Commutativity and non-commutativity of limits in the nonlinear bending theory for prestrained microheterogeneous plates

Abstract: In this paper, we look at the nonlinear bending theory for thin prestrained elastic sheets with an oscillating periodic structure. We show that all limiting (in the sense of $\Gamma-$convergence) energy functionals which formally correspond to an infinite thickness-to-period ratio are equivalent. In contrast, there are several different limit models that formally correspond to a $0$ thickness-to-period ratio.