Eshelby-based homogenization schemes with finite circular cylinders

TL;DR

This paper develops tools for homogenization of fibrous media using finite circular cylinders, addressing the challenge of non-uniform internal fields where analytical solutions are complex.

Contribution

It introduces methods to compute homogenization schemes based on Eshelby's problem for finite circular cylinders, expanding beyond ellipsoidal approximations.

Findings

Provides computational tools for finite cylinder homogenization

Extends Eshelby's solution application to cylindrical inclusions

Facilitates more accurate modeling of fibrous media

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.