  Understanding the mechanical response and failure of solids is of obvious
importance in their use as structural materials. The nature of plastic
deformation leading to yielding of amorphous solids has been vigorously pursued
in recent years. Investigations employing both unidirectional and cyclic
deformation protocols reveal a strong dependence of yielding behaviour on the
degree of annealing. Below a threshold degree of annealing, the nature of
yielding changes qualitatively, to progressively more discontinuous yielding.
Theoretical investigations of yielding in amorphous solids have almost
exclusively focused on yielding under unidirectional deformation, but cyclic
deformation reveals several interesting features that remain largely
un-investigated. Focusing on athermal cyclic deformation, I investigate a
family of models based on an energy landscape description. These models
reproduce key interesting features observed in simulations, and provide an
interpretation for the intriguing presence of a threshold energy.
