  This work is motivated by discrete-to-continuum modeling of the mechanics of
a graphene sheet, which is a single-atom thick macromolecule of carbon atoms
covalently bonded to form a hexagonal lattice. The strong covalent bonding
makes the sheet essentially inextensible and gives the sheet a resistance to
bending. We study a one-dimensional atomistic model that describes the
cross-section of a graphene sheet as a collection of rigid links connected by
torsional springs. $\Gamma$-convergence is used to rigorously justify an
upscaling procedure for the discrete bending energy of the atomistic model. Our
result establishes that as the bond length in the atomistic model goes to 0,
the bending energies $\Gamma$-converge to Euler's elastica.
