Fig. 1. A computational process for the discovery of extremal microstructure families.

Given a set of physical properties and design constraints, we estimate the material property gamut using stochastic sampling and topology optimization. Structures near the gamut boundary are grouped into families using NLDR. A representative from each family is fitted with a template represented as a skeleton. Beams are placed on the skeleton edges with optimized parameters to fit the original structure. Structure variations with the same topology can be generated by varying the beam parameters. Finally, reduced template parameters are computed to reveal domain-specific design principles.