Fibrous gels modelled as fluid-filled continua with double-well energy landscape.

Several biological materials are fibre networks infused with fluid, often referred to as fibrous gels. An important feature of these gels is that the fibres buckle under compression, causing a densification of the network that is accompanied by a reduction in volume and release of fluid. Displacement-controlled compression of fibrous gels has shown that the network can exist in a rarefied and a densified state over a range of stresses. Continuum chemo-elastic theories can be used to model the mechanical behaviour of these gels, but they suffer from the drawback that the stored energy function of the underlying network is based on neo-Hookean elasticity, which cannot account for the existence of multiple phases. Here we use a double-well stored energy function in a chemo-elastic model of gels to capture the existence of two phases of the network. We model cyclic compression/decompression experiments on fibrous gels and show that they exhibit propagating interfaces and hysteretic stress-strain curves that have been observed in experiments. We can capture features in the rate-dependent response of these fibrous gels without recourse to finite-element calculations. We also perform experiments to show that certain features in the stress-strain curves of fibrous gels predicted by our model can be found in the compression response of blood clots. Our methods may be extended to other tissues and synthetic gels that have a fibrous structure.