The growing interest in integrating liquid crystals (LCs)
into
flexible and miniaturized technologies brings about the need to understand
the interplay between spatially curved geometry, surface anchoring,
and the order associated with these materials. Here, we integrate
experimental methods and computational simulations to explore the
competition between surface-induced orientation and the effects of
deformable curved boundaries in uniaxially and biaxially stretched
nematic and smectic microdroplets. We find that the director field
of the nematic LCs upon uniaxial strain reorients and forms a larger
twisted defect ring to adjust to the new deformed geometry of the
stretched droplet. Upon biaxial extension, the director field initially
twists in the now oblate geometry and subsequently transitions into
a uniform vertical orientation at high strains. In smectic microdroplets,
on the other hand, LC alignment transforms from a radial smectic layering
to a quasi-flat layering in a compromise between interfacial and dilatation
forces. Upon removing the mechanical strain, the smectic LC recovers
its initial radial configuration; however, the oblate geometry traps
the nematic LC in the metastable vertical state. These findings offer
a basis for the rational design of LC-based flexible devices, including
wearable sensors, flexible displays, and smart windows.