Velocity of interfaces with short and long ranged elasticity under sinusoidal creep

Plenty of research on elastic interfaces has been done on systems where the interface is pushed with a constant force. We studied the average velocity of an interface under a sinusoidal driving in the creep region, considering both short-range elastic systems, such as magnetic domain walls during a hysteresis loop, and long ranged systems such as fractures. We obtained a modified version of the creep velocity with approximate power-law behaviour and a material dependent exponent for short ranged systems and simpler behaviour for long-range elasticity. We discuss whether the model can be applied to fatigue fractures, or if extra physics is needed.