Spatial pseudo-rigid body model for the analysis of a tubular mechanical metamaterial

In this paper, a pseudo-rigid body model is proposed for the analysis of a spatial mechanical metamaterial and its application is demonstrated. Using this model, the post-buckling behavior of the mechanical metamaterial can be determined without the need to consider the whole elastic structure, e.g., using finite-element procedures. This is done by analyzing a porous cylindrical mechanical metamaterial using a rigid body mechanism, consisting of rigid squares that are connected at their corners. Stiffness in this model comes from torsion springs placed at the connections between rigid parts. The theory of the model is presented and the results of two versions of this model are compared through experiments. One version describes the metamaterial in the free state, while the other, more extended, version includes clamped boundaries, matching the conditions of the experimental set-up. It is shown that the mechanical behavior of the spatial metamaterial is captured by the models and that the shape of the metamaterial in the deformed state can be obtained from the more extended model.