Phononic bandgap metamaterials, which consist of periodic cellular structures, are capable of absorbing energy within a certain frequency range, thus they are considered as promising solutions to the control of energy flow. It has been demonstrated that bandgaps that span different frequency ranges can be achieved by tailoring the topological features of the cellular structures, while finding metamaterial designs&nbsp;that trap waves across a wide wave frequency range is still a challenging task. In this study, we present two deep feature learning-based design approaches, a single-loop approach and an iterative approach, to maximize the bandgap width and the stiffness of the metamaterials. In the single-loop deep design framework, a Gaussian mixture variational autoencoder (GM-VAE) is employed to extract structural features and a Neural Network (NN) model is employed to enable property-driven structure optimization. We firstly compare the GM-VAE and a regular variational autoencoder (VAE), which is widely adopted in structural design in literature. We demonstrate that GM-VAE has the advantage of learning capability, and GM-VAE discovers a more diversified design set (in terms of the distribution in the performance space) in the unsupervised learning-based generative design. NN models are employed as supervised learning strategies to establish the relationship between the latent features and the properties of interest. With this NN model, a multi-objective optimization is conducted to find the Pareto frontier with respect to the two design objectives: the bandgap width and the stiffness. Furthermore, we investigated the relationship between the performances of the training data and the performance of the resultant optimal design. We observe that the range of the training data’s performances could affect the performance of the optimization result. With the same amount of training data, the better the performance the training data have, the better the performance of the design found by optimization. Therefore, an iterative VAE model updating-based design approach is proposed. In each iteration, a small set of training points with undesired properties are replaced by the same quantity of newly obtained designs with good properties. A new VAE model is trained on the updated training dataset for the optimization search in each iteration. This iterative process shifts the interpolation range of the machine learning model toward the high-performance region in the design space. A comparative study between the single-loop and iterative approaches is presented to demonstrate the effectiveness of the iterative approach. The caveats to designing phonic bandgap metamaterials are summarized.Keywords: Metamaterial; Phononic bandgap; Gaussian mixture variational autoencoder; Multi-objective optimization; Deep feature learning.&nbsp;

Design of Phononic Bandgap Metamaterials by Gaussian Mixture Variational Autoencoder With Iterative Model Updating

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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