1 results
Convergence of equilibria for bending-torsion models of rods with inhomogeneities
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 1 / February 2020
- Published online by Cambridge University Press:
- 24 January 2019, pp. 233-260
- Print publication:
- February 2020
-
- Article
- Export citation
-
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
$h\searrow 0$, stationary points of the energy 
, for a rod 
$\Omega _h\subset {\open R}^3$ with cross-sectional diameter h, subconverge to stationary points of the Γ-limit of 
, 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.
, for a rod 
, 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.