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Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 2):016602. Epub 2009 Jul 10.

Buckling transition and boundary layer in non-Euclidean plates.

Author information

1
The Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel.

Abstract

Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled equilibrium configurations at a critical value of the plate thickness. Depending on the reference metric, the buckling transition may be either continuous or discontinuous. In the infinitely thin plate limit, under the assumption that a limiting configuration exists, we show that the limit is a configuration that minimizes the bending content, among all configurations with zero stretching content (isometric immersions of the midsurface). For small but finite plate thickness, we show the formation of a boundary layer, whose size scales with the square root of the plate thickness and whose shape is determined by a balance between stretching and bending energies.

PMID:
19658827
DOI:
10.1103/PhysRevE.80.016602

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