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Abstract

Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and
tissues. Fiber-reinforced materials are also common in technology. An important characteristic of such materials is
their resistance to failure under load. Rupture occurs when fibers break under excessive force and when that failure
propagates. Therefore, it is crucial to understand force distributions. Force distributions within such networks are
typically highly inhomogeneous and are not well understood. Here we construct a simple one-dimensional model
system with periodic boundary conditions by randomly placing linear springs on a circle. We consider ensembles
of such networks that consist of N nodes and have an average degree of connectivity z but vary in topology.
Using a graph-theoretical approach that accounts for the full topology of each network in the ensemble, we show
that, surprisingly, the force distributions can be fully characterized in terms of the parameters (N ,z). Despite the
universal properties of such (N ,z) ensembles, our analysis further reveals that a classical mean-field approach
fails to capture force distributions correctly. We demonstrate that network topology is a crucial determinant of
force distributions in elastic spring networks.