1203.4329 (John Gemmer et al.)

Defects and boundary layers in non-Euclidean plates    [PDF]

John Gemmer, Shankar Venkataramani

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.

View original: http://arxiv.org/abs/1203.4329