  We consider a potential pathology in the derivation of plate theories as
Gamma-limits of 3-dimensional nonlinear elasticity by Friesecke James and
Muller (Comm. Pure Appl. Math., 55:1461-1506 and Arch. Ration. Mech. Anal.,
180:183-236), which consists in recovery sequences of invertible maps that
converge to a non-invertible limit. These pathologies have been noted by Muller
and Spector (Arch. Ration. Mech. Anal. 131:1-66) in a different context. Using
a combination of degree theory, the approximation of Sobolev functions by
Lipschitz functions and geometric rigidity we show that the potentially
pathological situation in the derivation of plate theories provides sufficient
conditions for the self-intersection of the graph of the recovery sequence
element, and thus the pathology is excluded.
