Convergence of equilibria for bending-torsion models of rods with inhomogeneities

Abstract

We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show that, as h ց 0, stationary points of the energy E h , for a rod Ω h ⊂ R 3 with cross-sectional diameter h, subconverge to stationary points of the Γ-limit of E h , provided that the bending energy of the sequence scales appropriately. This generalizes earlier results for homogeneous materials to the case of materials with (not necessarily periodic) inhomogeneities.