  Porous structures such as trabecular bone are widely seen in nature. These
structures exhibit superior mechanical properties whilst being lightweight. In
this paper, we present a method to generate bone-like porous structures as
lightweight infill for additive manufacturing. Our method builds upon and
extends voxel-wise topology optimization. In particular, for the purpose of
generating sparse yet stable structures distributed in the interior of a given
shape, we propose upper bounds on the localized material volume in the
proximity of each voxel in the design domain. We then aggregate the local
per-voxel constraints by their p-norm into an equivalent global constraint, in
order to facilitate an efficient optimization process. Implemented on a
high-resolution topology optimization framework, our results demonstrate
mechanically optimized, detailed porous structures which mimic those found in
nature. We further show variants of the optimized structures subject to
different design specifications, and analyze the optimality and robustness of
the obtained structures.
