  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.
