Special Cosserat rods with rate-dependent evolving natural configurations

Abstract

We present a nonlinear, geometrically exact, and thermodynamically consistent framework for modeling special Cosserat rods with evolving natural configurations. In contrast to the common usage of the point-wise Clausius–Duhem inequality to embody the Second Law of Thermodynamics, we enforce the strictly weaker form that the rate of total entropy production is non-decreasing. The constitutive relations between the state variables and applied forces needed to close the governing field equations are derived via prescribing frame indifferent forms of the Helmholtz energy and the total dissipation rate and requiring that the state variables evolve in a way that maximizes the rate of total entropy production. Due to the flexibility afforded by enforcing a global form of the Second Law, there are two models obtained from this procedure: one satisfying the stronger form of the Clausius–Duhem inequality and one satisfying the weaker global form of the Clausius–Duhem inequality. Finally, we show that in contrast to other viscoelastic Cosserat rod models introduced in the past, certain quadratic strain energies in our model yield both solid-like stress relaxation and creep.