  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-like 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 when fixed torsion does
not equal the equilibrium torsion of freely-rotating boundary conditions, due
to residual torques.
