  The elastic energy of a bending-resistant interface depends both on its
geometry and its material composition. We consider such a heterogeneous
interface in the plane, modeled by a curve equipped with an additional density
function. The resulting energy captures the complex interplay between curvature
and density effects, resembling the Canham-Helfrich functional. We describe the
curve by its inclination angle, so that the equilibrium equations reduce to an
elliptic system of second order. After a brief variational discussion, we
investigate the associated nonlocal $L^2$-gradient flow evolution, a coupled
quasilinear parabolic problem. We analyze the (non)preservation of quantities
such as convexity, positivity, and symmetry, as well as the asymptotic behavior
of the system. The results are illustrated by numerical experiments.
