Scaling Theory for Mechanical Critical Behavior in Fiber Networks

As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a rigidity transition with corresponding critical signatures as a...

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Bibliographic Details
Published in:Physical review letters 2019-05, Vol.122 (18), p.188003-188003, Article 188003
Main Authors: Shivers, Jordan L, Arzash, Sadjad, Sharma, Abhinav, MacKintosh, Fred C
Format: Article
Language:English
Subjects:
Computer simulation
Scaling
Transportation networks
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Summary:As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a rigidity transition with corresponding critical signatures as a function of strain. Experimental collagen networks were also shown to be consistent with these predictions. We develop a scaling theory for this strain-controlled transition. Using a real-space renormalization approach, we determine relations between the critical exponents governing the transition, which we verify for the strain-controlled transition using numerical simulations of both triangular lattice-based and packing-derived fiber networks.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.122.188003