Figure 4

Effect of loading direction γ on the mechanical response of the perforated sheets. Evolution of the (a) normalized stress σ x / E ¯ , (b) the in-plane macroscopic Poisson’s ratio ν y x and (c) the opening angle of cuts 2 θ o 1 and 2 θ o 2 as a function of the applied strain ϵ x for different values of γ . Note that ν y x is negative only for ϵ x < ϵ c (as at this stage the deformation of the structure is purely planar and identical to that of a network of rotating squares) and that it increases sharply and reaches positive values once the instability is triggered. (d) Numerical snapshots of 3D patterns obtained at ϵ x = 0.125 for different values of γ . The contours shows the normalized out-of-plane displacements.