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Fig. 1. A thin, rectangular band of width D and length L is symmetrically clamped with an angle ψ0, “compression” ΔL, and “shear” ΔD. The centerline of the band carries an orthonormal director frame (d1, d2, d3) corresponding to the width direction, the surface normal, and the tangent, respectively. Shown here are (a) S-like and (b) U-like configurations.
FROM:
T. Yu and J.A. Hanna, “Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations”, Journal of the Mechanics and Physics of Solids, Vol. 122, pp 657-685, January 2019, https://doi.org/10.1016/j.jmps.2018.01.015
ABSTRACT: Motivated by observations of snap-through phenomena in buckled elastic strips subject to clamping and lateral end translations, we experimentally explore the multi-stability and bifurcations of thin bands of various widths and compare these results with numerical continuation of a perfectly anisotropic Kirchhoff rod. Our choice of boundary conditions is not easily satisfied by the anisotropic structures, forcing a cooperation between bending and twisting deformations. We find that, despite clear physical differences between rods and strips, a naive Kirchhoff model works surprisingly well as an organizing framework for the experimental observations. In the context of this model, we observe that anisotropy creates new states and alters the connectivity between existing states. Our results are a preliminary look at relatively unstudied boundary conditions for rods and strips that may arise in a variety of engineering applications, and may guide the avoidance of jump phenomena in such settings. We also briefly comment on the limitations of current strip models.
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