Topology determines force distributions in one-dimensional random spring networks.

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Heidemann, KM; Sageman-Furnas, AO; Sharma, A; Rehfeldt, F; Schmidt, CF; Wardetzky, M

Published Date

  • February 2018

Published In

Volume / Issue

  • 97 / 2-1

Start / End Page

  • 022306 -

PubMed ID

  • 29548075

Electronic International Standard Serial Number (EISSN)

  • 2470-0053

International Standard Serial Number (ISSN)

  • 2470-0045

Digital Object Identifier (DOI)

  • 10.1103/physreve.97.022306

Language

  • eng