Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session X42: Topology, Geometry, and Physics of Elastic Networks
8:00 AM–11:00 AM,
Friday, March 9, 2018
LACC Room: 502B
Sponsoring Units: GSNP DPOLY GSNP
Chair: Eleni Katifori, University of Pennsylvania
Abstract: X42.00005 : Topology counts: Force distributions in random spring networks*
10:24 AM–11:00 AM
(Technical University of Berlin)
Under large stresses, filamentous polymer networks often exhibit highly inhomogeneous force distributions. Forces propagate along nontrivial loops that make up a network's topology, where each nontrivial loop is a path that connects one boundary of the system to another. By introducing a toy model comprising ensembles of one-dimensional, periodic, linear spring networks, we demonstrate that network topology is a crucial determinant of force distributions in elastic spring networks. In contrast to a mean-field approach, our graph-theoretic approach explicitly accounts for the full network topology and is in excellent agreement with numerical simulations. Our results are a first step towards understanding the concentration of forces along a few nontrivial loops, known as force chains, that has been observed in stressed 2D and 3D nonlinear networks.
*Funding from the Deutsche Forschungsgemeinschaft (DFG) within the collaborative research center SFB 755, project A3, is gratefully acknowledged.
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