Mechanics of liquid crystal inclusions in soft matrices

The mechanical behaviour of composites of liquid crystal inclusions embedded in soft matrices involves a complex interplay between the elasticity of the matrix, the surface elasticity of the interfaces, and the reorientation of the liquid crystal molecules. Directors of the (nematic) liquid crystal tend to be aligned in the bulk, but may "anchor" along the interface. In addition, the interface deforms according to the bulk deformation, while trying to minimise the surface area. In this paper, we present a continuum theory for an incompressible hyperelastic matrix containing nematic liquid crystal inclusions. The elastic energy of the inclusions, attributed to the distortion of the director field, is described using Landau-de Gennes theory. The matrix is described as an incompressible neo-Hookean solid. Anchoring effects at the inclusion-matrix interface are described through anisotropic surface tension. The model is implemented numerically using the FEniCSx finite element code. Through parametric study, we investigate the impact of energy competitions on the macroscopic and inclusion responses. Similar to the case of liquid inclusions, composites containing liquid crystal inclusions can be stiffer or softer than the matrix, depending on the value of the elasto-capillary number. The softening or stiffening effect is further affected by the distortional energy of the inclusion and the anchoring strength of the interface. Conversely, applied mechanical loads can reorient the director field. In particular, we show that stress-induced reorientation is significant when the dimensionless volume of the inclusion is large, involving alignment of the directors under tension, and disorientation under compression. The proposed theory and new physical insights could be useful for the design of smart stimuli-responsive materials.