Piezoelectric materials generate electric charge (voltage) when stressed/flexed. They move in one direction when a positive voltage is applied and in the other direction when a negative voltage is applied.
Nowhere in the above statements can you find the term "current".
I imagine if you had the piezoelectric material mounted on a substrate. And it was segregated. then when you bent it to be convex, the piezo electric elements would have gaps in between it and thus be under significantly less stress.