Yield Criterion for a Surface-Based Gyroid Structure: a Homogenization Approach

Cellular structures based on Triply-Periodic Minimal Surfaces are a popular option in the design of load bearing structures, because of their high, yet tunable, mechanical properties. Additive Manufacturing has made these structures feasible in a finished product, increasing their popularity even more. The simulation of large components which include these structures usually require high computational costs if the effective geometry of the lattice is included in the model. This problem may be solved by adopting a homogeneous material equivalent to the effective lattice. Many techniques have been developed for the homogenization of the elastic properties of lattice structures, but much less is known about their resistance. A yielding criterion is required to determine the initial collapse of these structures with the limited set of information provided by the homogenized material. This paper proposes a criterion to determine the yielding of periodic structures subject to multi-axial loading conditions. This criterion is applied to the surface based Gyroid at varying relative density. Finite Element methods will be performed in linear elastic conditions to link the macroscopic loads on an infinite lattice to the failure conditions of the material within the unit cell.