Torsion and Bistability of Double-Twist Elastomers

We investigate the elastic properties of anisotropic elastomers with a double-twist director field, which is a model for collagen fibrils or blue phases. We observe a significant Poynting effect, coupling torsion (fibril twist) and extension. For freely-rotating boundary conditions, we identify a structural bistability at very small extensional strains which undergoes a saddle-node bifurcation at a critical strain -- at approximately 1% strain for a parameterization appropriate for collagen fibrils. With clamped boundary conditions appropriate for many experimental setups, the bifurcation is not present. We expect significant helical shape effects due to residual torques when fixed torsion does not equal the equilibrium torsion of freely-rotating boundary conditions.