  We study a mean field elastoplastic model, embedded within a disordered
landscape of local yield barriers, to shed light on the behaviour of athermal
amorphous solids subject to oscillatory shear. We show that the model presents
a genuine dynamical transition between an elastic and a yielded state, and
qualitatively reproduces the dependence on the initial degree of annealing
found in particle simulations. For initial conditions prepared below the
analytically derived threshold energy, we observe a non-trivial, non-monotonic
approach to the yielded state. The timescale diverges as one approaches the
yielding point from above, which we identify with the fatigue limit. We finally
discuss the connections to brittle yielding under uniform shear.
