Abstract
This thesis explores the non-linear elasticity of smectic-A and smectic-C liquid crystal elastomers. These materials consist of "rod-like" liquid crystal mesogens arranged in a layered phase, cross-linked into a polymer matrix. The alignment direction of the mesogens is termed the director, and in the smectic-A phase the director and layer normal are parallel, whereas in the smectic-C phase the director is tilted at an angle to the layer normal. For smectic-C elastomers deformations that rotate the director in a conical path around the layer normal are ideally perfectly soft. Realistically non-idealities destroy perfect softness, and the resulting elasticity is termed semi-softness. The semi-soft elasticity of monodomain smectic-C elastomer is investigated starting from a model consisting of smectic layering and nematic elasticity terms, and a penalty for changing the tilt angle. A semi-soft elasticity term is then added to this energy. The elastic response to uniaxial deformation in various stretching geometries is calculated using an energy minimization routine. The stress-strain curves are diverse and depend strongly on the orientation of the layer normal, director and stretch axis. Remarkably, for an elongation parallel to the layer normal the stress-strain curve is non-monotonic, and the sample expands laterally in one direction over a range of strains. The stretching of monodomain smectic-A elastomer sheet under realistic clamping conditions is studied to examine the effects of stretching angle and sample aspect ratio on microstructure formation. Results generated by finite element analysis show that stretching parallel to the director the sample bulk forms bidirectionally buckled microstructure, with unidirectional buckling near the clamped edges. The aspect ratio significantly affects the microstructure distribution, but weakly influences the stress-strain behaviour. It is shown that existing smectic models require an additional energy term, related to the energy of deforming buckled layers or non-Gaussian effects, to reproduce the experimentally observed Poisson’s ratios.