Physically interpretable discrete latent representations for the design of advanced mechanical metamaterials in complex geometries

초록

Recent advancements in artificial intelligence (AI)-based design strategies for mechanical metamaterials have significantly improved the ability to create customizable architectures across nano-to macro-scale dimensions. However, challenges persist in expanding the flexibility of design space and generating multiple microstructures within complex geometries. This study introduces an innovative approach that combines topology optimization (TO) with a deep generative model for mechanical metamaterials, enabling the generation of multiple microstructure compositions within arbitrarily shaped domains. The model leverages discrete latent vectors to achieve high prediction accuracy for mechanical properties, with R2 = 0.99 on in-distribution sets and R2 = 0.97 on outof-distribution sets, surpassing the performance of traditional machine learning methods. Detailed analysis reveals strong correlations between these latent vectors and the mechanical, structural, and geometrical characteristics of microstructures, offering new insights into their physical interpretation. The proposed approach significantly enhances the ability to represent complex geometries with high resolution, enabling intricate designs while achieving results 7-8 times faster than conventional methods and a 10 % reduction in compliance without increasing the volume fraction. This innovative framework has broad potential applications in aerospace, biomedical engineering, and robotics, representing a pivotal advancement in understanding the complex latent design spaces of mechanical metamaterials.

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