  Metamaterials are emerging as a new paradigmatic material system to render
unprecedented and tailorable properties for a wide variety of engineering
applications. However, the inverse design of metamaterial and its multiscale
system is challenging due to high-dimensional topological design space,
multiple local optima, and high computational cost. To address these hurdles,
we propose a novel data-driven metamaterial design framework based on deep
generative modeling. A variational autoencoder (VAE) and a regressor for
property prediction are simultaneously trained on a large metamaterial database
to map complex microstructures into a low-dimensional, continuous, and
organized latent space. We show in this study that the latent space of VAE
provides a distance metric to measure shape similarity, enable interpolation
between microstructures and encode meaningful patterns of variation in
geometries and properties. Based on these insights, systematic data-driven
methods are proposed for the design of microstructure, graded family, and
multiscale system. For microstructure design, the tuning of mechanical
properties and complex manipulations of microstructures are easily achieved by
simple vector operations in the latent space. The vector operation is further
extended to generate metamaterial families with a controlled gradation of
mechanical properties by searching on a constructed graph model. For multiscale
metamaterial systems design, a diverse set of microstructures can be rapidly
generated using VAE for target properties at different locations and then
assembled by an efficient graph-based optimization method to ensure
compatibility between adjacent microstructures. We demonstrate our framework by
designing both functionally graded and heterogeneous metamaterial systems that
achieve desired distortion behaviors.
