Interacting dislocations create shape multistability in flexible cylindrical crystals

Many biological and synthetic systems are self-organized in the form of ordered two-dimensional assemblies, including microtubules, carbon nanotubes and colloidal systems. Motivated by these observations and topological defects associated with geometrically frustrated tubular assemblies, we investigate a minimal model of dislocation dynamics in flexible 2D crystals wrapped into a cylindrical topology. We theoretically study how interacting dislocations distort the crystalline order and affect the three-dimensional shape - bends, kinks, and helicity - of tubular crystals. Using numerical simulations we explore plastic deformations by dislocation glide. We demonstrate that the periodicity of cylindrical topology leads to states where glide is energetically restricted, allowing precise prediction of defect location, and creating multiple metastable tube geometries that do not exist in crystals on rigid cylindrical surfaces. We also show that transitions between metastable defect patterns associated with different 3D shapes can be triggered by applied external stress. This opens possibilities for designing mechanically multistable systems of target geometry, topology and shape.