  We deduce a 1D model of elastic planar rods starting from the F\"{o}ppl--von
K\'{a}rm\'{a}n model of thin shells. Such model is enhanced by additional
kinematical descriptors that keep explicit track of the compatibility condition
requested in the 2D parent continuum, that in the standard rods models are
identically satisfied after the dimensional reduction. An inextensible model is
also proposed, starting from the nonlinear Koiter model of inextensible shells.
These enhanced models describe the nonlinear planar bending of rods and allow
to account for some phenomena of preeminent importance even in 1D bodies, such
as formation of singularities and localization (d-cones), otherwise
inaccessible by the classical 1D models. Moreover, the effects of the
compatibility translate into the possibility to obtain multiple stable
equilibrium configurations.
