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Semiflexible biopolymer networks are commonly found in biological systems,from the cytoskeleton of cells to the extracellular matrix. Such networks oftennaturally occur as composites, in which various components interact to generaterich mechanical behaviours. In this work we examine the mechanics of compositesformed when a single fibre inclusion is placed within discrete fibre networksof two distinct architectures. In particular, we computationally andtheoretically investigate the mechanics of composites formed when an inclusionis introduced to Voronoi- and Mikado--type networks within the nonaffineregime. On subjecting these single inclusion composites to small sheardeformations, we observe different behaviours dependent on the choice ofnetwork geometry. This divergence in mechanical responses is interpreted as aconsequence of architecture-dependent differences in the nonaffine displacementfield. Scaling laws for the increase in network energy due to inclusions ofdifferent lengths, orientations, and elastic properties are proposed andcomputationally verified. We present theoretical predictions for criticalvalues of the inclusion bending and stretching stiffnesses, above which nofurther increases in network energy are observed for a given shear deformation.These predictions are supported by extensive computational evidence. We expectthe architectural differences identified in this work to be pertinent totheoretical investigations into the complex behaviour of biopolymer networks,and to experimental work, where complex mechanics has been observed incomposite fibre networks.

The mechanical influence of single fibre inclusions in discrete fibre networks