Tian Yu
Mechanics of thin structures
Multi-stability and bifurcations of buckled and clamped thin strips
We study the mechanics of clamped thin bands subjecting to combinations of compression and shear at the two ends, through numerical continuation and experiments. Rich stable configurations and new jump phenomena/snap-throughs are observed for different widths of bands. The following videos are part of the supplementary materials of our published paper in JMPS.
Following shapes are constructed from inextensible strip model by following van der Heijden's formulation.
The inextensible strip model captures more realistic shapes of wide bands, than an anisotropic Kichhoff rod model does. But it fails to capture some of the behavior in our experiments, which involve the creation and destruction of inflection points on the centerline, where edge of regression contacts the material surface and bending energy blows up locally. We conclude that there is a need for new strip models that interpolate between rod models and wide, inextensible strip models.
References:
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A. P. Korte, E. L. Starostin, and G. H. M. van der Heijden. Triangular buckling patterns of twisted inextensible strips. Proceedings of the Royal Society A, 467(2125): 285–303, 2010.
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E. L. Starostin and G. H. M. van der Heijden. Equilibrium shapes with stress localisation for inextensible elastic Mobius and other strips. Journal of Elasticity, 119(1-2): 67–112, 2015.
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Tian Yu, James Hanna. Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations. Journal of the Mechanics and Physics of Solids, 122: 657-685, 2019.