  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-section 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 not only to interpret the optimality of phases but also to improve the
computational efficiency of the proposed optimization technique.
