Bio-inspired programmable metamaterials with logarithmic spiral hierarchy for energy absorption

• A rotation-governed self-similar chiral hierarchical honeycomb is constructed via an explicit rotate–tangential-extend–closure geometric rule, enabling recursive multilevel nesting. • The hierarchical evolution of cell vertices is quantitatively described by logarithmic spirals r = a · e b θ , linking the rotation angle α to a tunable radial scale gradient. • The spiral parameters q α and b α reveal how geometric chirality and hierarchy jointly govern multistage buckling and densification delay. • Under relative-density-matched conditions, the pure contributions of α and hierarchy level n are isolated, revealing a clear trade-off between SEA enhancement and load efficiency. To enable programmable energy-absorbing buffers, a rotation-driven recursive generation rule is introduced into a conventional hexagonal honeycomb to create a self-similar chiral hierarchical honeycomb (SCHH) with multilevel nesting. Closed-form geometry shows that the rotation angle α simultaneously governs the hierarchical similarity ratio r ( α ) and the tangential feed, such that hierarchical vertices follow a logarithmic-spiral locus in polar coordinates. Specifically, r ( θ ) = r 0 exp b ( α ) θ , where b ( α ) = ln q ( α ) / Δ θ and the growth factor q ( α ) is determined by r ( α ) . These spiral descriptors provide a quantitative bridge from structural evolution to crushing mechanisms: by tuning geometric-gradient intensity and the sequence of contact activation, α regulates rotation-assisted progressive collapse, plateau stability, and the onset of densification, while the hierarchy order n amplifies multi-scale participation and contact-mediated dissipation. Quasi-static compression experiments and validated finite-element simulations quantify the effects of wall thickness t , n , and α , including equal-relative-density benchmarking. Moderate α promotes a stable plateau, and increasing n delays densification while enhancing specific energy absorption and crushing load efficiency. The parameters b ( α ) and the radial growth ratio q ( α ) rationalise the observed non-monotonic performance trends.