Elasticity, Geometry and Buckling

strain, leading to the formation of a periodic array of elongated, almost closed ellipses, as shown in Fig. 2D for 3 1⁄4 "0.21. Since the specimens are made of an elastomeric material, the process is fully reversible and repeatable. Upon release of the applied vertical displacement, the deformed structures recover their original congurations. Interestingly, Figs. 2C–D clearly shows that the porous structures 3.6.3.6 and 3.4.6.4 buckle into a chiral pattern, while the initially expanded congurations are non-chiral. Therefore, in these two systems buckling acts as a reversible chiral symmetry breaking mechanism. Despite many studies on pattern formation induced by mechanical instabilities, relatively little is known about the use of buckling as a reversible chiral symmetry breaking mechanism. Although several processes have been recently reported to form chiral patterns, all of these work only at a specic length-scale, preventing their use for the formation of chiral structures over a wide range of length scales, as required by applications. Furthermore, most of these chiral symmetry breaking processes are irreversible and only few systems have been demonstrated to be capable of reversibly switching between non-chiral and chiral congurations. Remarkably, since the mechanism discovered here exploits a mechanical instability that is scale independent, our results raise opportunities for reversible chiral symmetry breaking over a wide range of length scales. Both experiments and simulations reported in Fig. 2 clearly indicate that the onset of instability is strongly affected by the arrangement of the holes. A more quantitative comparison between the response of the structures investigated in this paper can be made by inspecting the evolution of stress during both experiments and simulations (see Fig. 3). Although all structures are characterized by roughly the same porosity, the hole arrangement is found to strongly affect both the effective modulus Ē (calculated as the initial slope of the stress–strain curves reported in Fig. 3) and the critical strain 3cr (calculated as the strain at which the stress–strain curves reported in Fig. 3 plateau), demonstrating that through a careful choice of the Fig. 2 Numerical (left) and experimental (right) images of all four structures (4.4.4.4, 3.3.3.3.3.3, 3.6.3.6 and 3.4.6.4) at different levels of deformation: (A) 31⁄4 0.00, (B) 3 1⁄4 "0.07, (C) 3 1⁄4 "0.15 and (D) 3 1⁄4 "0.21. All configurations are characterized by an initial void-volume-fraction j z 0.5. Scale bars: 20 mm.