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Dynamic stress in a semi-infinite solid with a cylindrical nano-inhomogeneity considering nanoscale microstructure

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Abstract

In this paper, the dynamic stress around a cylindrical nano-inhomogeneity embedded in a semi-infinite solid under anti-plane shear waves is investigated. The surface/interface stress effects around the nano-inhomogeneity and at the straight edge of the semi-infinite solid are both considered. The boundary condition at the straight edge of the semi-infinite solid with surface/interface effects is satisfied by the image method. The incident, scattered and refracted displacement fields in the nano-sized composites are expressed by employing the wave function expansion method. The addition theorem for a cylindrical wave function is applied to accomplish the superposition of wave fields in the two semi-infinite solids. Analyzes show that the effect of interface properties, especially that at the straight edge, on the dynamic stress is significant, and the effect increases noticeably due to the nanoscale of the structure. The incident frequency and angle of waves and the shear modulus ratio of the nano-inhomogeneity to matrix also show a pronounced effect on the dynamic stress distribution if the semi-infinite solid shrinks to nanoscale.

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Authors and Affiliations

  1. School of Civil Engineering, Shijiazhuang Tiedao University, Shjiazhuang, 050043, People’s Republic of China

    Q. Yang

  2. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, People’s Republic of China

    J. X. Liu & X. Q. Fang

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  1. Q. Yang
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  2. J. X. Liu
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  3. X. Q. Fang
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Correspondence to J. X. Liu.

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Yang, Q., Liu, J.X. & Fang, X.Q. Dynamic stress in a semi-infinite solid with a cylindrical nano-inhomogeneity considering nanoscale microstructure. Acta Mech 223, 879–888 (2012). https://doi.org/10.1007/s00707-012-0613-4

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  • DOI: https://doi.org/10.1007/s00707-012-0613-4

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