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Elasto-plastic models are among the most successful ways to study thecritical properties of the plastic yielding transition of amorphous solids.Typically these models are studied under a condition of constant transitionrates from one plastic configuration to another, and in this form they predictthe existence of well defined critical exponents that display universality, inthe same sense that in standard equilibrium phase transitions. I show howeverthat very naturally the transition rates must not be taken as a constant, butdependent of the local stress excess above the critical value. Thismodification in the model is seen to affect the values of some of the exponentsof the transition, concretely, of the dynamical exponents that are related tothe speed at which the system is driven. I argue about the reason for thisdependence, claiming that it is due to the quasi-mean field nature of theplastic yielding transition originated in the fact that elastic interactionsare long range.

Elasto-plastic models of the yielding transition with stress-dependent transition rates