Boundary layer techniques for deriving the effective properties of composite materials

Article type: Research Article

Authors: Ammari, Habib^{; ;} | Kang, Hyeonbae^; | Touibi, Karim

Affiliations: Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau cedex, France E‐mails: {ammari; touibi}@cmapx.polytechnique.fr | School of Mathematical Sciences, Seoul National University, Seoul 151‐747, Korea E‐mail: hkang@math.snu.ac.kr

Note: [] Corresponding author.

Note: [] Partly supported by ACI Jeunes Chercheurs (0693) from the Ministry of Education and Scientific Research, France.

Note: [] Partly supported by grant R02‐2003‐000‐10012‐0 from the Korea Science and Engineering Foundation.

Abstract: In this paper we present mathematically rigorous derivations of asymptotic expansions of the effective electrical conductivity of periodic dilute composites in terms of the volume fraction occupied by the inclusions. Our derivations are based on layer potential techniques, and valid for high contrast mixtures and inclusions with Lipschitz boundaries. They are motivated by the practically important inverse problem of determining the volume fraction of a suspension of complicated shaped particles from boundary measurements of voltage potentials.

Keywords: effective properties, composite materials, layer potentials, generalized polarization tensors

Journal: Asymptotic Analysis, vol. 41, no. 2, pp. 119-140, 2005