  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.

Soft Condensed Matter