Phonon description and the Euler buckling instability of a mesoscopic bar at fixed strain

ABSTRACTWe review recent systematic investigations of the dynamics of the classical Euler buckling of compressed solid membranes and thin sheets. We relate the membrane buckling dynamics to phase ordering phenomena. Evolving membranes develop wavelike patterns whose wavelength grows, via coarsening, as a power of time. We find that evolving membranes are similar to interfaces of thin films in molecular-beam epitaxy growth with slope selection: They are characterized by the presence of mounds whose typical size grows as a power of time. The morphologies of the evolving membranes are characterized by the presence of a network of growing ridges where the elastic energy is mostly concentrated. We used this fact to develop a scaling theory of the buckling dynamics that gives analytic estimates of the coarsening exponents. Our findings show that the membrane buckling dynamics is characterized by a distinct scaling behavior not found in other coarsening phenomena.

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Violent buckling benefits galactic bars

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz3625 ◽

2019 ◽

Vol 492 (2) ◽

pp. 2241-2249 ◽

Cited By ~ 2

Author(s):

Angela Collier

Keyword(s):

Dark Matter ◽

Landau Damping ◽

Local Universe ◽

Buckling Instability ◽

Euler Buckling ◽

Isolated Galaxies ◽

Non Linear ◽

Analytical Result ◽

Bar Formation ◽

Kinematic Properties

ABSTRACT Galactic bars are unstable to a vertical buckling instability which heats the disc and in some cases forms a boxy/peanut shaped bulge. We analyse the buckling instability as an application of classical Euler buckling followed by non-linear gravitational Landau damping in the collisionless system. We find that the buckling instability is dictated by the kinematic properties and geometry of the bar. The analytical result is compared to simulations of isolated galaxies containing the disc and dark matter components. Our results demonstrate that violent buckling does not destroy bars while a less energetic buckling can dissolve the bar. The discs that undergo gentle buckling remain stable to bar formation which may explain the observed bar fraction in the local Universe. Our results align with the results from recent surveys.

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On Buckling of Long Interface Cracks

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.417-418.217 ◽

2009 ◽

Vol 417-418 ◽

pp. 217-220

Author(s):

Andrei G. Kotousov ◽

Steven Harding

Keyword(s):

Compressive Loading ◽

Compressive Load ◽

Plate Bending ◽

Snow Avalanches ◽

Interface Cracks ◽

Buckling Instability ◽

Euler Buckling ◽

Numerical Studies ◽

Classical Strategy ◽

Simplified Mathematical Model

The paper deals with the buckling instability of long interface cracks subjected to shear and tensile (compressive) loading parallel to the interface. A simplified mathematical model is developed within the Kirchhoff’s plate bending theory; and a general semi-analytical solution is obtained based on the classical strategy for solving for the Euler buckling load. Asymptotic solutions are derived for extreme cases of the applied shear to tensile (compressive) load ratios. The obtained results correlate well with previous numerical studies and can be used to analyze many traditional problems in composite as well as many others, for example, the problem of triggering snow avalanches.

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