  The bistability of embedded elements provides a natural route through which
to introduce reprogrammability to elastic meta-materials. One example of this
is the soft morphable sheet, in which bistable elements that can be snapped up
or down, are embedded within a soft sheet. The state of the sheet can then be
programmed by snapping particular elements up or down, resulting in different
global shapes. However, attempts to leverage this programmability have been
limited by the tendency for the deformations induced by multiple elastic
elements to cause large global shape bifurcations. We study the root cause of
this bifurcation in the soft morphable sheet by developing a detailed
understanding of the behaviour of a single bistable element attached to a flat
'skirt' region. We study the geometrical limitations on the bistability of this
single element, and show that the structure of its deformation can be
understood using a boundary layer analysis. Moreover, by studying the
compressive strains that a single bistable element induces in the surrounding
skirt we show that the shape bifurcation in the soft morphable sheet can be
delayed by an appropriate design of the lattice on which bistable elements are
placed.
