The freestanding twisted bilayer graphene (TBG) is unstable, below a critical twist angle ${\theta }_c\sim 3.7^{\circ }$, against a moiré $(2\times 1)$ buckling distortion at $T=0$. Realistic simulations reveal the concurrent unexpected collapse of the bending rigidity, an unrelated macroscopic mechanical parameter. An analytical model connects bending and buckling anomalies at $T=0$, but as temperature rises the former fades, while buckling persists further. The $(2\times 1)$ electronic properties are also surprising. The magic twist angle narrow bands, now eight in number, fail to show zone boundary splittings despite the different periodicity. Symmetry shows how this is dictated by an effective single-valley physics. These structural, critical, and electronic predictions promise to make the freestanding state of TBG especially interesting.

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• Electronic structure
• Twisted bilayer graphene
• Molecular dynamics