpose of calculating strain presents a challenge. Due to the nature of the porous structure, non-uniform displacements are possible, introducing difficulty in assessing aggregate displacements. The possibility of using the radius of gyration as a measure of displacements within a structure is explored in the present study. The positions of finite element meshing nodes were used to calculate mass distribution within unit cells of a gyroid structure, and from this, a radius of gyration was derived. Unit strain, and consequently Young’s modulus and Poisson’s ratio were obtained for the porous structure from the changes in radii of gyration, which can be used to describe an equivalent bulk material. Excellent agreement was obtained when directly comparing the elastic response of a gyroid cluster and equivalent homogeneous material under identical loading conditions.