  We present a tunable phononic crystal which undergoes a phase transition from
mechanically insulating to mechanically transmissive (metallic). Specifically,
in our simulations for a phononic lattice under biaxial tension ($\sigma_{xx}
=\sigma_{yy}$ = 0.01 N$/$m), we find a bandgap for out-of-plane phonons in the
range of 48.8 - 56.4 MHz, which we can close by increasing the degree of
tension uniaxiality ($\sigma_{xx} / \sigma_{yy}$) to 1.7. To manipulate the
tension distribution, we design a realistic device of finite size, where
$\sigma_{xx} / \sigma_{yy}$ is tuned by applying a gate voltage to a phononic
crystal made from suspended graphene. We show that the phase transition can be
probed via acoustic transmission measurements and that the phononic bandgap
persists even after the inclusion surface contaminants and random tension
variations present in realistic devices. The proposed system acts as a
transistor for phonons with an on/off ratio of $10^5$ (100 dB suppression) and
is thus a valuable extension for phonon logic applications. In addition, this
mechanical analogue to a metal-insulator transition (mMIT) allows tunable
coupling between mechanical entities (e.g. mechanical qubits).
