The Gibson-Ashby model for additively manufactured metal lattice materials: Its theoretical basis, limitations and new insights from remedies

Abstract

The Gibson-Ashby (G-A) model has been instrumental in the design of additively manufactured (AM-ed) metal lattice materials or mechanical metamaterials. The first part of this work reviews the proposition and formulation of the G-A model and emphasizes that the G-A model is only applicable to low-density lattice materials with strut length-to-diameter ratios greater than 5. The second part evaluates the applicability of the G-A model to AM-ed metal lattice materials and reveals the fundamental disconnections between them. The third part assesses the deformation mechanisms of AM-ed metal lattices in relation to their strut length-to-diameter ratios and identifies that AM-ed metal lattices deform by concurrent bending, stretching, and shear, rather than just stretching or bending considered by the G-A model. Consequently, mechanical property models coupling stretching, bending and shear deformation mechanisms are developed for various lattice materials, which show high congruence with experimental data. The last part discusses new insights obtained from these remedies into the design of strong and stiff metal lattices. In particular, we recommend that the use of inclined struts be avoided.