  We study the micromechanics of collagen-I gel with the goal of bridging the
gap between theory and experiment in the study of biopolymer networks.
Three-dimensional images of fluorescently labeled collagen are obtained by
confocal microscopy and the network geometry is extracted using a 3d network
skeletonization algorithm. Each fiber is modeled as a worm-like-chain that
resists stretching and bending, and each cross-link is modeled as torsional
spring. The stress-strain curves of networks at three different densities are
compared to rheology measurements. The model shows good agreement with
experiment, confirming that strain stiffening of collagen can be explained
entirely by geometric realignment of the network, as opposed to entropic
stiffening of individual fibers. The model also suggests that at small strains,
cross-link deformation is the main contributer to network stiffness whereas at
large strains, fiber stretching dominates. Since this modeling effort uses
networks with realistic geometries, this analysis can ultimately serve as a
tool for understanding how the mechanics of fibers and cross-links at the
microscopic level produce the macroscopic properties of the network. While the
focus of this paper is on the mechanics of collagen, we demonstrate a framework
that can be applied to many biopolymer networks.
