A Cosserat theory for fiber-reinforced elastic solids developed in Steigmann (2012) is generalized to accommodate initial curvature and twist of the fibers. The basic variables of the theory are a conventional deformation field and a rotation field that describes the local fiber orientation. Constraints on these fields are introduced to model the materiality of the fibers with respect to the underlying matrix deformation. A variational argument delivers the relevant equilibrium equations and boundary conditions and furnishes the interpretation of the Lagrange multipliers associated with the constraints as shear tractions acting on the fiber cross sections. Finally, the theory of material symmetry for such solids is developed and applied to the classification of some explicit constitutive functions.

中文翻译：

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由一系列弯曲和扭曲纤维增强的弹性固体的 Cosserat 模型

Steigmann (2012) 开发的用于纤维增强弹性固体的 Cosserat 理论被推广以适应纤维的初始曲率和扭曲。该理论的基本变量是常规变形场和描述局部纤维取向的旋转场。引入对这些场的约束来模拟纤维相对于基础基体变形的重要性。变分论证提供了相关的平衡方程和边界条件，并提供了与约束相关的拉格朗日乘子的解释，作为作用在纤维横截面上的剪切牵引力。最后，发展了此类固体的材料对称理论，并将其应用于一些显式本构函数的分类。