  This paper evaluates qualitatively as well as quantitatively the accuracy of
a recently proposed Peierls--Nabarro Finite Element (PN-FE) model for
dislocations by a direct comparison with an equivalent molecular statics
simulation. To this end, a two-dimensional microstructural specimen subjected
to simple shear is considered, consisting of a central soft phase flanked by
two hard-phase regions. A hexagonal atomic structure with equal lattice spacing
is adopted, the interactions of which are described by the Lennard--Jones
potential with phase specific depths of its energy well. During loading, edge
dislocation dipoles centred in the soft phase are introduced, which progress
towards the phase boundaries, where they pile up. Under a sufficiently high
external shear load, the leading dislocation is eventually transmitted into the
harder phase. The homogenized PN-FE model is calibrated to an atomistic model
in terms of effective elasticity constants and glide plane properties as
obtained from simple uniform deformations. To study the influence of different
formulations of the glide plane potential, multiple approaches are employed,
ranging from a simple sinusoidal function of the tangential disregistry to a
complex model that couples the influence of the tangential and the normal
disregistries. The obtained results show that, qualitatively, the dislocation
structure, displacement, strain fields, and the dislocation evolution are
captured adequately. The simplifications of the PN-FE model lead, however, to
some discrepancies within the dislocation core. Such discrepancies play a
dominant role in the dislocation transmission process, which thus cannot
quantitatively be captured properly. Despite its simplicity, the PN-FE model
proves to be an elegant tool for a qualitative study of edge dislocation
behaviour in two-phase microstructures, although it may not be quantitatively
predictive.
