  We study the effect of the fragility of glass formers on the yielding
transition under oscillatory shear via extensive computer simulations.
Employing sphere assemblies interacting with a harmonic potential as our model
glass former, we tune fragility by changing the system's density - higher
density corresponds to large fragility. Our study reveals significant
differences in the yielding transition between strong and fragile glass
formers. While both glass formers exhibit similar behaviour under poorly
annealed initial conditions, the yielding transition shifts to larger values
with increased annealing for fragile glasses while remaining relatively
constant for strong glasses. We rationalize our results by introducing a new
elastoplastic model, which qualitatively reproduces the simulation results and
offers valuable insight into the physics of yielding transition under
oscillatory shear deformation.
