Defects and boundary layers in non-Euclidean plates

Details Defects and boundary layers in non-Euclidean plates Defects and boundary layers in non-Euclidean plates

2012-03-20

arxiv.org/abs/1203.4329v1

Mathematics

Optimization and Control

Scientific paper

We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. We also investigate the scaling with thickness of boundary layers where the stretching energy is concentrated with decreasing thickness.

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