The Effect of Structure on the Elastic and Fracture Properties of Stochastic Fiber Networks

Network microstructures are ubiquitous in biological matter, ranging from nanometer to millimeter length scales.  In many of these natural network materials, the fibers are significantly longer than required for geometric percolation, i.e. much shorter fibres would suffice to form a connected network. This raises the question of functional purpose that this 'surplus' in material may serve. Using numerical simulations, this project investigates how microstructure and in particular the excess material affect the homogenized mechanical properties of the network material.

We model these physical systems as discrete networks where fiber segments with defined mechanical properties are connected by pin-jointed cross-links. We compare networks obtained from Voronoi tessellation with structurally more complex ones, obtained by dedicated modifications in topology. These modified networks are characterized by a surplus, i.e. an increased total amount of material at a constant cross-link density, and therefore by longer mean fiber length. Most important, they feature additional fiber-fiber intersections, so that our study is also relevant for understanding the transition from cellular to fiber-like networks on the one hand, and from planar to quasi-planar ones on the other hand. The computational analysis of networks with elastic and brittle fibers allows us to compute the homogenized stress-stretch response, for each network from which key mechanical descriptors like stiffness, ultimate strength and toughness can be extracted. 

In addition to providing understanding for the relation between structure and function in general, and the role of additional fiber material in particular, the simulations also allow establishing quantitative relationships between the homogenized mechanical properties of the networks, their topological and the mechanical characteristics of the fibers, which can be used for network design on the one hand, and for the inverse analysis of experimentally observed behavior on the other hand.