Compression stiffening of fibrous networks with stiff inclusions

Various biological tissues stiffen under applied compression. However, due to their structural complexity, the mechanism for this stiffening is not obvious. Recent work has shown similar behavior in a simple tissue analogue consisting of a reconstituted biopolymer network containing inert colloidal particles. We show that compressing such a material can, under the right conditions, lead to significant rearrangement of the particles, which then heterogeneously deform the interstitial network. This leads to an unusual regime in which the mechanical response of the compressed material is controlled by the resistance of the interstitial network to stretching. Utilizing a coarse-grained model, we generate predictive phase diagrams for compression-driven stiffening and particle jamming as a function of particle volume fraction, network critical strain, and applied compression, which we test by simulating the rheology of disordered fiber networks containing rigid particles.