Data-driven design of thermal-mechanical multifunctional metamaterials

Achieving effective control of thermal and mechanical distributions has been a long-standing goal, and metamaterials have emerged as a crucial tool for customizing functional structures to manipulate these physical fields. However, existing design paradigms do not apply to thermal-mechanical metamaterials that operate on thermal and mechanical fields simultaneously and independently. First, Due to the different geometric requirements imposed by the thermal and mechanical fields on the unit cells, there is a conflict between functional coupling and design coupling, which limits the design of thermal-mechanical metamaterials. Second, the fact that continuum mechanical equations do not remain invariant under general coordinate transformations hinders the application of conventional theories. Additionally, balancing minimal design costs, manufacturability, and optimal functionality remains a significant challenge. Here, we propose a global data-driven design method using Bayesian hyperparameter optimization. This method creates thermal-mechanical metamaterials from a large, pre-computed unit cell database. Our flexible method allows designing thermal-mechanical metamaterials with various functional combinations (e.g., cloaks, concentrators, and rotators) and shapes. Compared to traditional solutions, this approach balances manufacturability and functionality while offering unparalleled universality and low design costs. Experimental measurements validate the effectiveness of our method. Our approach can rapidly respond to new design scenarios and address design challenges related to the multi-physical effects.