Towards optimal heterogeneity in lattice structures

We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into a cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are present, the domain resembles a densely connected ground structure. The cross-sectional area of beam segments in lattice units, modelled using Timoshenko beam theory, are the design variables. All beam segments in a particular lattice phase have the same area of cross section to keep the number of design variables low. The optimization problem is formulated for stiff structures and is solved using the optimality criteria algorithm. We present a case study to show the superiority of topology-optimized heterogeneous structures over uniform lattices of a single phase. In order to interpret the phase composition, we perform four basic load tests on single phases, namely, tension or compression, shear, bending, and torsion. The phases are ranked based on the stiffness corresponding to individual loading conditions. The results show that in the optimized structure, the local internal load configuration drives the selection of phases. We also note that micropolar elasticity captures the bulk behaviour of heterogeneous lattice structures, and helps us to interpret the optimality of phases.