Fig. 2. Bucklable materials (κ₁, μ₁ > 0) rectify towards contraction (yellow), while very anti-bucklable materials (κ₁, μ₁ < −3/2) rectify towards expansion (blue). Contour plot of α, indicating the overall sign of rectification as a function of the relative system size r_out/r_in, the Poisson ratio ν (ν = 1 denotes incompressibility in 2D) and the nonlinear corrections to the moduli κ₁, μ₁. The contour lines denote |α|μ = 2 (thick), 1 (thin), 0.5 (dashed). Crosses indicate constitutively linear materials where only geometrical nonlinearities are present (for ν = 1 they are far to the right). As shown in eqn (7), κ₁ and μ₁ encapsulate both geometrical and constitutive (through κ′, μ′) contributions. As a result, these crosses do not lie at the origin. Circles and squares point out specific media discussed in Fig. 4.