On the basis of the theory of functions of complex variable and the method of jump functions, we propose a procedure of taking into account the additional influence of surface stresses in the problem of thin interface inclusion in the bimaterial. In this problem, we take into account the possibility of imperfect contact between the inclusion and the matrix and, in particular, the possibility of contact with surface tension. This significantly extends the field of applicability of the results of simulation within the framework of the concept of representative volume element in micro- and macromechanics. We propose a generalized model of thin inclusion with arbitrary mechanical properties. The analysis of test problems reveals high accuracy and efficiency of the proposed approach. We present the results of numerical analyses of the stress fields in the case of interaction of the inclusion with concentrated forces and screw dislocations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Z. Piskozub and H. T. Sulym, “Asymptotics of stresses in the vicinity of a thin elastic interface inclusion,” Fiz.-Khim. Mekh. Mater., 32, No. 4, 39–48 (1996); English translation: Mater. Sci., 32, No. 4, 421–432 (1996); https://doi.org/10.1007/BF02538967.
H. T. Sulym, Foundations of the Mathematical Theory of Thermoelastic Equilibrium of Deformable Solids with Thin Inclusions [in Ukrainian], NTSh Res.-Publ. Center, Lviv (2007).
H. T. Sulym and I. Z. Piskozub, “Nonlinear deformation of a thin interface inclusion,” Fiz.-Khim. Mekh. Mater., 53, No. 5, 24–30 (2017); English translation: Mater. Sci., 53, No. 5, 600–608 (2018).
Y. Benveniste and T. Miloh, “Imperfect soft and stiff interfaces in two-dimensional elasticity,” Mech. Mater., 33, No. 6, 309–323 (2001); https://doi.org/10.1016/S0167-6636(01)00055-2.
H. L. Duan, J. Wang, Z. P. Huang, and B. L. Karihaloo, “Eshelby formalism for nano-inhomogeneities,” Proc. Roy. Soc. London, Ser. A, 461, No. 2062, 3335–3353 (2005); https://doi.org/10.1098/rspa.2005.1520.
J. D. Eshelby, “The determination of the elastic field of an ellipsoidal inclusion, and related problem,” Proc. R. Soc. London, Ser. A, 241, No. 1226, 376–396 (1957); https://doi.org/10.1098/rspa.1957.0133.
M. E. Gurtin and A. I. Murdoch, “A continuum theory of elastic material surfaces,” Arch. Ration. Mech. Anal., 57, No. 4, 291–323 (1975); https://doi.org/10.1007/BF00261375.
M. E. Gurtin and A. I. Murdoch, “Surface stress in solids,” Int. J. Solids Struct., 14, No. 6, 431–440 (1978); https://doi.org/10.1016/0020-7683(78)90008-2.
C. I. Kim, P. Schiavone, and C.-Q. Ru, “The effect of surface elasticity on Mode-III interface crack,” Arch. Mech., 63, No. 3, 267–286 (2011).
. P. Kizler, D. Uhlmann, and S. Schmauder, “Linking nanoscale and macroscale: calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress–strain curves owing to dislocation theory,” Nucl. Eng. Des., 196, No. 2, 175–183 (2000); https://doi.org/10.1016/S0029-5493(99)00219-8.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 2, pp. 98–108, April–June, 2020.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Piskozub, Y.Z., Sulym, H.Т. Effect of Surface Stresses on the Antiplane Stress-Strain State of a Thin Ribbon-Like Interface Inclusion. J Math Sci 272, 112–124 (2023). https://doi.org/10.1007/s10958-023-06403-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06403-3