Bending and Stretching in a Narrow Ribbon of Nematic Polymer Networks

We study the spontaneous out-of-plane bending of a planar untwisted ribbon composed of nematic polymer networks activated by a change in temperature. Our theory accounts for both stretching and bending energies, which compete to establish equilibrium. We show that when equilibrium is attained these energy components obey a complementarity relation: one is maximum where the other is minimum. Moreover, we identify a bleaching regime: for sufficiently large values of an activation parameter (which measures the mismatch between the degrees of order in polymer organization in the reference and current configurations), the ribbon's deformation is essentially independent of its thickness.