Lower and upper bounds for the Rayleigh conductivity of a perforated plate
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1691-1712.

Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational principlesin the context of Beppo-Levi spaces. The derivations are validated by numerical experiments in 2D for the axisymmetric case as well as for the full three-dimensional problem.

DOI : 10.1051/m2an/2013082
Classification : 35Q35, 35J05, 35J25
Mots clés : Rayleigh conductivity, perforated plate, Kelvin principle, Dirichlet principle
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     title = {Lower and upper bounds for the {Rayleigh} conductivity of a perforated plate},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1691--1712},
     publisher = {EDP-Sciences},
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Laurens, S.; Tordeux, S.; Bendali, A.; Fares, M.; Kotiuga, P. R. Lower and upper bounds for the Rayleigh conductivity of a perforated plate. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 6, pp. 1691-1712. doi : 10.1051/m2an/2013082. http://archive.numdam.org/articles/10.1051/m2an/2013082/

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