  Tissues commonly consist of cells embedded within a fibrous biopolymer
network. Whereas cell-free reconstituted biopolymer networks typically soften
under applied uniaxial compression, various tissues, including liver, brain,
and fat, have been observed to instead stiffen when compressed. The mechanism
for this compression stiffening effect is not yet clear. Here, we demonstrate
that when a material composed of stiff inclusions embedded in a fibrous network
is compressed, heterogeneous rearrangement of the inclusions can induce tension
within the interstitial network, leading to a macroscopic crossover from an
initial bending-dominated softening regime to a stretching-dominated stiffening
regime, which occurs before and independently of jamming of the inclusions.
Using a coarse-grained particle-network model, we first establish a phase
diagram for compression-driven, stretching-dominated stress propagation and
jamming in uniaxially compressed 2- and 3-dimensional systems. Then, we
demonstrate that a more detailed computational model of stiff inclusions in a
subisostatic semiflexible fiber network exhibits quantitative agreement with
the predictions of our coarse-grained model as well as qualitative agreement
with experiments.
