We determine an improved lower bound for the conductivity of three-component composite materials. Our bound is strictly larger than the well-known Hashin Shtrikman bound outside the regime where the latter is known to be optimal. The main ingredient of our result is a new quantitative rigidity estimate for gradient fields in two dimensions.
Improved bounds for composites and rigidity of gradient fields / N. N., Conti Albin; Nesi, Vincenzo. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. - ISSN 1364-5021. - 463:2084(2007), pp. 2031-2048. [10.1098/rspa.2007.1863]
Improved bounds for composites and rigidity of gradient fields
NESI, Vincenzo
2007
Abstract
We determine an improved lower bound for the conductivity of three-component composite materials. Our bound is strictly larger than the well-known Hashin Shtrikman bound outside the regime where the latter is known to be optimal. The main ingredient of our result is a new quantitative rigidity estimate for gradient fields in two dimensions.File allegati a questo prodotto
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