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Effect of a circular Eshelby inclusion on the non‐elliptical shape of a coated neutral inhomogeneity with internal uniform stresses
Author(s) -
Wang Xu,
Schiavone Peter
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900058
Subject(s) - conformal map , coating , materials science , inclusion (mineral) , annulus (botany) , plane (geometry) , internal stress , geometry , dislocation , stress (linguistics) , function (biology) , composite material , physics , mathematics , linguistics , philosophy , evolutionary biology , biology , thermodynamics
Abstract Using conformal mapping techniques, we present the design of a coated non‐elliptical neutral inhomogeneity with internal uniform stresses which does not disturb a prescribed uniform anti‐plane stress field in the surrounding matrix when both a circular Eshelby inclusion present in the thick coating and the inhomogeneity itself undergo uniform eigenstrains. An appropriately chosen conformal mapping function maps the doubly connected domain of the thick coating onto an annulus in the image plane. All of the unknown complex constants appearing in the mapping function can be uniquely determined. Detailed numerical results are presented to demonstrate the proposed theory. We also consider a related problem concerning a neutral coated inhomogeneity with internal uniform stresses in the presence of a screw dislocation dipole in the thick coating.