Auxetic materials and related systems with negative Poisson's ratios have recently received physical and mathematical interest. Their mechanical properties induced by particular solid deformations are expected to allow remarkable advances to be made in the field of engineering. In our previous study, we proposed a structural unit that transforms into two types of diamond‐ and square‐patterned cells and discussed its bi‐stiffness property [Proc. R. Soc. A 469, 20130063 (2013)]. In this study, we applied the structural concept to a periodic framework. In numerical analyses with cell deflection, we revealed that the modified structure with periodicity has a similar switching mechanism and exhibits interesting post‐switching behaviors with nonlinear elasticity.

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