  Variable-density cellular structures can overcome connectivity and
manufacturability issues of topologically-optimized, functionally graded
structures, particularly when those structures are represented as discrete
density maps. One na\"ive approach to creating variable-density cellular
structures is simply replacing the discrete density map with an unselective
type of unit cells having corresponding densities. However, doing so breaks the
desired mechanical behavior, as equivalent density alone does not guarantee
equivalent mechanical properties. Another approach uses homogenization methods
to estimate each pre-defined unit cell's effective properties and remaps the
unit cells following a scaling law. However, a scaling law merely mitigates the
problem by performing an indirect and inaccurate mapping from the material
property space to single-type unit cells. In contrast, we propose a deep
generative model that resolves this problem by automatically learning an
accurate mapping and generating diverse cellular unit cells conditioned on
desired properties (i.e., Young's modulus and Poisson's ratio). We demonstrate
our method via the use of implicit function-based unit cells and conditional
generative adversarial networks. Results show that our method can 1) generate
various unit cells that satisfy given material properties with high accuracy
(relative error <5%), 2) create functionally graded cellular structures with
high-quality interface connectivity (98.7% average overlap area at interfaces),
and 3) improve the structural performance over the conventional
topology-optimized variable-density structure (84.4% reduction in concentrated
stress and extra 7% reduction in displacement).
