Elastic axial stiffness properties of lattice structures: Analytical approach and experimental validation for bcc and f2cc,z unit cells

Abstract

Additive manufacturing (AM) is a key technology for the individualized and resource-efficient production of structural components. Recent developments in manufacturing technologies enable improved quality of additively manufactured components and therefore they become more and more important in lightweight constructions. An example is the substitution of solid material by porous lattice structures. Those embedded lattice structures lead to highly weight-efficient structures. Most recent investigations focus on numerical and experimental studies to describe the mechanical behavior of lattice structures. In this paper, a method to determine analytical expressions for the axial stiffness properties of lattice structures is presented. The displacement method and direct stiffness method are used to derive symbolic parameter-dependent formulas for the axial stiffnesses and effective Young’s moduli for f2cc,z, and bcc unit cells. Furthermore, an empirical approach based on Finite Element simulations is presented to describe the stiffness reduction for non-embedded or rather free lattice structures. The results are further validated by physical experiments. Stereolithography is used for specimen production. f2cc,z, and bcc lattice structures are embedded in thin-walled rectangular aluminum tubes and tested under compression load. Furthermore, lattices without a surrounding tube are tested. The analytical and empirical solutions are in good agreement with the experimental and numerical results.