On Thin Rods with Misfit

There are many examples in nature of thin rods with misfit, such as the metallic bilayer and the tendrils of a plant.  We explain the shape that these thin rods take.  In particular, we show that the thin-rod Gamma limit of a three-dimensional elastic energy functional with misfit yields a rod theory with intrinsic bend or twist.  In the examples mentioned above we show that our rod theory agrees with the literature, and explain the connection between the classical calculations and the present result.  Finally, we ask what additional information we can gain if we do not know the exact form of the misfit, but only that it has certain symmetries.