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Triply periodic minimal surface (TPMS) metamaterials characterized bymathematically-controlled topologies exhibit better mechanical propertiescompared to uniform structures. The unit cell topology of such metamaterialscan be further optimized to improve a desired mechanical property for aspecific application. However, such inverse design involves multiple costly 3Dfinite element analyses in topology optimization and hence has not beenattempted. Data-driven models have recently gained popularity as surrogatemodels in the geometrical design of metamaterials. Gyroid-like unit cells aredesigned using a novel voxel algorithm, a homogenization-based topologyoptimization, and a Heaviside filter to attain optimized densities of 0-1configuration. Few optimization data are used as input-output for supervisedlearning of the topology optimization process from a 3D CNN model. These modelscould then be used to instantaneously predict the optimized unit cell geometryfor any topology parameters, thus alleviating the need to run any topologyoptimization for future design. The high accuracy of the model was demonstratedby a low mean square error metric and a high dice coefficient metric. Thisaccelerated design of 3D metamaterials opens the possibility of designing anycomputationally costly problems involving complex geometry of metamaterialswith multi-objective properties or multi-scale applications.

Gyroid-like metamaterials: Topology optimization and Deep Learning