  Topological defects (including disclinations and dislocations) which commonly
exist in various materials have shown an amazing ability to produce excellent
mechanical and physical properties of matters. In this paper, disclinations and
dislocations are firstly introduced into the valley-polarized elastic phononic
plate. Deformation of the lattice yields the interface expressing as the
topologically protected wave guiding, due to the valley-polarized phase
transition of phononic crystals (PnCs) across the interface. Then,
disclinations are introduced into the Wannier-type elastic phononic plate. The
deformation of the lattice yielded by disclinations produces a pentagonal core
with the local five-fold symmetry. The topological bound states are well
localized around the boundaries of the pentagonal cores with and without the
hollow regions. The topological interface state and the topological bound state
immunize against the finite sizes and the moderate disturbances of plates,
essentially differing from the trivial defect states. The discovery of
topological defect states unveils a new horizon in topological mechanics and
physics, and it provides a novel platform to implement large-scale elastic
devices with robust topological waveguides and resonators.
