In the modelling of fibre-reinforced composites, it is well established to consider the fibre direction in the stored energy in order to account for the transverse isotropy of the overall material, induced by a single family of fibres. However, this approach does not include any length scale and therefore lacks in the prediction of size effects that may occur from the fibre diameter or spacing. By making use of a generalised continuum model including non-symmetric stresses and couple-stresses, the gradient of the fibre direction vector can be taken into account as an additional parameter of the stored energy density function. As a consequence, the enhanced model considers the bending stiffness of the fibres and includes information on the material length scale. Along with additional material parameters, increased continuity requirements on the basis functions follow in the finite element analysis. The isogeometric finite element method provides a framework which can fulfil these requirements of the corresponding weak formulation. In the present contribution, the method is applied to two representative numerical examples. At first, the bending deformation of a cantilever beam is studied in order to analyse the influence of the fibre properties. An increasingly stiff response is observed as the fibre bending stiffness increases and as the fibre orientation aligns with the beam’s axis. Secondly, a fibre-reinforced cylindrical tube under a pure azimuthal shear deformation is considered. The corresponding simulation results are compared against a semi-analytical solution. It is shown that the isogeometric analysis yields highly accurate results for the boundary value problem under consideration.

在纤维增强复合材料的建模中，已经很好地考虑了存储能量中的纤维方向，以说明由单个纤维家族引起的整个材料的横向各向同性。然而，这种方法不包括任何长度尺度，因此缺乏对可能因纤维直径或间距而产生的尺寸影响的预测。通过使用包括非对称应力和耦合应力的广义连续模型，可以将纤维方向矢量的梯度作为存储的能量密度函数的附加参数考虑在内。结果，增强的模型考虑了纤维的弯曲刚度，并包括了有关材料长度尺度的信息。连同其他材料参数，在有限元分析中增加了对基函数的连续性要求。等几何有限元方法提供了可以满足相应弱公式的这些要求的框架。在本贡献中，该方法被应用于两个代表性的数值示例。首先，研究悬臂梁的弯曲变形，以分析纤维特性的影响。随着光纤弯曲刚度的增加以及光纤方向与光束轴的对齐，刚性响应会越来越强。其次，考虑了在纯方位角剪切变形下的纤维增强圆柱管。将相应的仿真结果与半解析解进行比较。