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We derive, by means of Gamma-convergence, the equations of homogenizedbending rod starting from $3D$ nonlinear elasticity equations. The mainassumption is that the energy behaves like h^2 (after dividing by the order h^2of vanishing volume) where h is the thickness of the body. We do not presupposeany kind of periodicity and work in the general framework. The result showsthat, on a subsequence, we always obtain the equations of bending-torsion rodand identifies, in an abstract formulation, the limiting quadratic formconnected with that model. This is a generalization from periodic tonon-periodic homogenization of bending-torsion rod theory already present inthe literature.

General homogenization of bending-torsion theory for inextensible rods from 3D elasticity