Surface instability in a nematic elastomer

Abstract: Liquid crystal elastomers (LCEs) are soft phase-changing solids that exhibit large reversible contractions upon heating, Goldstone-like soft modes and resultant microstructural instabilities. We heat a planar LCE slab to isotropic, clamp the lower surface then cool back to nematic. Clamping prevents macroscopic elongation, producing compression and microstructure. We see that the free surface destabilizes, adopting topography with amplitude and wavelength similar to thickness. To understand the instability, we numerically compute the microstructural relaxation of a "non-ideal" LCE energy. Linear stability reveals a Biot-like scale-free instability, but with oblique wavevector. However, simulation and experiment show that, unlike classic elastic creasing, instability culminates in a cross-hatch without cusps or hysteresis, and is constructed entirely from low-stress soft modes.