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Continuum Mechanics and Thermodynamics

, Volume 31, Issue 1, pp 71–77 | Cite as

Anti-plane eigenstrain problem of an inclusion of arbitrary shape in an anisotropic bimaterial with a semi-infinite interface crack

  • Xu Wang
  • Peter SchiavoneEmail author
Original Article
  • 29 Downloads

Abstract

We consider an Eshelby inclusion of arbitrary shape with uniform anti-plane eigenstrains embedded in one of two bonded dissimilar anisotropic half planes containing a semi-infinite interface crack situated along the negative real axis. Using two consecutive conformal mappings, the upper and lower halves of the physical plane are first mapped onto two separate quarters of the image plane. The corresponding boundary value problem is then analyzed in this image plane rather than in the original physical plane. Corresponding analytic functions in all three phases of the composite are derived via the construction of an auxiliary function and repeated application of analytic continuation across the real and imaginary axes in the image plane. As a result, the local stress intensity factor is then obtained explicitly. Perhaps most interestingly, we find that the satisfaction of a particular condition makes the inclusion (stress) invisible to the crack.

Keywords

Eshelby inclusion Interface crack Anisotropic bimaterial Conformal mapping Analytic continuation 

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Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11272121) and through a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-2017-03716115112).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical and Power EngineeringEast China University of Science and TechnologyShanghaiChina
  2. 2.Department of Mechanical Engineering, 10-203 Donadeo Innovation Centre for Engineering EdmontonUniversity of AlbertaEdmontonCanada

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