Nonlinear elasticity of polymer networks and hydrogels with inclusions

Tissues consist of cells embedded within a fibrous biopolymer network. Whereas pure reconstituted biopolymer networks typically soften under compression, various tissues such as liver, brain, and fat, are seen to stiffen under compression. We show that when a material composed of stiff inclusions embedded in a fibrous network is compressed, nonaffine rearrangements of the inclusions can induce tension within the interstitial network, leading to a crossover from a soft bending-dominated regime to a stretching-dominated 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 two- and three-dimensional systems. We then 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.