  Liquid Crystalline Elastomers (LCEs) are active materials that are of
interest due to their programmable response to various external stimuli such as
light and heat. When exposed to these stimuli, the anisotropy in the response
of the material is governed by the nematic director, which is a continuum
parameter that is defined as the average local orientation of the mesogens in
the liquid crystal phase. This nematic director can be programmed to be
heterogeneous in space, creating a vast design space that is useful for
applications ranging from artificial ligaments to deployable structures to
self-assembling mechanisms. Even when specialized to long and thin strips of
LCEs -- the focus of this work -- the vast design space has required the use of
numerical simulations to aid in experimental discovery. To mitigate the
computational expense of full 3-d numerical simulations, several
dimensionally-reduced rod and ribbon models have been developed for LCE strips,
but these have not accounted for the possibility of initial transverse
curvature, like carpenter's tape spring. Motivated by recent experiments
showing that transversely-curved LCE strips display a rich variety of
configurations, this work derives a dimensionally-reduced 1-d model for
pre-curved LCE strips. The 1-d model is validated against full 3-d finite
element calculations, and it is also shown to capture experimental
observations, including tape-spring-like localizations, in activated LCE
strips.
