Multiscale analysis of a 3D fibrous collagen tissue

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 similar to 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.