Investigation of the nonlinear response of gyroid infills for prediction of the effective yield strength

A combined numerical and experimental approach is implemented to determine the effective yield strength of additively manufactured gyroid infills. A representative volume element of the infill geometry is discretized using solid elements and analyzed using the finite element method with an elastic–plastic constitutive model. The effective compressive and shear yield strengths of the cellular material are obtained for varying infill densities through compressive and shear deformations of the representative volume element under periodic boundary conditions. The numerically obtained compressive and shear yield strengths compare well with experimental data for gyroid infill prototypes manufactured using a polymer extrusion-based 3D printer. The numerical predictions are used to develop a simple semi-empirical relationship for the effective yield strength as a function of the relative density. This relationship is expected to be useful in design workflows utilizing the gyroid infill, specifically those involving topology optimization.