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Interaction between an edge dislocation and a circular elastic inhomogeneity with Steigmann-Ogden interface.

Xu Wang1, Peter Schiavone2

  • 1School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai, China.

Mathematics and Mechanics of Solids : MMS
|November 16, 2023
PubMed
Summary

This study presents a new method to analyze edge dislocations near circular inhomogeneities with a Steigmann-Ogden interface. The approach determines analytic functions and calculates the image force on dislocations.

Keywords:
Steigmann-Ogden interfaceanalytic continuationanalytical solutioncircular inhomogeneityedge dislocation

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Continuum Mechanics

Background:

  • Understanding material behavior under stress is crucial.
  • Dislocations significantly impact material properties.
  • Interface conditions govern stress distribution in composite materials.

Purpose of the Study:

  • To develop an effective analytical method for edge dislocations near circular inhomogeneities.
  • To analyze the Steigmann-Ogden interface conditions.
  • To derive the image force on an edge dislocation.

Main Methods:

  • Analytic continuation to relate functions inside and outside the inhomogeneity.
  • Taylor series expansion of analytic functions within the inhomogeneity.
  • Complex form representation of Steigmann-Ogden interface conditions.
  • Peach-Koehler formula for image force calculation.

Main Results:

  • A method to uniquely determine analytic functions describing the stress field.
  • Explicit determination of complex coefficients in Taylor series expansions.
  • Derivation of a general expression for the image force on an edge dislocation.

Conclusions:

  • The proposed method provides a complete solution for the plane problem of an edge dislocation near a circular inhomogeneity.
  • The derived image force expression is explicit and general.
  • This work contributes to the understanding of stress concentration and material failure in heterogeneous materials.