We investigate the yielding transition of dense suspensions of colloids interacting via a soft repulsive potential by simultaneously measuring their mechanical response and microscopic dynamics under an oscillating shear deformation. At low strain amplitude, the system exhibits ultraslow, ballistic dynamics characterized by a compressed exponential relaxation of correlators, similar to those reported for many jammed soft materials at rest.

Upon increasing the strain amplitude, the system undergoes a dynamic transition towards a steady state characterized by fast stretched exponential, diffusive-like relaxations. The dynamic transition coincides with the onset of the non-linear rheological response. While this scenario seems to be generic to soft colloids, the sharpness of the transition appears to depend on the potential details.

We present a simple model that accounts for this dynamic transition.