Volume-averaging theory for the study of the mechanics of collagen networks

A multiscale methodology has been developed for modeling mechanical behavior of collagen fiber networks. The methodology addresses scale separation between the macroscopic, tissue-level scale and the microscopic, fiber-level scale. A three-dimensional, Galerkin finite-element model has been employed for the macroscopic scale, while the tissue microstructure is represented as a three-dimensional fibrillar network. The model was applied to a rectangular slab in uniaxial extension. A heterogeneous microstructure resulted in a non-uniform deformation field, and Poisson’s ratio varied for networks with different alignments. The model was also specified and compared to published data relating microstructure to macroscopic behavior of collagen gels.