Skip to main content

Anti-plane Surface Waves in Materials with Surface Energy

  • 72 Accesses


Anti-plane motions localized near a boundary of a half-space; SH surface waves in solids with surface stresses


Surface wave is a wave whose amplitude decays exponentially with the distance from surface.

By anti-plane surface wave, we mean the surface wave when anti-shear is realized.


Surface energy and surface stresses play an important role for material behavior at the nanoscale; see, e.g., Duan et al. (2008), Wang et al. (2011), Javili et al. (2013), and Eremeyev (2016). In particular, they are responsible for size effect at the nanoscale as well as for significant changes in effective (apparent) properties of nanostructured materials. In addition, in materials with surface energy and surface stresses may even exist new phenomena which are absent within the classic continuum models. As an example of such phenomenon, one can consider propagation of anti-plane surface waves in media with surface stresses.

Following Eremeyev et al. (2016), we discuss...

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2


  • Achenbach J (1973) Wave Propagation in elastic solids. North Holland, Amsterdam

    MATH  Google Scholar 

  • Duan HL, Wang J, Karihaloo BL (2008) Theory of elasticity at the nanoscale. In: Van der Giessen E, Aref H (eds) Advances in applied mechanics, vol 42. Elsevier, Burlington, pp 1–68

    Google Scholar 

  • Eremeyev VA (2016) On effective properties of materials at the nano-and microscales considering surface effects. Acta Mech 227(1):29–42

    MathSciNet  CrossRef  Google Scholar 

  • Eremeyev VA (2019) Surface elasticity models: comparison through the condition of the anti-plane surface wave propagation. In: "Altenbach H, Öchsner A (eds) State of the art and future trends in material modeling. Advanced structured materials, vol 100. Springer, Cham, pp 113–124

    Google Scholar 

  • Eremeyev VA, Sharma BL (2019) Anti-plane surface waves in media with surface structure: discrete vs. continuum model. Int J Eng Sci 143:33–38

    MathSciNet  CrossRef  Google Scholar 

  • Eremeyev VA, Rosi G, Naili S (2016) Surface/interfacial anti-plane waves in solids with surface energy. Mech Res Commun 74:8–13

    CrossRef  Google Scholar 

  • Eremeyev VA, Cloud MJ, Lebedev LP (2018) Applications of tensor analysis in continuum mechanics. World Scientific, New Jersey

    CrossRef  Google Scholar 

  • Eremeyev VA, Rosi G, Naili S (2019) Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses. Math Mech Solids 24:2526–2535.

    MathSciNet  CrossRef  Google Scholar 

  • Georgiadis H, Vardoulakis I, Lykotrafitis G (2000) Torsional surface waves in a gradient-elastic half-space. Wave Motion 31(4):333–348

    MathSciNet  CrossRef  Google Scholar 

  • Gourgiotis P, Georgiadis H (2015) Torsional and {SH} surface waves in an isotropic and homogenous elastic half-space characterized by the Toupin–Mindlin gradient theory. Int J Solids Struct 62(0):217–228

    CrossRef  Google Scholar 

  • Gurtin ME, Murdoch AI (1975) A continuum theory of elastic material surfaces. Arch Ration Mech Anal 57(4):291–323

    MathSciNet  CrossRef  Google Scholar 

  • Gurtin ME, Murdoch AI (1978) Surface stress in solids. Int J Solids Struct 14(6):431–440

    CrossRef  Google Scholar 

  • Javili A, McBride A, Steinmann P (2013) Thermomechanics of solids with lower-dimensional energetics: on the importance of surface, interface, and curve structures at the nanoscale. A unifying review. Appl Mech Rev 65(1):010802

    Google Scholar 

  • Lebedev LP, Cloud MJ, Eremeyev VA (2010) Tensor analysis with applications in mechanics. World Scientific, New Jersey

    CrossRef  Google Scholar 

  • Vardoulakis I, Georgiadis HG (1997) SH surface waves in a homogeneous gradient-elastic half-space with surface energy. J Elast 47(2):147–165

    MathSciNet  CrossRef  Google Scholar 

  • Wang J, Huang Z, Duan H, Yu S, Feng X, Wang G, Zhang W, Wang T (2011) Surface stress effect in mechanics of nanostructured materials. Acta Mech Solida Sin 24: 52–82

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Victor A. Eremeyev .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer-Verlag GmbH Germany, part of Springer Nature

About this entry

Verify currency and authenticity via CrossMark

Cite this entry

Eremeyev, V.A. (2019). Anti-plane Surface Waves in Materials with Surface Energy. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering