Cyclic perturbations facilitate athermal creep in yield-stress materials

Yield stress materials deform irreversibly at a finite strain-rate if loaded with a fixed stress <i>σ</i> larger than some critical yield stress <i>σ</i>_c. When <i>σ</i> < <i>σ</i>_c deformation is absent, except for transient or thermally activated processes. However, the cyclic temporal variation of system parameters can induce a persistent irreversible deformation under sub-critical athermal conditions. We characterize this phenomenon using well established models in the fields of the yielding and depinning transitions. We find that the amount of deformation per cycle increases if <i>σ</i>_c is approached from below, and it decreases and even vanishes at a novel critical stress <i>σ</i>₀ < <i>σ</i>_c when this is reached from above. Interestingly, <i>σ</i>₀ plays a role similar to the fatigue limit in the context of fatigue damage propagation. Our study is inspired by the literature on soft Earth geophysics where soil creep mechanisms have been correlated with cyclic changes of environmental conditions, such as daily or seasonal fluctuations in temperature and humidity, which in turn promote fluctuations in the systems internal mechanical properties. We believe our findings can motivate an interdisciplinary perspective on the study of sub-critical landform evolution, as the creep of hill slopes over long periods of time.