Deep learning for the rare-event rational design of 3D printed multi-material mechanical metamaterials

Emerging multi-material 3D printing techniques have paved the way for the rational design of metamaterials with not only complex geometries but also arbitrary distributions of multiple materials within those geometries. Varying the spatial distribution of multiple materials gives rise to many interesting and potentially unique combinations of anisotropic elastic properties. While the availability of a design approach to cover a large portion of all possible combinations of elastic properties is interesting in itself, it is even more important to find the extremely rare designs that lead to highly unusual combinations of material properties (e.g., double-auxeticity and high elastic moduli). Here, we used a random distribution of a hard phase and a soft phase within a regular lattice to study the resulting anisotropic mechanical properties of the network in general and the abovementioned rare designs in particular. The primary challenge to take up concerns the huge number of design parameters and the extreme rarity of such designs. We, therefore, used computational models and deep learning algorithms to create a mapping from the space of design parameters to the space of mechanical properties, thereby (i) reducing the computational time required for evaluating each designand (ii) making the process of evaluating the different designs highly parallelizable. Furthermore, we selected ten designs to be fabricated using polyjet multi-material 3D printing techniques, mechanically tested them, and characterized their behavior using digital image correlation (DIC, 3 designs) to validate the accuracy of our computational models. The results of our simulations show that deep learning-based algorithms can accurately predict the mechanical properties of the different designs, which match the various deformation mechanisms observed in the experiments.