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.

我们提出了一个非线性、几何精确且热力学一致的框架，用于对具有不断变化的自然配置的特殊 Cosserat 杆进行建模。与通常使用逐点克劳修斯-迪昂不等式来体现热力学第二定律相反，我们强制采用严格较弱的形式，即总熵产生率不递减。状态变量和关闭控制场方程所需的作用力之间的本构关系是通过规定框架与亥姆霍兹能量的不同形式导出的和总耗散率并要求状态变量以最大化总熵产生率的方式演变。由于执行第二定律的全局形式所提供的灵活性，从该过程中获得了两种模型：一种满足克劳修斯-迪昂不等式的较强形式，另一种满足克劳修斯-迪昂不等式的较弱全局形式。最后，我们表明，与过去引入的其他粘弹性 Cosserat 杆模型相比，我们模型中的某些二次应变能产生类固体应力松弛和蠕变。