Impact of the Lattice Angle on the Effective Properties of the Octet-Truss Lattice Structure

Cellular materials are found extensively in nature, such as wood, honeycomb, butterfly wings, and foam-like structures like trabecular bone and sponge. This class of materials proves to be structurally efficient by combining low weight with superior mechanical properties. Recent studies have shown that there are coupling relations between the mechanical properties of cellular materials and their relative density. Due to its favorable stretching‐dominated behavior, continuum models of the octet‐truss were developed to describe its effective mechanical properties. However, previous studies were only performed for the cubic symmetry case, where the lattice angle $θ=45$ deg. In this work, we study the impact of the lattice angle on the effective properties of the octet-truss: namely, the relative density, effective stiffness, and effective strength. The relative density formula is extended to account for different lattice angles up to a higher-order of approximation. Tensor transformations are utilized to obtain relations of the effective elastic and shear moduli, and Poisson's ratio at different lattice angles. Analytical formulas are developed to obtain the loading direction and value of the maximum and minimum specific elastic moduli at different lattice angles. In addition, tridimensional polar representations of the macroscopic strength of the octet‐truss are analyzed for different lattice angles. Finally, collapse surfaces for plastic yielding and elastic buckling are investigated for different loading combinations at different lattice angles. It has been found that lattice angles lower than $45$ deg result in higher maximum values of specific effective elastic moduli, shear moduli, and strength.