Coupled macroscopic and microscopic scale modeling of fibrillar tissues and tissue equivalents

Collagen mechanics are crucial to the function and dysfunction of many. tis sues, including blood vessels and articular cartilage, and bioartificial ti ssues. Previous attempts to develop computer simulations of collagenous tis sue based on macroscopic property descriptions have often been limited in a pplication by, the simplicity of the model; simulations based on microscopi c descriptions, in contrast, have numerical limitations imposed by, the siz e of the mathematical problem. We present a method that combines the tracta bility of the macroscopic approach with the flexibility of the microstructu ral approach. The macroscopic domain is divided into finite elements (as in standard FEM). Each element contains a microscopic scale network. Instead of a stress constitutive equation; the macroscopic problem is distributed o ver the microscopic scale network, and solved in each element to satisfy, t he weak formulation of Cauchy's stress continuity equation over the macrosc opic domain. The combined method scales by, order 1.1 us the overall number of degrees of freedom is increased, allowing it to handle larger problems than a direct microstructural approach. Model predictions agree qualitative ly with tensile tests on isotropic and aligned reconstituted type I collage n gels.