Eshelby-based homogenization schemes with finite circular cylinders

Abstract

Commonly, for homogenization of fibrous media, fibers are approximated by ellipsoidal inclusions. Indeed, the solution of Eshelby's problem for an ellipsoid is well-known analytically. However, for a cylinder, the analytical solution is not easy to compute, and the internal field is not uniform (which makes the Hill tensor useless). We here propose to give some tools for computing main homogenization schemes based on Eshelby's problem, for finite circular cylinders. This document is also a companion to [1], where homogenization schemes like Dilute Scheme, Mori-Tanaka scheme [2] and Ponte Casta{\~n}eda and Willis scheme [3] are used.