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Minimizing the elastic free energy of a thin sheet of nematic polymer networkamong smooth isometric immersions is the strategy purported by the mainstreamtheory. In this paper, we broaden the class of admissible spontaneousdeformations: we consider ridged isometric immersions, which can cause a sharpridge in the immersed surfaces. We propose a model to compute the extra energydistributed along such ridges. This energy comes from bending; it is shownunder what circumstances it scales quadratically with the sheet's thickness,falling just in between stretching and bending energies. We put our theory tothe test by studying the spontaneous deformation of a disk on which a radialhedgehog was imprinted at the time of crosslinking. We predict the number offolds that develop in terms of the degree of order induced in the material byexternal agents (such as heat and illumination).

Ridge energy for thin nematic polymer networks