Helfrich-Hurault elastic instabilities driven by geometrical frustration

The Helfrich-Hurault instability is a well-known mechanism behind the undulations that occur as a result of strain upon liquid crystal systems with periodic ground states. In this review, the Helfrich-Hurault elastic instability is examined with a focus on layered liquid crystals that are geometrically frustrated. The frustration is relieved by undulations in the layered structure to maintain the preferred layer spacing. Examples of cholesteric and smectic liquid crystals confined between two spherical fluid interfaces are described and the effects of topological constraints, anchoring conditions, and curvature on the instability are examined. Lastly, the Helfrich-Hurault instability is surveyed as a pattern formation mechanism across a range of materials, both biological and synthetic.