Interplay between elasticity and order in 2D biological tissues*

The interplay between order and shape in cellular tissues is an essential feature of certain biological processes, such as morphogenesis. Most theoretical treatments of ordered biological tissues are based on fluid models, however there are examples of tissues, such as hydra, which are not freely flowing but which are, nonetheless, often modeled as such. With this motivation, we have developed a Foppl-van Karman model for an active elastic sheet with nematic order, inspired by nematic elastomers, which couples in-plane passive and active stresses to bending and order. Passive nematic elastomers exhibit soft-elasticity which may be utilized to blueprint shape via a prescribed nematic texture. Building upon this framework, we investigate how active stresses – as mediated by elasticity - may select shape. Our work is relevant for understanding the role of elasticity in controlling how 2D ordered biological tissues acquire 3D shapes.