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Uniformity of anti-plane stresses within a three-phase nonlinear elastic inhomogeneity of arbitrary shape

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Abstract

We first investigate the anti-plane shear deformation of a three-phase nonlinear elastic elliptical inhomogeneity under uniform remote anti-plane stresses. In the three-phase composite, the p-Laplacian nonlinear elastic elliptical inhomogeneity is bonded to the infinite linear elastic matrix via a linear elastic interphase layer resulting in two confocal elliptical interfaces. It is proved that the internal stress field inside the nonlinear elliptical inhomogeneity is nevertheless unconditionally uniform. Secondly, we examine the uniformity of internal anti-plane stresses within a three-phase nonlinear elastic non-elliptical inhomogeneity. In this case, the p-Laplacian nonlinear elastic non-elliptical inhomogeneity is again bonded to the infinite linear elastic matrix through a linear elastic interphase layer. The internal uniform stress field is achieved via the solution of two coupled nonlinear equations. Detailed numerical results validate our theoretical analysis.

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Acknowledgements

The authors thank the two reviewers for their constructive comments and suggestions. This work is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN-2023-03227 Schiavo).

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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, China

    Xu Wang

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

    Peter Schiavone

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

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Wang, X., Schiavone, P. Uniformity of anti-plane stresses within a three-phase nonlinear elastic inhomogeneity of arbitrary shape. Arch Appl Mech 93, 4261–4272 (2023). https://doi.org/10.1007/s00419-023-02492-3

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