TY - JOUR
T1 - Mechanics of Metric Frustration in Contorted Filament Bundles
T2 - From Local Symmetry to Columnar Elasticity
AU - Atkinson, Daria W.
AU - Santangelo, Christian D.
AU - Grason, Gregory M.
N1 - Funding Information:
The authors gratefully acknowledge useful discussions with R. Kusner, S. Zhou, and B. Davidovitch. M. Dimitriyev, D. Hall, and R. Kamien provided feedback on an early draft of this manuscript. This work was supported by the NSF under Grants No. DMR-1608862 and No. NSF DMR-1822638; D. A. received additional funding from the Penn Provost’s postdoctoral fellowship and NSF MRSEC DMR-1720530.
Publisher Copyright:
© 2021 American Physical Society.
PY - 2021/11/19
Y1 - 2021/11/19
N2 - Bundles of filaments are subject to geometric frustration: certain deformations (e.g., bending while twisted) require longitudinal variations in spacing between filaments. While bundles are common - from protein fibers to yarns - the mechanical consequences of longitudinal frustration are unknown. We derive a geometrically nonlinear formalism for bundle mechanics, using a gaugelike symmetry under reptations along filament backbones. We relate force balance to orientational geometry and assess the elastic cost of frustration in twisted-toroidal bundles.
AB - Bundles of filaments are subject to geometric frustration: certain deformations (e.g., bending while twisted) require longitudinal variations in spacing between filaments. While bundles are common - from protein fibers to yarns - the mechanical consequences of longitudinal frustration are unknown. We derive a geometrically nonlinear formalism for bundle mechanics, using a gaugelike symmetry under reptations along filament backbones. We relate force balance to orientational geometry and assess the elastic cost of frustration in twisted-toroidal bundles.
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U2 - 10.1103/PhysRevLett.127.218002
DO - 10.1103/PhysRevLett.127.218002
M3 - Article
C2 - 34860079
AN - SCOPUS:85120008003
SN - 0031-9007
VL - 127
JO - Physical Review Letters
JF - Physical Review Letters
IS - 21
M1 - 218002
ER -