Abstract
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.
Similar content being viewed by others
References
Mansfield, E.H.: Neutral holes in plane sheet-reinforced holes which are equivalent to the uncut sheet. Q. J. Mech. Appl. Math. 6, 371–378 (1953)
Budiansky, B., Hutchinson, J.W., Evans, A.G.: On neutral holes in tailored, layered sheets. ASME J. Appl. Mech. 60, 1056–1058 (1993)
Senocak, E., Waas, A.M.: Neutral holes in laminated plates. AIAA J. Aircr. 30, 428–432 (1993)
Senocak, E., Waas, A.M.: Neutral cutouts in laminated plates. Mech. Compos. Mater. Struct. 2, 71–89 (1995)
Ru, C.Q.: Interface design of neutral elastic inclusions. Int. J. Solids Struct. 35, 557–572 (1998)
Benveniste, Y., Miloh, T.: Neutral inhomogeneities in conduction phenomena. J. Mech. Phys. Solids 47, 1873–1892 (1999)
Richards, R.: Principles of Solid Mechanics. CRC Press LLC, Boca Raton (2001)
Milton, G.W., Serkov, S.K.: Neutral inclusions for conductivity and anti-plane elasticity. Proc. R. Soc. Lond. A 457, 1973–1997 (2001)
Chen, T., Benveniste, Y., Chuang, P.C.: Exact solution in torsion of composite bars: thickly coated neutral inhomogeneities and composite cylinder assemblages. Proc. R. Soc. Lond. A 458, 1719–1959 (2002)
Wang, X., Schiavone, P.: Neutral coated circular inclusions in finite plane elasticity of harmonic materials. Euro. J. Mech. A/Solids 33, 75–81 (2012)
Wang, X., Schiavone, P.: A neutral multi-coated sphere under non-uniform electric field in conductivity. Z. Angew. Math. Phys. 64, 895–903 (2013)
Jarczyk, P., Mityushev, V.: Neutral coated inclusions of finite conductivity. Proc. R. Soc. Lond. A 468(2140), 954–970 (2012)
Dai, M., Schiavone, P., Gao, C.F.: Neutral nano-inhomogeneities in hyperelastic materials with a hyperelastic interface model. Int. J. Nonlinear Mech. 87, 38–42 (2016)
Ting, T.C.T.: Anisotropic Elasticity-Theory and Applications. Oxford University Press, New York (1996)
Kythe, P.K.: Computational Conformal Mapping. Birkhäuser, Basel (1998)
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).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, X., Schiavone, P. Neutrality of a partially debonded rigid inclusion in anti-plane shear. Arch Appl Mech 89, 1513–1519 (2019). https://doi.org/10.1007/s00419-019-01524-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-019-01524-1