The mechanical influence of single fibre inclusions in discrete fibre networks

Abstract: Semiflexible biopolymer networks are commonly found in biological systems, from the cytoskeleton of cells to the extracellular matrix. Such networks often naturally occur as composites, in which various components interact to generate rich mechanical behaviours. In this work we examine the mechanics of composites formed when a single fibre inclusion is placed within discrete fibre networks of two distinct architectures. In particular, we computationally and theoretically investigate the mechanics of composites formed when an inclusion is introduced to Voronoi- and Mikado--type networks within the nonaffine regime. On subjecting these single inclusion composites to small shear deformations, we observe different behaviours dependent on the choice of network geometry. This divergence in mechanical responses is interpreted as a consequence of architecture-dependent differences in the nonaffine displacement field. Scaling laws for the increase in network energy due to inclusions of different lengths, orientations, and elastic properties are proposed and computationally verified. We present theoretical predictions for critical values of the inclusion bending and stretching stiffnesses, above which no further increases in network energy are observed for a given shear deformation. These predictions are supported by extensive computational evidence. We expect the architectural differences identified in this work to be pertinent to theoretical investigations into the complex behaviour of biopolymer networks, and to experimental work, where complex mechanics has been observed in composite fibre networks.