Shear Yieldind and Percolation Transition in Smectics Liquid Crystals

Yielding in complex fluids is a poorly understood phenomenon which consists of a solid-like behavior at low strain rates characterized by a divergent viscosity, while a Newtonian flowing regime is observed at larger forcing. Many amorphous soft materials -such as foams, emulsions and microgels- exhibit yielding behaviors.
Here, we numerically study the rheology of lyotropic smectic liquid crystals by means of a continuous approach based on the Brazovskii theory for microphase separation [1].
We show that the transition from the solid-like regime toward the flowing state occurs due to the unbinding of dislocation pairs and their consequent annihilation. Importantly, we analyze how dislocations pairs lead to long-ranged plumes of elastic stress which result in the development of large unstrained regions and long-lasting shear banding.
Morever, we furnish solid evidence that the yielding (subcritical) transition belongs to the direct percolation universality class.

[1] F. Bonelli, L.N. Carenza et al., Sci. Rep., 9, 2019.