Active nematic response to a deformable body or boundary: elastic deformations and anchoring-induced flow

A body immersed in a nematic liquid crystal disturbs the fluid's preferred molecular configuration and increases its stored elastic energy. In an active nematic, the fluid components also generate a stress in the bulk fluid. By introducing either an immersed body or boundary, a large scale flow can be triggered due to anchoring boundary conditions alone -- a global pressure built by active stresses at equilibrium is instantly released everywhere. The fluid then imposes viscous, elastic, and active stresses on such surfaces which, if compliant, may result in a surface deformation. We study the deformations and stresses of a linearly elastic body placed in an active nematic in two dimensions. Using complex variables techniques, exact expressions for the fluid flow, director field, surface tractions, and body deformation are derived. Qualitative differences between elastic and active stress-driven deformations are identified, depending on an active Ericksen number, anchoring conditions, and body material properties, thereby suggesting a new method for measuring mechanical stresses in active anisotropic environments. Flow profiles, external confinement, and anchoring-induced stirring are also addressed.