期刊
JOURNAL OF NONLINEAR SCIENCE
卷 10, 期 6, 页码 661-683出版社
SPRINGER-VERLAG
DOI: 10.1007/s003320010007
关键词
thin film elasticity; blistering; von Karman theory of plates; optimal scaling laws
We study the Foppl-von Karman theory for isotropically compressed thin plates in a geometrically linear setting, which is commonly used to model weak buckling of thin films. We consider generic smooth domains with clamped boundary conditions, and obtain rigorous upper and lower bounds on the minimum energy linear in the plate thickness sigma. This energy is much lower than previous estimates based on certain dimensional reductions of the problem, which had lead to energies of order 1 + sigma (scalar approximation) or sigma (2/3) (two-component approximation).
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