Analytic materials

DOI10.1098/RSPA.2016.0613zbMATH Open1371.74103arXiv1610.06059OpenAlexW3037887845WikidataQ55100029 ScholiaQ55100029MaRDI QIDQ5363705

Graeme W. Milton

Publication date: 29 September 2017

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Abstract: The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer $p$. If $p$ takes its maximum value then we have a complete analytic material. Otherwise it is incomplete analytic material of rank $p$. For two-dimensional materials further progress can be made in the identification of analytic materials by using the well-known fact that a $90^{c}irc$ rotation applied to a divergence free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.

Full work available at URL: https://arxiv.org/abs/1610.06059

Mathematics Subject Classification ID

Inhomogeneity in solid mechanics (74E05) Explicit solutions of equilibrium problems in solid mechanics (74G05) Quantum equilibrium statistical mechanics (general) (82B10) Solutions to PDEs in closed form (35C05) PDEs in connection with mechanics of deformable solids (35Q74)

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