Considering a recently proposed model for the yielding of amorphous solids under cyclic shear deformation, we show that it can be analyzed by mapping it, in the simplest case, to a random walk in a confining potential with an absorbing boundary. The dynamics is governed by the first passage time into the absorbing state, which captures the essential features of the original model, thereby providing insight into the observed robustness of earlier results. Including the possibility of activated escape from absorbing states leads to a unique determination of a threshold energy and yield strain, and further, suggests an appealing approach to understanding fatigue failure.
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