  Fibrous networks such as collagen are common in biological systems. Recent
theoretical and experimental efforts have shed light on the mechanics of single
component networks. Most real biopolymer networks, however, are composites made
of elements with different rigidity. For instance, the extracellular matrix in
mammalian tissues consists of stiff collagen fibers in a background matrix of
flexible polymers such as hyaluronic acid (HA). The interplay between different
biopolymer components in such composite networks remains unclear. In this work,
we use 2D coarse-grained models to study the nonlinear strain-stiffening
behavior of composites. We introduce a local volume constraint to model the
incompressibility of HA. We also perform rheology experiments on composites of
collagen with HA. We demonstrate both theoretically and experimentally that the
linear shear modulus of composite networks can be increased by approximately an
order of magnitude above the corresponding moduli of the pure components. Our
model shows that this synergistic effect can be understood in terms of the
local incompressibility of HA, which acts to suppress density fluctuations of
the collagen matrix with which it is entangled.
