  We study the modulational instability of recently designed magnetoelastic
metamaterials composed of elastic-mediated split-ring resonators (SRR). An
effective circuit model is developed. Then four cases are studied: a dimer of
SRR, one-dimension (1D) dimerized array, 1D uniform array and two-dimension
layered array. It is found that except for the dimer case, all the other
many-body cases can present modulational instability which may disturb the
bistability (if any) under uniform assumption.
