A matrix formulation of the plane elastostatic inclusion problem via geometric function theory
Analysis of PDEs
2025-10-08 v2
Abstract
We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these methodologies to the more general case of elastic inclusions with arbitrary Lam\'{e} constants. Our approach integrates layer potential techniques, geometric function theory, and the complex-variable formulation in plane elasticity. As a main result, we derive a matrix formulation of the elastostatic inclusion problem using basis functions defined via the exterior conformal mapping of the inclusion. This leads to a series solution framework that incorporates the geometry of the inclusion.
Keywords
Cite
@article{arxiv.2403.15713,
title = {A matrix formulation of the plane elastostatic inclusion problem via geometric function theory},
author = {Daehee Cho and Doosung Choi and Mikyoung Lim},
journal= {arXiv preprint arXiv:2403.15713},
year = {2025}
}