A number of different stochastic models exist in the literature, and a review demonstrates the diversity of such models.
Markov chains can be used to model fatigue in materials. The assumption that damage is a function of independent parameters, combined with damage accumulated to date is consistent with the Markov property, and hence such methods are employed in a natural fashion. Of specific interest to this research is work on short cracks by Cox and Morris [12], [13]. The continuous version, the Markov diffusion, has also been examined.
The differential equation approach assumes that cracks grow continuously. In reality, crack growth can be a discontinuous process. In order to model this, it may help to consider growth as a combination of a growth event, together with a certain growth magnitude attributable to that event. Such has been modelled in the cumulative jump models [49] [23] [48].