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An edge dislocation interacting with an elliptical incompressible liquid inclusion

Xu Wang and Peter Schiavone

Vol. 19 (2024), No. 1, 131–140
DOI: 10.2140/jomms.2024.19.131
Abstract

We use Muskhelishvili’s complex variable formulation to derive a closed-form solution to the plane strain problem of an elliptical incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation applied at an arbitrary position. The internal uniform hydrostatic tension within the liquid inclusion and the pair of analytic functions characterizing the elastic field in the matrix are completely determined. The image force acting on the edge dislocation is the sum of two parts: the first part has been obtained in previous studies and is due to the edge dislocation near a traction-free elliptical hole; the second modified part is caused by the induced uniform hydrostatic tension on the elliptical boundary: this part has not been considered previously and is given here explicitly.

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Keywords
elliptical incompressible liquid inclusion, edge dislocation, complex variable method, uniform hydrostatic tension, image force, Peach–Koehler formula
Milestones
Received: 30 August 2023
Revised: 14 October 2023
Accepted: 23 October 2023
Published: 22 December 2023
Authors
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
Shanghai
China
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
Edmonton, AB
Canada