Assessment of analytical relationships for mechanical properties of truncated octahedron and diamond lattice structures

Although several analytical models for the prediction of mechanical properties for truncated octahedron and cubic diamond lattices are available in the literature, no validation has been previously reported for most of them. In the present study, different analytical models were compared to results from compression tests of lattice structures built by material extrusion additive manufacturing, to determine their validity. For truncated octahedron lattices the relative error in geometry-based analytical models was significant, while models based on relative density showed better accuracy. In cubic diamond lattices, the relative error of the models was substantial, although performance improved for relative density values under 0.1. Discrepancies between the assumptions in the analytical models and the fabricated samples, in addition to size and edge effects were identified as possible sources of the large error margins observed. A second approach based on scaling laws was explored, and models for plateau stress and elastic modulus were obtained for both lattice structures, confirming its capabilities as an effective tool for the prediction of mechanical properties. Scaling laws and other models based on experimental data seem promising for the design of additive manufacturing lattice structures with a higher relative density, while further evaluation and development of the analytical models is considered necessary.