Inverse-Designed Spinodoid Metamaterials

After a decade of periodic truss-, plate-, and shell-based architectures having dominated the design of metamaterials, we introduce the non-periodic class of spinodoid topologies. Inspired by natural self-assembly processes, spinodoid metamaterials are a close approximation of microstructures observed during spinodal phase separation. Their theoretical parametrization is so intriguingly simple that one can bypass costly phase-field simulations and obtain a rich and seamlessly tunable property space, as demonstrated, e.g., by their tailorable anisotropic elastic moduli – creating materials that are stiff in some directions and soft in others. Their topologies consist of smooth, non-intersecting, and bi-continuous surfaces that avoid points of stress concentration (unlike truss- and plate-based metamaterials) while also showing excellent scaling of stiffness and strength with respect to density (leveraging the benefits of doubly-curved surfaces that engage slender structures primarily in stretching rather than bending). Counter-intuitively, breaking with the periodicity of classical metamaterials is the enabling factor to the large property space and the ability to introduce seamless functional grading. The non-periodicity and lack of symmetry in spinodoid topologies also make them more resilient to fabrication-based symmetry-breaking defects – by contrast to periodic metamaterials whose sensitivity to defects deteriorates their mechanical properties.

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. Towards the creation of metamaterials with as-designed properties, we address the inverse design question, i.e., how can we systematically and efficiently find a topology from the nearly infinite design space to achieve a sought combination of macroscale properties. Conventional design methods based on trial and error and/or topology optimization are beneficial but also computationally expensive (relying on repeated sampling and computation of the effective properties) and are highly dependent on initial guesses. To this end, we introduce a novel, efficient, and robust machine learning technique for inverse design which, when applied to spinodoid topologies, enables us to generate uniform and functionally-graded cellular mechanical metamaterials with tailored direction-dependent (anisotropic) stiffness, density and pore-sizes. Despite the inverse problem being ill-posed (e.g., significantly different design parameters may yield the same desired stiffness), our algorithm, based on the integration of two neural networks for the forward- and inverse-problems, renders the challenge well-posed. We specifically present inverse-designed and biomimetic synthetic bone architectures based on spinodoid topologies that not only reproduce the properties of trabecular bone accurately but also even geometrically resemble natural bone. 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).

Reference:

Kumar, S., Tan, S., Zheng, L. et al. Inverse-designed spinodoid metamaterials. npj Comput Mater 6, 73 (2020). https://doi.org/10.1038/s41524-020-0341-6