Amplitude-induced bandgap: New type of bandgap for nonlinear elastic metamaterials

•We found a new type of bandgap in nonlinear elastic metamaterials, called an “amplitude-induced bandgap”, which originates from amplitude.•When this amplitude-induced bandgap forms, various unique phenomena can be found analytically, such as the dual wavevector phenomenon and the change of the amplitude dependency of the bandgap.•In addition, we found that the amplitude-induced bandgap transforms into the general Bragg gap in actual metamaterials, and the wave transmission curve has an abnormal inflection point.•We validated the above findings by using various nonlinear wave simulations.