Archive of Applied Mechanics

, Volume 89, Issue 12, pp 2449–2461 | Cite as

Effective conductivity and the effect of electric current on thermal stress around an arbitrarily shaped inhomogeneity

  • K. Song
  • H. P. Song
  • P. SchiavoneEmail author
  • C. F. GaoEmail author


We consider the electric, thermal and elastic fields in an infinite conductor or semiconductor plate containing an arbitrarily shaped inhomogeneity. Complex variable and numerical methods are used to discuss effective conductivities and the effect of electric current on the thermal stress distribution. Our results show that the effective electric and thermal conductivities depend strongly on the shape and size of the inhomogeneity. In addition, the electric current generates considerable thermal stress in the vicinity of the inhomogeneity allowing for the possibility of enhancing or neutralizing any thermal stress induced by heat flux. Detailed analyses indicate that the remote electric current suppresses the maximum normal stress while either suppressing or enhancing the maximum shear and hoop stresses around an arbitrarily shaped inhomogeneity depending on the material parameters and shape of the inhomogeneity. Our findings also allow us to conclude that the electric current suppresses maximum normal and shear stresses on the interface in the case of a triangular inhomogeneity, which, of course, dramatically reduces the threat of interface debonding which is known to be one of the main causes of failure in composites. This research provides a theoretical basis for the prediction of the effective performance as well as for the control of thermal stress in composites.


Electric current Thermal stress Arbitrarily shaped inhomogeneity Effective conductivity 



K. Song appreciates the support of the China Scholarship Council. H. P. Song and C. F. Gao acknowledge the support of the National Natural Science Foundation of China (Grant Nos. 11872203 and 11202099), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). Schiavone thanks the Natural Sciences and Engineering Research Council of Canada for their support through a Discovery Grant (Grant # RGPIN 155112).


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Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanics and Control of Mechanical StructuresNanjing University of Aeronautics & AstronauticsNanjingChina
  2. 2.Department of Mechanical EngineeringUniversity of AlbertaEdmontonCanada

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