We first consider an elastic thin heterogeneous cylinder of radius of order
epsilon: the interior of the cylinder is occupied by a stiff material (fiber)
that is surrounded by a soft material (matrix). By assuming that the elasticity
tensor of the fiber does not scale with epsilon and that of the matrix scales
with epsilon square, we prove that the one dimensional model is a nonlocal
We then consider a reference configuration domain filled out by periodically
distributed rods similar to those described above. We prove that the
homogenized model is a second order nonlocal problem.
In particular, we show that the homogenization problem is directly connected
to the 3D-1D dimensional reduction problem.