Structure-property relations of all existing (meta-)materials have primarily been explored in a forward fashion: given a microstructure, one extracts the effective properties by methods of homogenization. The inverse challenge – identifying a microstructural topology that meets the mechanical property requirements – has often been addressed by inefficient trial and error. Systematic approaches such as topology optimization and genetic algorithms are beneficial but also computationally expensive (relying on repeated sampling and computation of the effective properties) and are highly dependent on initial guesses. Machine-learning-based surrogate models, which can bypass expensive simulations and experiments, have been developed for applications including metamaterials, composites, and nanomaterials. However, such approaches require solving an optimization problem based on the (forward-only) surrogate model, which prevents an on-demand inverse design framework. In addition, while the forward problem, i.e., mapping from topological parameters to property space, is well-defined, the inverse problem is ill-posed (multiple topologies can have the same or similar effective properties). 

To this end, we introduce a novel data-driven approach based on the integration of two neural networks for the forward- and inverse-problems that renders the inverse design challenge well-posed. This approach, in contrast to surrogate optimization methods, provides a computationally inexpensive two-way relationship between design parameters and mechanical properties. We apply this framework to generate spinodoid metamaterials with as-designed anisotropic elastic stiffness. With possible integration into multiscale topology optimization or as a standalone framework to explore the design space (e.g., via genetic algorithms), the combination of forward and inverse maps of the structure-property relation accelerates the design process of (meta-)materials with a wide range of tunable mechanical response (anisotropic stiffness only being the tip of the iceberg). 

Ref: S. Kumar, S. Tan, L. Zheng, D. M. Kochmann, Inverse-designed spinodoid metamaterials, npj Comput. Mater., 6 (2020), 73.

Codes: https://doi.org/10.5905/ethz-1007-267