When free flux flow is pushed beyond its instability, the homogeneous flow becomes spatially distorted leading to a new class of dynamic phases with steps in resistivity. At high-flux densities B, the relatively incompressible vortex matter fragments into domains of constant shear curvature, leading to a horizontalsawtooth-shaped current-voltage characteristic. Measurements on Y1Ba2Cu3O7-δ films confirm this behavior and are quantitatively consistent with the model, which has no adjustable parameters.