Homogenization of the yield surface of body-centered cubic and octet lattice structures under multiaxial loadings

Lattice structures are gaining increasing popularity, owing to their superior mechanical properties per weight. Modelling these structures is computationally demanding, and homogenizing their mechanical response is a promising approach to model porous materials. While attention is paid to the elastic response, the yield surface is less discussed, especially in multiaxial loading conditions. In this study, we consider body-centered cubic (BCC) and octet lattice structures as two representative structures, and explore yield criteria for a homogenized model. We use finite element modelling (FEM) to simulate lattices under various loading conditions: uniaxial compression, simple shearing, proportional biaxial and triaxial loadings, and define the yield states based on the principle of equivalent plastic work. Both BCC and octet structures obey anisotropic yielding, while BCC is stronger in shearing than in compression direction, making it more anisotropic. We explore different homogenized yield criteria and find that Liu–Huang–Stout yield criteria is the most comparable to the simulation results. This model, which is anisotropic and considers a linear dependence of mean stress, was found to be the best candidate to describe the multiaxial plastic behavior of lattice structures.