Two-scale asymptotics for non-local effects in composites with highly anisotropic fibres

Article type: Research Article

Authors: Cherednichenko, Kirill D.

Affiliations: St. John's College, Oxford OX1 3JP, UK E-mail: cheredni@maths.ox.ac.uk

Abstract: The problem of periodic homogenisation for a conducting two-phase composite exhibiting non-locality in the overall behaviour is considered. The matrix is isotropic and its conductivity is constant, while the fibre-shaped inclusions are assumed to be anisotropic, with high contrast between conductivities along the fibres and in the transverse directions. The contrast is set to correspond to the so-called double-porosity scaling, which is of special interest. A full two-scale asymptotic expansion for the solution is constructed and rigorously justified via appropriate error estimates. An example of the non-local homogenised operator in the case of fibres with circular cross-sections is given.

Keywords: composite materials, homogenisation, non-local effects, asymptotic expansions

Journal: Asymptotic Analysis, vol. 49, no. 1-2, pp. 39-59, 2006