On mean Green operator and Eshelby tensor of hollow cylinders with length from infinite tubes to flat rings in isotropic elastic media

Using the (RT-IRT) Radon transform and inversion formula method, the author has previously reported the exact formal expressions for the mean shape function (mSF) of a finite solid cylinder of general aspect ratio in any infinite medium and for the related mean Green operator (mGO) and mean Eshelby tensor (mET) in cases of isotropic elastic-like (including dielectric-like) linear properties. Nearly exact solutions were obtained provided an accurate analytical approximation of an elliptic integral. Using the same RT-IRT method, the present work addresses the case of hollow cylinders with finite length in same isotropic property contexts. From examining the general formal mSF expression (and comparing with the limits of infinitely long cylinders and infinitely flat platelets) a simple accurate approximation is provided for the mSF, mGO and mET of thin hollow cylinders, from tubes to rings what covers a wide range of practical situations. The same expression being shown to hold on the thick side limit, the conjecture that it may be relevant over the whole thickness range is questioned.

Automated summary

Using the Radon transform and inversion formula method, the author provides exact expressions for the mean shape function, mean Green operator, and mean Eshelby tensor of finite solid cylinders and hollow cylinders in an infinite medium.