A simple method for determining large deflection states of arbitrarily curved planar elastica

Sitar, Matej; Kosel, Franc; Brojan, Miha

doi:10.1007/s00419-013-0798-6

Cited by 10 publications

(2 citation statements)

References 27 publications

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“…Therefore axial buckling presents a good test case for validating the assignment of moment arms and force transformations in a method for solving large-strain bending. The SOCB approach predicts an evolution of segment contours during the course of buckling similar to those published elsewhere 24 (Fig. 5b).…”

Section: Resultssupporting

confidence: 77%

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Capturing 3D large-strain Euler-bending filament dynamics in fibrous media simulations; sample case of compression collapse in dendritic actin network

Simhadri

Chandran

2019

Sci Rep

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Cytoskeletal networks to transmission towers are comprised of slender elements. Slender filaments bend and buckle more easily than stretch. Therefore a deforming network is expected to exhaust all possible bending-based modes before engaging filament stretch. While the large-strain bending critically determines fibrous-media response, simulations use small-strain and jointed approximations. At low resolution, these approximations inflate bending resistance and delay buckling onset. The proposed string-of-continuous-beams (SOCB) approach captures 3D nonlinear Euler bending of filaments with high fidelity at low cost. Bending geometry (i.e. angles and its differentials) is solved as primary variables, to fit a 5 th order polynomial of the contour angle. Displacement, solved simultaneously as length conservation, is predicted with C3 and C6 smoothness between and within segments, using only 2 nodes. In the chosen analysis frame, in-plane and out-plane moments can be decoupled for arbitrarily-curved segments. Complex crosslink force-transfers can be specified. Simulations show that when a daughter branch is appended, the buckling resistance of a filament changes from linear to nonlinear before reversible collapse. An actin outcrop with 8 generations of mother-daughter branching produced the linear, nonlinear, and collapse regimes observed in compression experiments. ‘Collapse’ was a redistribution of outcrop forces following the buckling of few strands.

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Section: Resultssupporting

confidence: 77%

“…The analytical comparison is obtained from Sitar et al . 24 . ( d ) Resisting force vs. x-deflection produced as a unit cantilever buckles under a tipping load of FL 2 /EI = 23.3.…”

Section: Resultsmentioning

confidence: 99%