  The origin of "giant" flexoelectricity, orders of magnitude larger than
theoretically predicted, yet frequently observed, is under intense scrutiny.
There is mounting evidence correlating giant flexoelectric-like effects with
parasitic piezoelectricity, but it is not clear how piezoelectricity
(polarization generated by strain) manages to imitate flexoelectricity
(polarization generated by strain gradient) in typical beam-bending
experiments, since in a bent beam the net strain is zero. In addition, and
contrary to flexoelectricity, piezoelectricity changes sign under space
inversion, and this criterion should be able to distinguish the two effects and
yet "giant" flexoelectricity is insensitive to space inversion, seemingly
contradicting a piezoelectric origin. Here we show that, if a piezoelectric
material has its piezoelectric coefficient be asymmetrically distributed across
the sample, it will generate a bending-induced polarization impossible to
distinguish from true flexoelectricity even by inverting the sample. The
effective flexoelectric coefficient caused by piezoelectricity is functionally
identical to, and often larger than, intrinsic flexoelectricity: the
calculations show that, for standard perovskite ferroelectrics, even a tiny
gradient of piezoelectricity (1% variation of piezoelectric coefficient across
1 mm) is sufficient to yield a giant effective flexoelectric coefficient of 1
$\mu$C/m, three orders of magnitude larger than the intrinsic expectation
value.
