  Understanding the mechanical instabilities of two-dimensional membranes has
strong connection to the subjects of structure instabilities, morphology
control and materials failures. In this work, we investigate the plastic
mechanism developed in the annular crystalline membrane system for adapting to
the shrinking space, which is caused by the controllable gradual expansion of
the inner boundary. In the process of plastic deformation, we find the
continuous generation of dislocations at the inner boundary, and their
collective migration to the outer boundary; this neat dynamic scenario of
dislocation current captures the complicated reorganization process of the
particles. We also reveal the characteristic vortex structure arising from the
interplay of topological defects and the displacement field. These results may
find applications in the precise control of structural instabilities in
packings of particulate matter and covalently bonded systems.
