The stiffness and strength of the gyroid lattice

Abstract

Recently, a nanoscale lattice material, based upon the gyroid topology has been self-assembled by phase separation techniques (Scherer et al., 2012) and prototyped in thin film applications. The mechanical properties of the gyroid are reported here. It is a cubic lattice, with a connectivity of three struts per joint, and is bending-dominated in its elasto-plastic response to all loading states except for hydrostatic: under a hydrostatic stress it exhibits stretching-dominated behaviour. The three independent elastic constants of the lattice are determined through a unit cell analysis using the finite element method; it is found that the elastic and shear modulus scale quadratically with the relative density of the lattice, whereas the bulk modulus scales linearly. The plastic collapse response of a rigid, ideally plastic gyroid lattice is explored using the upper bound method, and is validated by finite element calculations for an elastic-ideally plastic lattice. The effect of geometrical imperfections, in the form of random perturbations to the joint positions, is investigated for both stiffness and strength. It is demonstrated that the hydrostatic modulus and strength are imperfection sensitive, in contrast to the deviatoric response. The macroscopic yield surface of the imperfect lattice is adequately described by a modified version of Hill’s anisotropic yield criterion. The article ends with a case study on the stress induced within a gyroid thin film, when the film and its substrate are subjected to a thermal expansion mismatch.