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

Non-local effects by homogenization or 3D-1D dimension reduction in elastic materials reinforced by stiff fibers