Perturbation analysis of the effective conductivity of a periodic composite

Paolo Luzzini; Paolo Musolino

doi:10.3934/nhm.2020015

Article Contents

2020, Volume 15, Issue 4: 581-603. Doi: 10.3934/nhm.2020015

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Perturbation analysis of the effective conductivity of a periodic composite

Paolo Luzzini^1, and
Paolo Musolino^2, ,

1.
Dipartimento di Matematica 'Tullio Levi-Civita', Università degli Studi di Padova, Via Trieste 63, 35121 Padova, Italy
2.
Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari Venezia, via Torino 155, 30172 Venezia Mestre, Italy

^* Corresponding author: Paolo Musolino
^* Corresponding author: Paolo Musolino

Received: March 2020

Revised: June 2020

Early access: July 2020

Published: December 2020

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Abstract

We consider the effective conductivity $ \lambda^{\mathrm{eff}} $ of a periodic two-phase composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material. Then we study the behavior of $ \lambda^{\mathrm{eff}} $ upon perturbation of the shape of the inclusions, of the periodicity structure, and of the conductivity of each material.

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Mathematics Subject Classification: Primary: 74E30, 74G10, 31B10; Secondary: 35J25, 35J05, 45A05, 74M15.

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Figure 1. The sets $ \mathbb{S}_{q}[q\mathbb{I}[\phi]]^- $, $ \mathbb{S}_{q}[q\mathbb{I}[\phi]] $, and $ q\phi(\partial\Omega) $ in case $ n = 2 $

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