Uniform field within a non-elliptical inhomogeneity in the vicinity of a nearby non-circular Eshelby inclusion

Downloads

Authors

  • X. Wang School of Mechanical and Power Engineering, East China University of Science and Technology, China
  • P. Schiavone Department of Mechanical Engineering, University of Alberta, Canada

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.

Keywords:

non-elliptical inhomogeneity, Booth’s lemniscate inclusion, uniform field, conformal mapping, anti-plane elasticity, inverse problem

Other articles by the same author(s)

1 2 > >>