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

2017/07/14 by Matthäus Pawelczyk, Pawelczyk, Matthäus
Mathematics · #74B20 #74E30 #74G10 #74K10 #74Q05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:74B20 #msc:74E30 #msc:74G10 #msc:74K10 #msc:74Q05

paper · pdf · doi:10.48550/arxiv.1707.04521

27 pages

arxiv created 2017/07/14 · arxiv updated 2017/07/17

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 → 0, stationary points of the energy E^h, for a rod Ω_h ⊂ \mathbb R³ 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.

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