Effects of local incompressibility on the rheology of biocomposite networks*

Fibrous networks such as collagen are common in biological systems. Recent theoretical and experimental efforts have shed light on the mechanics of single component networks. Most real biopolymer networks, however, are composites made of elements with different rigidity. For instance, extracellular matrix consists of stiff collagen fibers in a soft background matrix. Understanding the interplay between different biopolymer networks remains unclear. In this work, we use 2D coarse-grained models to study the nonlinear strain-stiffening behavior in composites. The local volume constraints due to a soft matrix are implemented by adding an energetic penalty for changes in local density. When subjected to linear shear strain, the composite network was observed to have a substantially stiffer response. As we show, this can be understood in terms of a partial suppression of the non-affine strain due to the local volume constraint. In contrast with the effect of added elastic elements that resist deformation, such as additional springs or fibers, local volume constraints do not lead ultimately to an affine response. We explore the physical compressible and incompressible limits of composite networks by varying material parameters. We further test these predictions in composite collagen-hyaluronan networks that mimic the extracellular matrix of connective tissues.