Professor of Solid and Structural Mechanics

# Effects of the constraint’s curvature on structural instability: tensile buckling and multiple bifurcations

An elastic structure subjected to a purely compressive force buckles when a deflection appears, an occurrence strongly influenced by the end constraints. We show theoretically and we provide definitive experimental verification that an appropriate curvature of the constraint over which the end of a structure is prescribed to slide strongly affects buckling loads and can induce: (i.) tensile buckling; (ii.) decreasing- (softening), increasing- (hardening), or constant-load (null stiffness) postcritical behaviour; (iii.) multiple bifurcations, determining for instance two bifurcation loads (one tensile and one compressive) in a single-degree-of-freedom elastic system. We show how to design a constraint profile to obtain a desired postcritical behaviour and we provide the solution for the elastica constrained to slide along a circle on one end. These results have important practical implications in the design of compliant mechanisms and may find applications in devices operating in quasi-static or dynamic conditions, even at the nanoscale.*If you're having trouble playing videos on YouTube,*

*click here to watch it.***Related papers:**

- D. Bigoni, D. Misseroni, G. Noselli and D. Zaccaria,
Effects of the constraint’s curvature on structural instability: tensile buckling and multiple bifurcations.
*Proceedings of the Royal Society A*, 2012, 468, 2191-2209; doi:10.1098/rspa.2011.0732. - D. Bigoni, Nonlinear Solid Mechanics Bifurcation Theory and Material Instability. Cambridge University Press, 2012, ISBN:9781107025417.
- D. Bigoni, D. Misseroni, G. Noselli, D. Zaccaria Surprising instabilities of simple elastic structures. In
*Nonlinear Physical Systems - Spectral Analysis, Stability and Bifurcations*, Kirillov, N. and Pelinovsky, D.E. Eds., Wiley, pp. 1-14, 2014; ISBN: 978-1-84821-420-0.

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