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Elastic waves guided by a material interface

Authors
Journal
European Journal of Mechanics - A/Solids
0997-7538
Publisher
Elsevier
Publication Date
Volume
27
Issue
3
Identifiers
DOI: 10.1016/j.euromechsol.2007.10.002
Keywords
  • Non-Linear Elasticity
  • Bifurcation
  • Wave Propagation
  • Pre-Stress
  • Residual Stress
  • Thin Films
  • Stoneley Waves
  • Elastic Foundation

Abstract

Abstract The propagation of interfacial small-amplitude waves along a rectilinear thin film separating two pre-stressed, incompressible, elastic media is addressed. The film is modelled as a material surface possessing its own mass density and normal and flexural stiffnesses. It is shown that these features induce dispersion as the obtained secular equations are polynomials of the second degree in the wavenumber when bending stiffness is absent ( membrane-like interface), and of the fourth degree otherwise ( plate-like interface). In both case, beyond the modified Stoneley mode, a bending mode for the interface, an additional propagating wave can exist, with amplitude polarized along the interface ( extensional mode). The associated bifurcation problem is analyzed with focus on the effects of compressive residual forces at the interface. The buckling strain of a compressed metal layer embedded in an elastomeric medium is computed also with an exact approach, to provide the range of validity of the proposed simplified model of material interface.

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