Abstract Composite materials reinforced by crimped fibers, such as collagen fibers, have a widely application in the advanced structures. Therefore, an effective and achievable model is significant for explicitly describing the geometry of the crimped fibers and evaluating their mechanical behaviors. Aiming at this purpose, a three-dimensional (3D) unit cell model (UCM) is developed based on the microstructure of the collagen fibers, in which a controllable modified sinusoidal waviness fiber is explicitly embedded into the soft matrix, and an effective periodic boundary condition is applied on the proposed 3D UCM by using the multi-points constraint equations. The accuracy and validity of the proposed model are verified by comparing with the existing experimental results. For investigating the influence of the geometric parameters on the mechanical responses of the crimped fiber reinforced composites, several numerical UCMs with different geometric parameters are presented. The obtained results reveal that the parameters of crimp amplitude H and waviness χ of the fibers mainly contribute to the flexibility of the materials. The parameter ω for characterizing the roughness of the fibers is associated with the size and position of largest stress region. Moreover, the fiber radius R plays an important role in determining the bearing capacity of the materials and an excellent mechanical property, e.g., not only withstands the large initial tensile load but also has a special ability to guarantee the flexibility of the materials, may be achieved by controlling the number of the fibers with big and small radii.

中文翻译：

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具有可控卷曲结构的三维晶胞模型，用于研究胶原纤维增强生物复合材料的有限应变响应

摘要 胶原纤维等卷曲纤维增强复合材料在先进结构中有着广泛的应用。因此，一个有效且可实现的模型对于明确描述卷曲纤维的几何形状和评估其机械行为具有重要意义。为此，基于胶原纤维的微观结构开发了三维 (3D) 晶胞模型 (UCM)，其中可控改性正弦波纹纤维明确嵌入软基体中，以及有效的周期性边界通过使用多点约束方程，将条件应用于建议的 3D UCM。通过与已有实验结果的对比，验证了所提出模型的准确性和有效性。为了研究几何参数对卷曲纤维增强复合材料的机械响应的影响，提出了几种具有不同几何参数的数值 UCM。所得结果表明，纤维的卷曲幅度 H 和波纹度 χ 参数主要影响材料的柔韧性。表征纤维粗糙度的参数ω与最大应力区域的大小和位置有关。此外，纤维半径 R 在决定材料的承载能力方面起着重要作用，具有优良的机械性能，例如，不仅能承受较大的初始拉伸载荷，而且具有特殊的能力来保证材料的柔韧性，可通过控制大半径和小半径的纤维数量来实现。