On an elastic strain-limiting special Cosserat rod model

Motivated by recent strain-limiting models for solids and biological fibers, we introduce the first intrinsic set of nonlinear constitutive relations, between geometrically exact strains components contact force couple, describing a uniform, hyperelastic, special Cosserat rod. After discussing some attractive features relations (orientation preservation, transverse symmetry monotonicity), exhibit several explicit equilibrium states under either an isolated end thrust or couple. In particular, certain Poynting like effects, show that mild assumptions on material parameters, model predicts tensile shearing bifurcation: straight rod large enough parallel to its center line can shear.