Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations

TL;DR

This study investigates the complex buckling and bifurcation behaviors of anisotropic elastic rods and thin bands under lateral end translations, revealing new multi-stability states and the effectiveness of a Kirchhoff model despite physical differences.

Contribution

It introduces a combined experimental and numerical analysis of anisotropic rods and strips under boundary conditions that induce cooperation between bending and twisting.

Findings

Anisotropy creates new stable states.

Kirchhoff model effectively predicts bifurcation behavior.

Boundary conditions influence state connectivity.

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.