  A unified form of time-reversal symmetry (TRS) breaking terms in phononic
crystals, leading to nontrivial phononic topology, has been proposed recently,
but is contradicted by some other works which introduce gyroscopic effect as
TRS-breaking. We re-study gyroscopic phononic crystals using Newtonian
mechanical method, and find the correct TRS-breaking term in consistent with
the unified form. Applying this term we calculate the basic topological
phononics in a honeycomb lattice. Furthermore, we study nonlinear phonon-phonon
scattering effect on topological phononic edge states by molecular dynamics
simulation. Generally edge states are not immune to such scattering effect, but
under specific conditions some edge states run into bulk much more slowly,
depending on the parameters of the model. This opens up the potential for
effectively suppressing phonon dissipation by tuning the parameters, thereby
realizing near-100% efficiency of one-way phonon transport in phonon devices.
