Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses - Publication - Bridge of Knowledge

Search

Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses

Abstract

Here we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model are more localised near the free surface. For the strain-gradient elasticity model there is a range of wavenumbers where the amplitude of displacements decays very slowly.

Citations

  • 5 2

    CrossRef

  • 0

    Web of Science

  • 5 5

    Scopus

Authors (3)

Cite as

Full text

download paper
downloaded 137 times
Publication version
Accepted or Published Version
License
Copyright (The Authors 2018)

Keywords

Details

Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
MATHEMATICS AND MECHANICS OF SOLIDS no. 24, pages 2526 - 2535,
ISSN: 1081-2865
Language:
English
Publication year:
2019
Bibliographic description:
Eremeev V., Rosi G., Naili S.: Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses// MATHEMATICS AND MECHANICS OF SOLIDS. -Vol. 24, iss. 8 (2019), s.2526-2535
DOI:
Digital Object Identifier (open in new tab) 10.1177/1081286518769960
Bibliography: test
  1. M. E. Gurtin, A. I. Murdoch, A continuum theory of elastic material surfaces, Arch. Ration. Mech. An. 57 (4) (1975) 291-323. open in new tab
  2. D. J. Steigmann, R. W. Ogden, Plane deformations of elastic solids with intrinsic boundary elasticity, Proceedings of the Royal Society A 453 (1959) (1997) 853-877. open in new tab
  3. D. J. Steigmann, R. W. Ogden, Elastic surface-substrate interactions, Proceedings of the Royal Society A 455 (1982) (1999) 437-474. open in new tab
  4. R. A. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis 11 (1) (1962) 385-414. open in new tab
  5. R. D. Mindlin, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis 16 (1) (1964) 51-78. open in new tab
  6. R. D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures 1 (4) (1965) 417-438. open in new tab
  7. R. D. Mindlin, H. F. Tiersten, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis 11 (1962) 415-448. open in new tab
  8. R. D. Mindlin, N. N. Eshel, On first strain-gradient theories in linear elasticity, International Journal of Solids and Structures 4 (1) (1968) 109-124. open in new tab
  9. F. dell'Isola, U. Andreaus, L. Placidi, At the origins and in the vanguard of peridynamics, non- local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola, Mathematics and Mechanics of Solids 20 (8) (2015) 887-928.
  10. N. Auffray, F. dell'Isola, V. A. Eremeyev, A. Madeo, G. Rosi, Analytical continuum mechan- icsà la Hamilton-Piola least action principle for second gradient continua and capillary fluids, Mathematics and Mechanics of Solids 20 (4) (2015) 375-417. open in new tab
  11. C. I. Kim, C. Q. Ru, P. Schiavone, A clarification of the role of crack-tip conditions in linear elasticity with surface effects, Mathematics and Mechanics of Solids 18 (1) (2013) 59-66. open in new tab
  12. H. Altenbach, V. A. Eremeyev, L. P. Lebedev, On the spectrum and stiffness of an elastic body with surface stresses, ZAMM 91 (9) (2011) 699-710. open in new tab
  13. J. Wang, H. L. Duan, Z. P. Huang, B. L. Karihaloo, A scaling law for properties of nano-structured materials, Proceedings of the Royal Society A 462 (2069) (2006) 1355-1363. open in new tab
  14. J. Wang, Z. Huang, H. Duan, S. Yu, X. Feng, G. Wang, W. Zhang, T. Wang, Surface stress effect in mechanics of nanostructured materials, Acta Mech. Solida Sin. 24 (2011) 52-82. open in new tab
  15. H. L. Duan, J. Wang, B. L. Karihaloo, Theory of elasticity at the nanoscale, in: Adv. Appl. Mech., Vol. 42, Elsevier, 2008, pp. 1-68. open in new tab
  16. A. Javili, A. McBride, P. Steinmann, Thermomechanics of solids with lower-dimensional energet- ics: On the importance of surface, interface, and curve structures at the nanoscale. A unifying review, Appl. Mech. Rev. 65 (2012) 010802-1-31. open in new tab
  17. V. A. Eremeyev, On effective properties of materials at the nano-and microscales considering surface effects, Acta Mechanica 227 (1) (2016) 29-42. open in new tab
  18. H. Askes, E. C. Aifantis, Gradient elasticity in statics and dynamics: An overview of formu- lations, length scale identification procedures, finite element implementations and new results, International Journal of Solids and Structures 48 (13) (2011) 1962-1990. open in new tab
  19. E. C. Aifantis, Gradient material mechanics: perspectives and prospects, Acta Mechanica 225 (4- 5) (2014) 999-1012. open in new tab
