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A circular inhomogeneity with mixed-type imperfect interface under in-plane deformations

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Abstract

We investigate the in-plane deformations of a circular inhomogeneity bonded to an infinite matrix through a mixed-type imperfect interface when the matrix is subjected to remote uniform stresses. The inhomogeneity and the matrix are endowed with separate and distinct Gurtin–Murdoch surface elasticities yet bonded together through a spring-type imperfect interface. This arrangement in which a soft interface (represented by the spring model) is bounded by two stiff interfaces (from the surface elasticities) is referred to as a ‘mixed-type imperfect interface’. A closed-form solution to the corresponding deformation problem is obtained via the use of complex variable methods, in particular, analytic continuation. We show that the introduction of the mixed-type imperfect interface leads to stress distributions in the composite which depend on six size-dependent parameters. In particular, the stress distribution inside the inhomogeneity is shown to be generally non-uniform except when a particular condition (which we identify explicitly) is satisfied by the material parameters, in which case the internal (size-dependent) stress distribution is uniform for any uniform remote loading. Finally, our solution is used to study the design of neutral and harmonic elastic inhomogeneities.

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Acknowledgments

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 # RGPIN 155112).

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, People’s Republic of China

    Xu Wang

  2. Department of Mechanical Engineering, Donadeo Innovation Centre for Engineering, University of Alberta, 10-203, Edmonton, AB, T6G 1H9, Canada

    Peter Schiavone

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  1. Xu Wang
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  2. Peter Schiavone
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Correspondence to Peter Schiavone.

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Wang, X., Schiavone, P. A circular inhomogeneity with mixed-type imperfect interface under in-plane deformations. Int J Mech Mater Des 13, 419–427 (2017). https://doi.org/10.1007/s10999-016-9345-2

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  • DOI: https://doi.org/10.1007/s10999-016-9345-2

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