Improved bounds for composites and rigidity of gradient fields-Reference-Cited by-同舟云学术

Improved bounds for composites and rigidity of gradient fields

Published:2007-06-13 Issue:2084 Volume:463 Page:2031-2048
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Albin Nathan¹,Conti Sergio¹,Nesi Vincenzo²

Affiliation:

1. Fachbereich Mathematik, Universität Duisburg-EssenLotharstrasse 65, 47057 Duisburg, Germany

2. Dipartimento di Matematica ‘Castelnuovo’, Sapienza Università di RomaPiazzale Aldo Moro, 2, 00185 Roma, Italy

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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2007.1863

Reference38 articles.

1. Albin N. 2006 Optimality of the translation bounds for linear conducting composites in two and three dimensions. PhD thesis University of Utah.

2. Multiphase laminates of extremal effective conductivity in two dimensions

3. Univalent σ-Harmonic Mappings

4. Composites and quasiconformal mappings: new optimal bounds in two dimensions

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Quantitative Estimates on Jacobians for Hybrid Inverse Problems;Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software";2015

2. Optimal anisotropic three-phase conducting composites: Plane problem;International Journal of Solids and Structures;2011-10

3. New optimal microstructures and restrictions on the attainable Hashin–Shtrikman bounds for multiphase composite materials;Philosophical Magazine Letters;2011-06-24

4. Hashin–Shtrikman bounds and their attainability for multi-phase composites;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2010-06-09

5. A microstructure diagram for known bounds in conductivity;Journal of Materials Research;2008-03