  20. S. Forest, N. M. Cordero, E. P. Busso, First vs. second gradient of strain theory for capillarity effects in an elastic fluid at small length scales, Computational Materials Science 50 (4) (2011) 1299-1304. open in new tab
  21. N. M. Cordero, S. Forest, E. P. Busso, Second strain gradient elasticity of nano-objects, Journal of the Mechanics and Physics of Solids 97 (2016) 92-124. open in new tab
  22. F. dell'Isola, D. Steigmann, A two-dimensional gradient-elasticity theory for woven fabrics, J. Elast. 118 (1) (2015) 113-125.
  23. M. Cuomo, F. dell'Isola, L. Greco, N. Rizzi, First versus second gradient energies for planar sheets with two families of inextensible fibres: Investigation on deformation boundary layers, discontinuities and geometrical instabilities, Composites Part B: Engineering 115 (2017) 423-448. open in new tab
  24. J. Achenbach, Wave Propagation in Elastic Solids, North Holland, Amsterdam, 1973. open in new tab
  25. V. A. Eremeyev, G. Rosi, S. Naili, Surface/interfacial anti-plane waves in solids with surface energy, Mechanics Research Communications 74 (2016) 8-13. open in new tab
  26. I. Vardoulakis, H. G. Georgiadis, SH surface waves in a homogeneous gradient-elastic half-space with surface energy, Journal of Elasticity 47 (2) (1997) 147-165.
  27. V. I. Yerofeyev, O. A. Sheshenina, Waves in a gradient-elastic medium with surface energy, Journal of Applied Mathematics and Mechanics 69 (1) (2005) 57 -69. open in new tab
  28. P. Gourgiotis, H. Georgiadis, Torsional and SH surface waves in an isotropic and homogenous elastic half-space characterized by the Toupin-Mindlin gradient theory, International Journal of Solids and Structures 62 (0) (2015) 217 -228. open in new tab
  29. I. Giorgio, N. L. Rizzi, E. Turco, Continuum modelling of pantographic sheets for out-of-plane bifurcation and vibrational analysis, Proceedings of the Royal Society of London A 473 (2207) (2017) 20170636. open in new tab
  30. I. Giorgio, A. Della Corte, F. dell'Isola, Dynamics of 1D nonlinear pantographic continua, Non- linear Dynamics 88 (1) (2017) 21-31. open in new tab
  31. G. Rosi, L. Placidi, V.-H. Nguyen, S. Naili, Wave propagation across a finite heterogeneous interphase modeled as an interface with material properties, Mechanics Research Communications 84 (2017) 43-48. open in new tab
  32. L. Placidi, G. Rosi, I. Giorgio, A. Madeo, Reflection and transmission of plane waves at sur- faces carrying material properties and embedded in second-gradient materials, Mathematics and Mechanics of Solids 19 (5) (2014) 555-578. open in new tab
  33. F. dell'Isola, A. Madeo, L. Placidi, Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua, ZAMM 92 (1) (2012) 52-71.
  34. F. Jia, Z. Zhang, H. Zhang, X.-Q. Feng, B. Gu, Shear horizontal wave dispersion in nanolayers with surface effects and determination of surface elastic constants, Thin Solid Films 645 (Supplement C) (2018) 134 -138. open in new tab
  35. F. dell'Isola, G. Sciarra, S. Vidoli, Generalized Hooke's law for isotropic second gradient materials, Royal Society of London Proceedings Series A 465 (2107) (2009) 2177-2196.
  36. M. E. Gurtin, A. I. Murdoch, Surface stress in solids, Int. J. Sol. Struct. 14 (6) (1978) 431-440. open in new tab
  37. F. dell'Isola, I. Giorgio, M. Pawlikowski, N. Rizzi, Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenisation, experimental and numerical examples of equilibrium, Proceedings of the Royal Society of London. Series A. 472 (2185) (2016) 20150790.
  38. Y. Rahali, I. Giorgio, J. Ganghoffer, F. dell'Isola, Homogenizationà la Piola produces second gradient continuum models for linear pantographic lattices, International Journal of Engineering Science 97 (2015) 148-172. open in new tab
  39. G. Rosi, N. Auffray, Anisotropic and dispersive wave propagation within strain-gradient frame- work, Wave Motion 63 (2016) 120-134. open in new tab
  40. G. Rosi, L. Placidi, N. Auffray, On the validity range of strain-gradient elasticity: a mixed static- dynamic identification procedure, European Journal of Mechanics-A/Solids 69 (2018) 179-191. open in new tab
  41. E. C. Aifantis, Update on a class of gradient theories, Mechanics of Materials 35 (3-6) (2003) 259-280. open in new tab
  42. M. Born, K. Huang, Dynamical Theory of Crystal Lattices, International series of monographs on physics, Clarendon Press, Oxford, 1954.
Verified by:
Gdańsk University of Technology

seen 138 times

Recommended for you

Meta Tags