Harmony of Self-Similarity: Overcoming the Strength–Ductility Trade-Off Through Harmonic Structure

Within the new generation of structural materials having heterogeneous microarchitectures, one of the top performers is harmonic structure (HS). Herewith, the exciting discovery of self-similarity in their stress–strain behavior is reported. HS materials consist of the 3D skeleton of ultrafine grains (UFG) encompassing coarse-grained (CG) counterparts. Our discovery simplifies the mathematical description of such a system and helps unraveling hidden patterns. Specifically, it is demonstrated that overcoming the strength–ductility trade-off in HS occurs since its components have a characteristic strengthening mechanism, which realizes the synergy of three factors: 1) hetero-deformation-induced (HDI) strengthening of the CG phase, the deformation of which increases with acceleration with respect to the deformation of the entire sample; 2) the transition of the CG phase to the strengthened to saturation UFG phase; and 3) the work of UFG phase deformation, which increases with acceleration when the sample is strained due to the rapidly growing value of (Formula presented.) and the factor (2).