Machine learning-encoded multiscale modelling and Bayesian optimization framework to design programmable metamaterials

Advanced programmable metamaterials with heterogeneous microstructures have become increasingly prevalent in scientific and engineering disciplines attributed to their tunable properties. However, exploring the structure-property relationship in these materials, including forward prediction and inverse design, presents substantial challenges. The inhomogeneous microstructures significantly complicate traditional analytical or simulation-based approaches. Here, we establish a novel framework that integrates the machine learning (ML)-encoded multiscale computational method for forward prediction and Bayesian optimization for inverse design. Unlike prior end-to-end ML methods limited to specific problems, our framework is both load-independent and geometry-independent. This means that a single training session for a constitutive model suffices to tackle various problems directly, eliminating the need for repeated data collection or training. We demonstrate the efficacy and efficiency of this framework using metamaterials with designable elliptical holes or lattice honeycombs microstructures. Leveraging accelerated forward prediction, we can precisely customize the stiffness and shape of metamaterials under diverse loading scenarios, and extend this capability to multi-objective customization seamlessly. Moreover, we achieve topology optimization for stress alleviation at the crack tip, resulting in a significant reduction of Mises stress by up to 41.2% and yielding a theoretical interpretable pattern. This framework offers a general, efficient and precise tool for analyzing the structure-property relationships of novel metamaterials.