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.
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