The rheological properties of fibrin networks have been of long-standing
interest. As such there is a wealth of studies of their shear and tensile
responses, but their compressive behavior remains unexplored. Here, by
characterization of the network structure with synchronous measurement of the
fibrin storage and loss moduli at increasing degrees of compression, we show
that the compressive behavior of fibrin networks is similar to that of cellular
solids. A non-linear stress-strain response of fibrin consists of three
regimes: 1) an initial linear regime, in which most fibers are straight, 2) a
plateau regime, in which more and more fibers buckle and collapse, and 3) a
markedly non-linear regime, in which network densification occurs {{by bending
of buckled fibers}} and inter-fiber contacts. Importantly, the spatially
non-uniform network deformation included formation of a moving "compression
front" along the axis of strain, which segregated the fibrin network into
compartments with different fiber densities and structure. The Young's modulus
of the linear phase depends quadratically on the fibrin volume fraction while
that in the densified phase depends cubically on it. The viscoelastic plateau
regime corresponds to a mixture of these two phases in which the fractions of
the two phases change during compression. We model this regime using a
continuum theory of phase transitions and analytically predict the storage and
loss moduli which are in good agreement with the experimental data. Our work
shows that fibrin networks are a member of a broad class of natural cellular
materials which includes cancellous bone, wood and cork
