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The scattering of SH-waves by a nano arc-shaped hole on a half-plane

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Abstract

Surface effects play an important role in the mechanical response at nanoscale. Based on the surface elasticity theory, the scattering of incident plane shear waves (SH-waves) by a nano-sized arc-shaped hole on a half-plane is analyzed through the wave function expansion method. The analytical solution of the stress field around the arc-shaped hole is obtained by the orthogonality of trigonometric function. The effects of surface effect, incident angle, and arc depth on the dynamic stress concentration factor around the hole are analyzed by numerical simulation.

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References

  1. Pao, Y.H., Mow, C.C.: Diffraction of Elastic Waves and Dynamic Stress Concentrations. Crane, Russak & Co. Inc., New York (1973)

    Book  Google Scholar 

  2. Liu, D.K.: Dynamic stress concentration around a circular hole due to SH-wave in anisotropic media. Acta Mech. Sin. Prc. 4(2), 146–155 (1988)

    Article  Google Scholar 

  3. Shi, W.P., Chen, R.P., Zhang, C.P.: Scattering of circular inclusion in right-angle plane to incident plane SH-wave. J. Appl. Mech. 24(1), 154–159 (2007)

    Google Scholar 

  4. Chen, Z.G.: Dynamic stress concentration around shallow cylindrical cavity by SH wave in anisotropically elastic half-space. Rock Soil Mech. 33(3), 899–905 (2012)

    Google Scholar 

  5. Amornwongpaibun, A., Luo, H., Lee, V.W.: Scattering of anti-plane (SH) waves by a shallow semi-elliptical hill with a concentric elliptical tunnel. J. Earthq. Eng. 20(3), 363–382 (2016)

    Article  Google Scholar 

  6. Zhang, H., Yang, G.G., Liu, Z.X., Wang, X.: An analytical solution to scattering of plane SH waves by a semi-circle lined tunnel in elastic half-space boundary. J. Appl. Mech. 34(2), 243–249 (2017)

    Google Scholar 

  7. Kalentev, E.A.: Stress-strain state of an elastic half-space with a cavity of arbitrary shape. Int. J. Mech. Mater. Eng. 13(1), 8–16 (2018)

    Article  Google Scholar 

  8. Nohegoo-Shahvari, A., Kamalianb, M., Panji, M.: A hybrid time-domain half-plane FE/BE approach for SH-wave scattering of alluvial sites. Eng. Anal. Bound. Elem. 105, 194–206 (2019)

    Article  MathSciNet  Google Scholar 

  9. Dai, D.H., Zhang, N., Lee, V.W., Gao, Y., Chen, H.: Scattering and amplification of SV waves by a semicylindrical hill in a half-space by a wavefunction-based meshless method using mapping and point-matching strategies. Eng. Anal. Bound. Elem. 106, 252–263 (2019)

    Article  MathSciNet  Google Scholar 

  10. Jiang, G.X.X., Yang, Z.L., Sun, C., Sun, B.T., Yang, Y.: Dynamic response of a circular inclusion embedded in inhomogeneous half-space. Arch. Appl. Mech. 88(10), 1791–1803 (2018)

    Article  Google Scholar 

  11. Yang, Z.L., Bian, J.L., Song, Y.Q., Yang, Y., Sun, M.H.: Scattering of cylindrical inclusions in half space with inhomogeneous shear modulus due to SH wave. Arch. Appl. Mech. 91, 3449–3461 (2021)

    Article  Google Scholar 

  12. Wong, E.W., Sheehan, P.E., Lieber, C.M.: Nanobeam mechanics: elasticity, strength and toughness of nanorods and nanotubes. Science 277(5334), 1971–1975 (1997)

    Article  Google Scholar 

  13. Gurtin, M.E., Weissmüller, J., Larché, F.: A general theory of curved deformable interfaces in solids at equilibrium. Philos. Mag. A 78(5), 1093–1109 (1998)

    Article  Google Scholar 

  14. Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3), 139–147 (2000)

    Article  Google Scholar 

  15. Shenoy, V.B.: Size-dependent rigidities of nanosized torsional elements. Int. J. Solids Struct. 39(15), 4039–4052 (2002)

