  We prove an homogenization result, in terms of $\Gamma$-convergence, for
energies concentrated on rectifiable lines in $\R^3$ without boundary. The main
application of our result is in the context of dislocation lines in dimension
$3$. The result presented here shows that the line tension energy of unions of
single line defects converge to the energy associated to macroscopic densities
of dislocations carrying plastic deformation. As a byproduct of our
construction for the upper bound for the $\Gamma$-Limit, we obtain an
alternative proof of the density of rectifiable $1$-currents without boundary
in the space of divergence free fields.

Analysis of PDEs