Numerical investigation of the effective mechanical properties of architected structures: a comparative study of flexural stiffness, homogenization, and elastic anisotropy

Abstract

The mechanical behavior of architected structures is influenced by various parameters, including the topology of their unit cells. This anisotropic nature requires the determination of the mechanical properties under different loading scenarios. This study employs numerical investigation to characterize the influence of topology on the mechanical properties of eight architected structures, focusing on effective elastic properties and anisotropic elastic behavior. The analyzed topologies encompass four based on struts (lattices) and four based on triply periodic minimal surfaces (TPMS), comprising Sheet and Network phases. Initially, beams composed of architected structures are subjected to flexure, with Euler–Bernoulli and Tymoshenko’s theories utilized in a first numerical approach to determine their effective properties. Subsequently, a numerical homogenization method along with the Voigt-Reuss-Hill scheme is employed in a second approach. A more substantial influence of topology on the effective properties is observed in low relative densities. The study revealed that for a relative density of 10%, the appropriate selection of the topology increases the stiffness of a structure by up to ∼126%. The EBT approach underestimated the stiffness by up to ∼26% due to neglecting the impact of shear on beam deflection. The tensorial anisotropy index revealed up to ∼27% higher anisotropy compared to the Zener index. These findings provide a valuable numerical tool for the comparison and selection of architected structures suitable for diverse applications.

Keywords

• architected structures
• lattice structures
• TPMS structures
• bending theory
• numerical homogenization
• anisotropy