    Article  Google Scholar 

  16. Chen, T., Chiu, M.S., Weng, C.N.: Derivation of the generalized Young–Laplace equation of curved interfaces in nanoscaled solids. J. Appl. Phys. 100(7), 074308 (2006)

    Article  Google Scholar 

  17. Sharma, P., Ganti, S., Bhate, N.: Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82(4), 535–537 (2003)

    Article  Google Scholar 

  18. Ou, Z.Y., Wang, G.F., Wang, T.J.: Effect of residual surface tension on the stress concentration around a nanosized spheroidal cavity. Int. J. Eng. Sci. 46(5), 475–485 (2008)

    Article  Google Scholar 

  19. Ou, Z.Y., Wang, G.F., Wang, T.J.: Elastic fields around a nanosized spheroidal cavity under arbitrary uniform remote loadings. Eur. J. Mech. A Solid 28(1), 110–120 (2009)

    Article  Google Scholar 

  20. Wang, L.H., Wang, L.Y., Han, H.J., Han, W., Wang, Y.: Surface effects on nano-contact based on surface energy density. Arch. Appl. Mech. 91, 4179–4190 (2021)

    Article  Google Scholar 

  21. Wang, G.F., Wang, T.J., Feng, X.Q.: Surface effects on the diffraction of plane compressional waves by a nanosized circular hole. Appl. Phys. Lett. 89(23), 231923 (2006)

    Article  Google Scholar 

  22. Wang, G.F.: Diffraction of plane compressional wave by a nanosized spherical cavity with surface effects. Appl. Phys. Lett. 90(21), 211907 (2007)

    Article  Google Scholar 

  23. Ou, Z.Y., Lee, D.W.: Effects of interface energy on scattering of plane elastic wave by a nano-sized coated fiber. J. Sound Vib. 331(25), 5623–5643 (2012)

    Article  Google Scholar 

  24. Ru, Y., Wang, G.F., Wang, T.J.: Diffraction of elastic waves and stress concentration near a cylindrical nano-inclusion incorporating surface effect. J. Vib. Acoust. 131(6), 1747–1750 (2009)

    Article  Google Scholar 

  25. Ru, Y., Wang, G.F., Su, L.C., Wang, T.J.: Scattering of vertical shear wave by a cluster of nanosized cylindrical holes with surface effect. Acta Mech. 224(5), 935–944 (2013)

    Article  MathSciNet  Google Scholar 

  26. Ru, Y.: Surface effect on diffractions of elastic waves and stress concentration near a cluster of cylindrical nanoholes arranged as quadrate shape. Adv. Mater. Sci. Eng. 2015, 134975 (2015)

    Google Scholar 

  27. Wu, H.M.: Application of the complex variable function method to SH-wave scattering around a circular nanoinclusion. Adv. Math. Phys. 2019, 7203408 (2019)

    MathSciNet  MATH  Google Scholar 

  28. Wu, H.M., Ou, Z.Y.: Surface effects on the scattering of SH-wave around an arbitrary shaped nano-cavity. Adv. Math. Phys. 2019, 3084581 (2019)

    MathSciNet  MATH  Google Scholar 

  29. Wu, H.M., Ou, Z.Y.: Dynamic stress around a cylindrical nano-inclusion with an interface in a right-angle plane under SH-wave. Math. Probl. Eng. 2020, 9717386 (2020)

    MathSciNet  Google Scholar 

  30. Yuan, X.M., Liao, Z.P.: Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section. Soil Dyn. Earthq. Eng. 13, 407–412 (1994)

    Article  Google Scholar 

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Acknowledgements

Thanks to Professor Wang Gangfeng from Xi’an Jiaotong University for his valuable suggestions during the revision of the paper. This work was supported by the National Natural Science Foundation of China (Grant No. 11862014).

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  1. School of Science, Lanzhou University of Technology, Lanzhou, China

    Hongmei Wu & Zhiying Ou

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  1. Hongmei Wu
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  2. Zhiying Ou
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Correspondence to Hongmei Wu.

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Wu, H., Ou, Z. The scattering of SH-waves by a nano arc-shaped hole on a half-plane. Acta Mech 233, 1649–1662 (2022). https://doi.org/10.1007/s00707-022-03190-x

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  • DOI: https://doi.org/10.1007/s00707-022-03190-x

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