Analytical Representation and Efficient Computation of the Effective Conductivity of Two-Phase Composite Materials
International Journal for Numerical Methods in Engineering
Many 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.
This 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.
acceleration of convergence, boundary integral equation, effective properties, heterogeneous materials, homogenization, padé approximants
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