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