The references of this article:
Fang, X., Yu, D., Wen, J. et al. Large recoverable elastic energy in chiral metamaterials via twist buckling. Nature 639 , 639–645 (2025). Large recoverable elastic energy in chiral metamaterials via twist buckling | Nature
Another excerpt, in “Buckling of chiral and non-chiral rods” section:
Lattices consisting of angled rods (Fig. 1c–e) show improved stiffness and max(F 1rod) with increased oblique angle (θ) (Fig. 2a). However, in buckled rods, σ cpr ≪ σ bend, resulting in nearly constant energy U1rod≈πr2L0σv2/16Es for a given stress σ v, regardless of the angle θ (Fig. 2b). Moreover, U bend in equation (1) is independent of buckling order (n). Thus, adjusting the oblique angle or inducing high-order buckling modes (n > 1) can change max(F 1rod) but cannot effectively improve U 1rod for a specified material strength (σ v). This severely limits energy storage in strut-based metamaterials.
To overcome this limitation, we must introduce additional deformation modes beyond bending and compression. Chiral metamaterials31,32,33, with coupling between axial deformation and twisting, offer exciting possibilities to store more energy by torsion.