Neutrality of a partially debonded rigid inclusion in anti-plane shear

  • Xu WangEmail author
  • Peter SchiavoneEmail author


We consider a coated rigid inclusion inserted into an elastic matrix subjected to uniform remote anti-plane shear stresses and examine whether the inclusion can be made neutral (meaning that its introduction will not disturb the original uniform stress field in the surrounding uncut matrix) despite the presence of partial debonding along the inclusion–coating interface. Our analysis involves the introduction of a conformal mapping function (expressed in terms of a Laurent series) for the (thick) coating, a Laurent series expansion for the corresponding Plemelj function and simple matrix algebra. Our method demonstrates that coated neutral inclusions continue to be available under these challenging yet more realistic physical conditions. Numerical results are presented to demonstrate the feasibility of the solution method.


Neutral coated inclusion Interface crack Conformal mapping Laurent series expansion Matrix algebra 



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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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

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 EngineeringUniversity of AlbertaEdmontonCanada

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