  The effect of interstitial hydrogen on the elastic properties of
$\alpha$-iron is investigated using \textit{ab initio} density functional
theory. We find that while the overall strength properties are reduced by H,
the effects are mainly due to the resulting local volume expansion. We use
these concentration-dependent elastic moduli to model the effects of
homogeneous strain fields on H solubility and make extrapolations to
H-solubility in the spatially-varying strain fields of realistic dislocations.
We find that H is strongly trapped by dislocations of both the edge and screw
variety, leading to a remarkable increase in the local H concentration near the
dislocation cores. The strain dependence of the solution energy leading to
accumulation of H near dislocation cores, as well as the reduction of elastic
moduli which our calculations predict, is consistent with numerous experimental
studies which indicate that the trapping of H near dislocations plays a
significant role in the embrittlement of iron and steels.
