Microarchitectured cellular solids – the hunt for statically determinate periodic trusses

Abstract The mechanical properties of open‐cell metallic foams and periodic lattice materials are explained by a structural analysis of their parent pin‐jointed truss structures. A matrix method of analysis is presented in order to elucidate whether a periodic truss structure can collapse by macroscopic strain producing mechanisms, or by periodic collapse mechanisms which induce zero macroscopic strain to first order. It is shown that the planar Kagome truss is of the latter type, and is consequently stiff. The in‐plane stiffness of the 2D Kagome grid and the bending stiffness of the 3D Kagome double‐layer grid (KDLG) are determined for elastic members. An alternative, statically determinate, double‐layer grid is derived from the octet truss, and is referred to as the modified octet truss (MOT). This structure has faces comprising a hexagonal grid and a semi‐regular triangular grid, and is much less stiff than the Kagome double‐layer grid. Both structures have morphing capability due to their static and kinematic determinacy.