Collagen fibers, a primary structural protein in the extracellular matrix, provides essential scaffolding for tissues. Functionally, these fibers are essential for providing mechanical support, ensuring tissues like tendons effectively transfer force from muscles to bones. Moreover, collagen is a dynamic component that plays a crucial role in mediating cell signaling, influencing various cellular behaviors and functions.

The intricate network of collagen fibers in tissues forms a highly interconnected system, highlighting the tissue's structural resilience. This complexity, especially when considering interactions between collagen fibers or with cells, presents challenges for detailed analyses.

Our study introduces a homogenization framework for 3D collagen networks with diverse number of connectivity (C ∼ 7 and 4), bridging micro-to-macro scale behaviors. We employed a numerical strategy to homogenize the RVE, incorporating boundary periodicity and uniaxial loading to determine elastic properties. Systematic evaluations yielded a stress-stretch curve, reflecting micro-scale material behavior. This behavior aligned with hyperelastic models for both highly and moderately connected collagen networks, mirroring experimental findings. Collectively, these insights enhance our understanding of collagen mechanics, setting the stage for more nuanced analyses, particularly in cellular interactions within collagen matrices.

胶原纤维是细胞外基质中的主要结构蛋白，为组织提供重要的支架。从功能上讲，这些纤维对于提供机械支撑、确保肌腱等组织有效地将力量从肌肉传递到骨骼至关重要。此外，胶原蛋白是一种动态成分，在介导细胞信号传导、影响各种细胞行为和功能方面发挥着至关重要的作用。

组织中胶原纤维错综复杂的网络形成了一个高度互连的系统，凸显了组织的结构弹性。这种复杂性，特别是在考虑胶原纤维之间或与细胞之间的相互作用时，给详细分析带来了挑战。

我们的研究引入了具有不同数量连接（C ∼ 7 和 4）的 3D胶原蛋白网络的均质化框架，桥接了微观到宏观尺度的行为。我们采用数值策略来均匀化 RVE，结合边界周期性和单轴载荷来确定弹性特性。系统评估产生了应力-拉伸曲线，反映了微观尺度的材料行为。这种行为与高度和中等连接的胶原蛋白网络的超弹性模型一致，反映了实验结果。总的来说，这些见解增强了我们对胶原蛋白力学的理解，为更细致的分析奠定了基础，特别是在胶原蛋白基质内的细胞相互作用方面。