  Amorphous solids are ubiquitous among natural and man-made materials. Often
used as structural materials for their attractive mechanical properties, their
utility depends critically on their response to applied stresses. Processes
underlying such mechanical response, and in particular the yielding behaviour
of amorphous solids, are not satisfactorily understood. Although studied
extensively[1-14], observed yielding behaviour can be gradual and depend
significantly on conditions of study, making it difficult to convincingly
validate existing theoretical descriptions of a sharp yielding transition[4, 6,
8, 13, 15]. Here, we employ oscillatory deformation as a reliable probe of the
yielding transition. Through extensive computer simulations for a wide range of
system sizes, we demonstrate that cyclically deformed model glasses exhibit a
sharply defined yielding transition with characteristics that are independent
of preparation history. In contrast to prevailing expectations[4, 8, 12], the
statistics of avalanches reveals no signature of the impending transition, but
exhibit dramatic, qualitative, changes in character across the transition.
