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Counter-rotating mechanical metamaterials have previously been found to haveanomalous characteristics or functions such as auxetics effects, shapechangers, and soliton transports, which are all under monostable conditions.The properties of counter-rotating mechanical metamaterials under bistableconditions have not yet been explored. Here, we found that for a bistablecounter-rotating metamaterial chain, the effective stiffnesses of the twosteady states are different in the chain with even-numbered nodes. For thechain with odd-numbered nodes, the effective stiffnesses corresponding to thetwo steady states are exactly the same. This special property is notcharacterized by the characteristic attenuation lengths of the underlyingmechanism, but depends on the different symmetries of the underlying mechanismof the chains with odd and even nodes. In addition, the relationship betweenthe abnormal non-monotonic size effect and equilibrium angle are clarified.More interestingly, for one-dimensional chains with even-numbered nodes, thesize effect of effective stiffness bifurcates at a specific equilibrium angle,and the according mechanisms are revealed.

Anomalous size effects of effective stiffnesses in bistable counter-rotating mechanical metamaterials