caa a22 4500 475805267 CHVBK 20180406123745.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1007/s003320010007 doi (NATIONALLICENCE)springer-10.1007/s003320010007 Rigorous Bounds for the Föppl—von Kármán Theory of Isotropically Compressed Plates [Elektronische Daten] [H. Ben Belgacem, S. Conti, A. DeSimone, S. Müller] Summary. : We study the Föppl—von Kármán 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 σ . This energy is much lower than previous estimates based on certain dimensional reductions of the problem, which had lead to energies of order 1+σ (scalar approximation) or σ 2/3 (two-component approximation). Springer-Verlag New York Inc., 2000 Key words. thin film elasticity, blistering, von Kármán theory of plates, optimal scaling laws nationallicence Ben Belgacem H. Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22—26, D 04103 Leipzig, Germany, DE aut Conti S. Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22—26, D 04103 Leipzig, Germany, DE aut DeSimone A. Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22—26, D 04103 Leipzig, Germany, DE aut Müller S. Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22—26, D 04103 Leipzig, Germany, DE aut Journal of Nonlinear Science Springer-Verlag 10/6(2000-12-01), 661-685 0938-8974 10:6<661 2000 10 332 https://doi.org/10.1007/s003320010007 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003320010007 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ben Belgacem H. Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22—26, D 04103 Leipzig, Germany, DE aut NATIONALLICENCE 700 1- Conti S. Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22—26, D 04103 Leipzig, Germany, DE aut NATIONALLICENCE 700 1- DeSimone A. Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22—26, D 04103 Leipzig, Germany, DE aut NATIONALLICENCE 700 1- Müller S. Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22—26, D 04103 Leipzig, Germany, DE aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/6(2000-12-01), 661-685 0938-8974 10:6<661 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer