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Uniform field within a non-elliptical inhomogeneity in the vicinity of a nearby non-circular Eshelby inclusion
Arch. Mech. 73 (5-6), 541-555, 2021, DOI: 10.24423/aom.3843
Keywords: non-elliptical inhomogeneity; Booth’s lemniscate inclusion; uniform field; conformal mapping; anti-plane elasticity; inverse problem
Abstract
We rigorously prove that a non-elliptical inhomogeneity continues to permit an internal uniform stress field despite the presence of a nearby non-circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding matrix is subjected to uniform remote anti-plane stresses. Here, we adopt a specific representation of the non-circular Eshelby inclusion as a Booth’s lemniscate inclusion. Our analysis indicates that the internal uniform stress field inside the non-elliptical inhomogeneity is independent of the existence of the Booth’s lemniscate inclusion whereas the non-elliptical shape of the inhomogeneity is attributed entirely to its presence. Representative numerical examples are presented to demonstrate the feasibility of the proposed method of general solution.