On an elastic strain-limiting special Cosserat rod model

TL;DR

This paper introduces a novel nonlinear constitutive model for a strain-limiting special Cosserat rod, capturing complex behaviors like Poynting effects and shear bifurcation, relevant for solids and biological fibers.

Contribution

It presents the first intrinsic nonlinear constitutive relations for a strain-limiting Cosserat rod, including explicit equilibrium states and bifurcation analysis.

Findings

Explicit equilibrium states under end loads

Identification of Poynting-like effects

Prediction of tensile shearing bifurcation

Abstract

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