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Abstract
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We use the theory of continuously distributed dislocations to formulate the static
equilibrium condition for an edge dislocation pileup near a circular elastic
inhomogeneity in terms of a singular integral equation. The singular integral equation
is solved numerically using the Gauss–Chebyshev integration formula to arrive at the
dislocation distribution function and the number of edge dislocations in the pileup. In
our discussion, either the leading edge or the trailing end of the pileup can be located
at the circular interface.
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Keywords
edge dislocation pileup, circular inhomogeneity,
equilibrium condition, continuous pileup, singular integral
equation, dislocation distribution function
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Mathematical Subject Classification
Primary: 45E99, 74B05, 74E30
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Milestones
Received: 12 January 2022
Revised: 14 January 2022
Accepted: 14 March 2022
Published: 20 October 2022
Communicated by David J. Steigmann
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