Estimates for two-phase nonlinear conductors via iterated homogenization-Reference-Cited by-同舟云学术

Estimates for two-phase nonlinear conductors via iterated homogenization

Published:2013-05-08 Issue:2153 Volume:469 Page:20120626
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:

Idiart Martín I.¹²,Castañeda Pedro Ponte³

Affiliation:

1. Departamento de Aeronáutica, Facultad de Ingeniería, Universidad Nacional de La Plata, Avda. 1 esq. 47 S/N, La Plata B1900TAG, Argentina

2. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), CCT La Plata, Calle 8 No. 1467, La Plata B1904CMC, Argentina

3. Department of Mechanical Engineering and Applied Mechanics and Graduate Group in Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, PA 19104-6315, USA

Abstract

Estimates for the overall response of two-phase nonlinear conductors are derived via an iterated homogenization approach. The approach consists in the construction of sequentially laminated microgeometries for which the overall response can be determined exactly. The estimate depends on the one- and two-point microstructural correlations through the volume fractions of each constituent phase and the H-measures of the microstructure. Sample results for power-law random conductors are provided and compared with earlier predictions. The work concludes with a discussion on the possible extremal character of sequential laminates.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2012.0626

Reference40 articles.

1. A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials

2. Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen

3. A generalized differential effective medium theory

4. The Theory of Composites

Cited by 7 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. A class of coherent potentials for two-phase creeping solids;Acta Mechanica;2021-08-11

2. Exact results for weakly nonlinear composites and implications for homogenization methods;Comptes Rendus. Mécanique;2021-01-13

3. The effective conductivity of strongly nonlinear media: The dilute limit;International Journal of Solids and Structures;2020-02

4. Bounds for nonlinear composite conductors via the translation method;Journal of the Mechanics and Physics of Solids;2017

5. Influence of second-phase inclusions on the electro-deformation of ferroelectric ceramics;International Journal of Solids and Structures;2016-02