Analytical Representation and Efficient Computation of the Effective Conductivity of Two-Phase Composite Materials

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Author(s)Roy, R. Valéry
Date Accessioned2022-05-09T19:31:07Z
Date Available2022-05-09T19:31:07Z
Publication Date2022-04-04
DescriptionThis is the peer reviewed version of the following article: Roy, RV. Analytical representation and efficient computation of the effective conductivity of two-phase composite materials. Int J Numer Methods Eng. 2022; 1- 27. doi:10.1002/nme.6980, which has been published in final form at https://doi.org/10.1002/nme.6980. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. This article will be embargoed until 04/04/2023.en_US
AbstractMany engineered materials display ordered or disordered microstructures. Such materials exhibit transport properties which are unmatched by their single-phase homogeneous counterparts. These properties are obtained by the mixture of two or more phases typically characterized by a large contrast in their properties. For the development of these materials, it is critical to develop a robust computational framework in order to provide a fundamental understanding of how microstructure affects performance. This hinges on predicting their macroscopic properties, given the constitutive laws and spatial distribution of their constituents. To this end, this work presents a computational framework based on formulating periodic conduction transport problems in terms of boundary integral equations whose kernel is expressed in terms of Weierstrass zeta-function. The components of the effective conductivity tensor are then sought in the form of power series expansions of a conductivity contrast parameter. To accelerate their convergence, these expansions are transformed into Padé approximants. Presently restricted to the case of two-dimensional, two-phase microstructures, this framework is shown to yield accurate results over the entire range of the contrast parameter. Representation of the kernel as a lattice sum allows the use the fast multipole method, thereby making computations significantly more efficient.en_US
CitationRoy, RV. Analytical representation and efficient computation of the effective conductivity of two-phase composite materials. Int J Numer Methods Eng. 2022; 1- 27. doi:10.1002/nme.6980en_US
ISSN1097-0207
URLhttps://udspace.udel.edu/handle/19716/30856
Languageen_USen_US
PublisherInternational Journal for Numerical Methods in Engineeringen_US
Keywordsacceleration of convergenceen_US
Keywordsboundary integral equationen_US
Keywordseffective propertiesen_US
Keywordsheterogeneous materialsen_US
Keywordshomogenizationen_US
Keywordspadé approximantsen_US
TitleAnalytical Representation and Efficient Computation of the Effective Conductivity of Two-Phase Composite Materialsen_US
TypeArticleen_US
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