  Cellular structures found in nature exhibit remarkable properties such as
high strength, high energy absorption, excellent thermal/acoustic insulation,
and fluid transfusion. Many of these structures are Voronoi-like; therefore
researchers have proposed Voronoi multi-scale designs for a wide variety of
engineering applications. However, designing such structures can be
computationally prohibitive due to the multi-scale nature of the underlying
analysis and optimization. In this work, we propose the use of a neural network
(NN) to carry out efficient topology optimization (TO) of multi-scale Voronoi
structures. The NN is first trained using Voronoi parameters (cell site
locations, thickness, orientation, and anisotropy) to predict the homogenized
constitutive properties. This network is then integrated into a conventional TO
framework to minimize structural compliance subject to a volume constraint.
Special considerations are given for ensuring positive definiteness of the
constitutive matrix and promoting macroscale connectivity. Several numerical
examples are provided to showcase the proposed method.
