After a decade of periodic truss-, plate-, and shell-based architectures having dominated the design of metamaterials, we introduce the new class of spinodoid topologies. Inspired by natural self-assembly processes, spinodoid metamaterials are a close approximation of microstructures observed during spinodal phase separation in, e.g., nanoporous metal foams, microemulsions, and polymer blends. Spinodoid metamaterials offer several advantages over conventional metamaterials.

• Spinodoid metamaterials 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). 

• Spinodoid topologies cover an extreme and seamless range of anisotropic (direction-dependent) mechanical properties, as demonstrated, e.g., by their tailorable anisotropic elastic moduli – creating materials that are stiff in some directions and soft in others. 

• The non-periodicity and lack of symmetry in spinodoid topologies make them more resilient to fabrication-based symmetry-breaking defects – by contrast to periodic metamaterials whose sensitivity to defects deteriorates their mechanical properties. 

• Spinodoid metamaterials offer unprecedented opportunities for spatially-variant architectures for functional grading without issues arising from unit cell tessellation and discontinuous topologies (which, in contrast, is an active challenge for periodic topologies including trusses, plates, and shells).

We show that the spinodoid design space can be integrated with an efficient and robust machine learning technique for the inverse design of (meta-)materials, in particular, uniform and functionally-graded cellular mechanical metamaterials with tailored direction-dependent (anisotropic) stiffness and density. 

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

Codes:  https://www.gibboncode.org
  https://www.gibboncode.org/html/HELP_spinodoid.html