  We present a numerical study of stretching monodomain smectic-A elastomer
sheets, computed using the finite element method. When stretched parallel to
the layer normal the microscopic layers in smectic elastomers are unstable to a
transition to a buckled state. We account for the layer buckling by replacing
the microscopic energy with a coarse grained effective free energy that
accounts for the fine scale deformation of the layers. We augment this model
with a term to describe the energy of deforming buckled layers, which is
necessary to reproduce the experimentally observed Poisson's ratios
post-buckling. We examine the spatial distribution of the microstructure phases
for various stretching angles relative to the layer normal, and for different
length-to-width aspect ratios. When stretching parallel to the layer normal the
majority of the sample forms a bi-directionally buckled microstructure, except
at the clamps where uni-directional microstructure is predicted. When
stretching at small inclinations to the layer normal the phase of the sample is
sensitive to the aspect ratio of the sample, with the bi-directionally buckled
phase persistent to large angles only for small aspect ratios. We relate these
theoretical results to experiments on smectic-A elastomers.
