Topology determines force distributions in one-dimensional random spring networks

  • 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 theNetworks 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.show moreshow less

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Metadaten
Author:Knut M. Heidemann, Andrew O. Sageman-Furnas, Abhinav SharmaGND, Florian Rehfeldt, Christoph F. Schmidt, Max Wardetzky
URN:urn:nbn:de:bvb:384-opus4-1038998
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/103899
ISSN:2470-0045OPAC
ISSN:2470-0053OPAC
Parent Title (English):Physical Review E
Publisher:American Physical Society (APS)
Place of publication:College Park, MD
Type:Article
Language:English
Year of first Publication:2018
Publishing Institution:Universität Augsburg
Release Date:2023/05/02
Volume:97
Issue:2
First Page:022306
DOI:https://doi.org/10.1103/physreve.97.022306
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Theoretische Physik II
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)