Extended Data Fig. 2: Buckling of perfect and nonperfect straight rods.
From: Large recoverable elastic energy in chiral metamaterials via twist buckling
Unless otherwise labeled, r = 1.5, L0 = 30 mm. For metamaterial consisting of oblique rods, applying a vertical compressive displacement (s) gets an equivalent strain ε = s/h0. In (b, c, d), the rods are vertical. (a) Normalized compressive force of the perfectly straight rod with different oblique angle. The dashed range represents σv > 0.1Es. Bending buckling happens abruptly. (b) Normalized strain energy of a micro-bending rod under different stress. The rod center is bended by 2°. This small imperfection greatly reduces the normalized energy under σv = 0.05Es, σv = 0.1Es and σv = 0.2Es by about 2/3, compared to the perfectly straight rod shown in Fig. 2 in the main text, due to stress concentration at the bent position. Fortunately, comparing Fig. 2a in the main text, the maximum force of this imperfect rod nearly unchanged. (c, d) Analytical solution of energy and von Mises stress as a function of equivalent strain for a rod. (e) Energy-stress curves combined from panels (c, d). The original rod is perfectly straight. Panel (d,e) indicates the two-stage deformation process of a nonchiral straight rod. Panel (c) indicates that: (1) When buckling occurs, the normalized energy U1rod/Us increases at a higher rate as strain increases; (2) When r < 2.5 mm, thicker rod achieves higher U1rod/Us within moderate strain (ε = 0.12) because the contribution from pure compression increases. However, further increasing r cannot increase U1rod/Us because buckling no longer occurs. (3) In the pure compression stage, U1rod/Us is independent of rod thickness. As indicated by equation (1), σcpr gets 8 times higher increment ratio than σbend when increasing stress. Thus, for a specified moderate stress, like σv = 0.1Es, a thicker rod obtains higher U1rod/Us until buckling disappears at this stress level. If the material strength limit is relaxed, hybrid bending and axial shortening will always result in higher energy storage within the specified material volume.
