We identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. In mathematical terms, we characterize the weak limits of sequences of Sobolev maps whose gradients on the fibers lie in the set of rotations. These limits are determined by an anisotropic constraint in the sense that they locally preserve length in the fiber direction. Our proof of the necessity emerges as a natural generalization and modification of the recently established asymptotic rigidity analysis for composites with layered reinforcements. However, the construction of approximating sequences is more delicate here due to the higher flexibility and connectedness of the soft material component. We overcome these technical challenges by a careful approximation of the identity that is constant on the rigid components, combined with a lifting in fiber bundles for Sobolev functions. The results are illustrated with several examples of attainable effective deformations. If an additional partial second-order regularization is introduced into the material model, only rigid body motions can occur macroscopically.

我们确定了增强复合材料模型中可达到的有效变形的受限类别，其中平行、长和完全刚性的纤维嵌入弹性体中。在数学术语中，我们描述了 Sobolev 映射序列的弱极限，其在纤维上的梯度位于旋转集合中。这些限制是由各向异性约束决定的，因为它们在纤维方向上局部保持长度。我们对必要性的证明是对最近建立的具有分层增强的复合材料的渐近刚度分析的自然概括和修改。然而，由于软材料组件具有更高的灵活性和连通性，这里的近似序列的构造更加精细。我们通过仔细近似刚性组件上恒定的恒等式来克服这些技术挑战，并结合 Sobolev 函数的纤维束提升。用几个可达到的有效变形示例说明了结果。如果在材料模型中引入额外的部分二阶正则化，则宏观上只能发生刚体运动。